rasayan-colligative

In chemistry, a solution is a homogeneous mixture composed of two or more substances. In such a mixture, a solute is dissolved in another substance, known as a solvent. Usually, the substance present in a greater amount is considered as the solvent. Solutions may have multiple solvents. Gases may dissolvein liquids, for example, carbon dioxide or oxygen in water. Liquids may dissolve in other liquids. Gases can combine with other gases to form mixtures, rather than solutions.^[1]

All solutions are characterized by interactions between the solvent phase and solute molecules or ions that result in a net decrease in free energy. Under such a definition, gases typically cannot function as solvents, since in the gas phase interactions between molecules are minimal due to the large distances between the molecules. This lack of interaction is the reason gases can expand freely and the presence of these interactions is the reason liquids do not expand.

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[edit]Introduction

Solutions, solutes and solvents may be combinations of solids, liquids or gases. The solution that forms has the same physical state as the solvent. For example, carbonated beverages are formed by dissolving CO2 (or carbon dioxide) gas in water. The air we breathe is a solution of oxygen and nitrogen gases. When we make solutions of coffee or tea, we use hot water to dissolve substances from coffee beans or tea leaves. In a hospital, the antiseptic tincture of iodine is a solution of iodine dissolved in alcohol. The ocean is an aqueous solution of many salts such as NaCl dissolved in water.

Body fluids are electrolyte solutions containing solute ions (e.g. potassium and sodium) as well as molecular sugar (or glucose) and urea dissolved in polar solvents such as blood plasma. Oxygen and carbon dioxide are also essential components of blood chemistry, where significant changes in their concentrations can be a sign of illness or injury.

Other examples of solid solutions are alloys and certain minerals and polymers containing plasticizers. Stainless steel, for example, is a solid solution of carbon atoms in a crystalline matrix of iron atoms. The ability of one compound to dissolve in another compound is called solubility. The physical properties of compounds such as melting point and boiling point change when other compounds are added. Together they are called colligative properties. There are several ways to quantify the amount of one compound dissolved in the other compounds collectively called concentration. Examples include molarity, mole fraction, and parts per million (ppm).

Solutions should be distinguished from non-homogeneous mixtures such as colloids and suspensions. When a liquid is able to completely dissolve in another liquid the two liquids are miscible. Two substances that can never mix to form a solution are called immiscible.

[edit]Properties of solutions

[edit]Types of bonding

Consider what happens when a Group I element combines with a Group VII element to form a chemical compound. The Group I element has one valence electron in its outermost shell, while the Group VII element has seven. In order for both of them to be satsified, one of two things has to occur. They will either share the entire set of eight valence electrons between them equally, or one atom will give up (or transfer) its valence electrons to the other.

In the first case, if the valence electrons are shared equally, the distribution of electrical charge will be fairly uniform in the region in between the two atoms. This type of bonding results in what is known as a covalent bond (or ”sharing of strength”).

In the second case, if the valence electrons are not shared equally, then one atom will need to give up its valence electrons to the other. In the case of sodium chloride, the sodium atom gives up its single valence electron ot become a sodium cation, and the chlorine atom takes the valence electron to become a chlorine anion. The forces responsible for the formation of this ionic compound are electrical in nature, and much stronger than those evidenced in covalently bonded materials. Thus, the ionic bond is characterized by such physical properties as a highmelting point and high boiling point (i.e. it takes more thermal energy to break apart the ionic bonds).

Crystal structure of sodium chloride (table salt)

Let us also consider the size of these atoms. The sodium atom, with atomic number Z = 11, started with 11 electrons orbiting around its nucleus. The chlorine atom started with 17. In NaCl, the sodium cation has only 10, while the chlorine anion has a total of 18. The result is that the chlorine ion is much larger than the sodium ion. The result is evident in the crystal lattice structure.

In covalent compounds, the valence electrons are shared equally between the atoms. Mosthydrogen compounds such as water H₂O are covalently bonded. 70% of earths surface is covered by water. The human body is about 60-65% water. Organic (C, H, O) compounds include carbohydrates, fats, proteins and nucleic acids such as DNA. Nearly all organic compounds are held together by covalent bonds. Since covalent bonds are not electrical in nature, the forces holding these compounds together are weaker than those evidenced in ionic compounds. Therefore organic compounds tend to exhibit lower melting and boiling points.

[edit]Bond polarity

There are many intermediate cases where valence electrons are not shared equally, but they are also not completely transferred from one atom to another. In this case, it can be said that the electrons will spend more time in the vicinity of one atom than the other. The result is that one end of the molecule will have a net negative charge, while the other end will have a net positive charge. When electrons in a covalent bond are not equally shared, the molecule is said to be polar.

A polar molecule contains an electrical dipole, meaning that it has a (+) and (-) end. In the depicted case of the hydrogen fluoride molecule, covalently bond electrons are displaced towards the more electronegative fluorine atom.

Hydrogen fluoride as a molecular dipole. Red represents partially negatively charged areas.

Thus, bond polarity is a simple result of the fact that electrons are not shared equally. In a polar covalent bond, the atom with the stronger affinity for electrons may be shown with a partial negative charge. The atom with the lower affinity for electrons is farther from the electron pair and is shown with a partial positive charge. The illustration depicts the electrical dipole resulting from the formation of a hydrogen fluoride (HF) molecule. The dipole is symbolized by a cross (+ end) pointing in the direction of the negative end with an arrowhead. Note the larger size of the molecule on the negative end. This is because the unequally shared electrons are spending more time there. This is known as a polar covalent bond -- a compromise between ionic and covalent bonding.

[edit]Aqeous solutions

A water molecule, a commonly-used example of polarity. The two charges are present with a negative charge in the middle (red shade), and a positive charge at the ends (blue shade).

It is the polar structure of the water molecule that is responsible for many of the unique physical properties of water. In the water molecule, the oxygen atom, with its eight (+) protons, has a much greater attraction for the shared valence electrons than do either of the hydrogen atoms with a single proton. Therefore, the shared electrons spend more time around the oxygen part of the molecule than they do around the hydrogen part. This results in the oxygen end being more negative than the hydrogen end.

Polar molecules of any substance have attractions between the positive end of one molecule and the negative end of another molecule. When the polar molecule has hydrogen at one end and fluorine, oxygen or nitrogen at the other end, the attractions are strong enough to qualify as type of chemical bonding called hydrogen bonding. Hydrogen bonds are weaker than either covalent bonds or ionic bonds.

Model of hydrogen bonds between molecules of water

A salt such as sodium chloride will form a solution with water because the positively charged sodium cations and the negatively charged chlorine anions are attracted to the positive and negative ends of the water molecule, respectively. The sodium and chlorine ions thus become dissolved (or hydrated) as part of the aqueous saltwater solution. Hydration occurs when the charged solute ions become surrounded by the polar solvent, or water molecules.

Thus, sodium chloride (NaCl) will form a solution with water because the Na+ and Cl- ions in the salt are attracted to the positive and negative parts of water molecules. When ionic compounds dissolve, the resulting solution contains separated ions. The conduction of electricity provides evidence for these ions in solution. Charged ions in solution act as mobile charge carriers (like electrons in metals). Sodium chloride and water together form a strong electrolyte aqueous solution.

Ethanol is one example of a non-ionic solute that is very soluble in water. All alcoholic beverages are aqueous solutions of ethanol. Why is ethanol so soluble in water? The answer lies in the structure of the ethanol molecule. The molecule contains a polar O-H bond like those found in water, which makes it very compatible with water. Just as hydrogen bonds form among water molecules in pure water, ethanol molecules can form hydrogen bonds with water molecules. Table sugar can also be dissolved in water because the glucose molecule has many polar OH groups which will attract the polar water molecules.

[edit]Non-polar solutions

Whether or not two given liquids form solutions depends to some degree on the similarity (or lack thereof) between their respective molecular structures. In general, the forces of attraction between molecules or ions of the solvent and solute will determine the limits of solubility. The water molecule, for example, is a polar molecule with a negative end and a positive end. Polar molecules (such as water) therefore require polar solvents.

Methane, the bonds are arranged symmetrically so there is no overall dipole

On the other hand, covalently bonded substances such as elemental gases, long chain hydrocarbon fuels, oil or grease do not dissolve in water or other polar solvents. Most grease and oil molecules have no polarity. They are virtually electrically neutral, and are therefore non-polar compounds. In general, “like dissolves like” and thus water will not dissolve oil and grease. Non-polar solutes require non-polar solvents.

A molecule may be polar either as a result of polar bonds due to differences inelectronegativity as described above, or as a result of an asymmetric arrangement of non-polar covalent bonds and non-bonding pairs of electrons known as a full molecular orbital. In a similar manner, a molecule may be non-polar either because there is (almost) no polarity in the bonds or because of the symmetrical arrangement of polar bonds. For example, in the methane, CH₄ molecule the four C–H bonds are arranged tetrahedrally around the carbon atom. Each bond has polarity (though not very strong). However, the bonds are arranged symmetrically so there is no overall dipole in the molecule.

Many substances do not dissolve in water. When petroleum leaks from a damaged tanker, it does not disperse uniformly in the water (does not dissolve) but rather floats on the surface because its density is less than that of water.

Petroleum is a mixture of molecules like the one illustrated in this slide. Since carbon and hydrogen have similar affinities for electrons, the bonding electrons are shared almost equally and the bonds are essentially non-polar. Covalently bonded substances such as long chain hydrocarbon fuels, oil or grease do not dissolve in water or other polar solvents. Most grease and oil molecules have no polarity. They are virtually electrically neutral, and are therefore non-polar compounds.

In general, “like dissolves like” and thus water will not dissolve oil and grease. Similarly, non-polar solutes require non-polar solvents.

[edit]Solubility

Main article: Solvation

When no more of a solute can be dissolved into a solvent, the solution is said to be saturated. However, the point at which a solution can become saturated can change significantly with different environmental factors, such as temperature, pressure, and contamination. For some solute-solvent combinations a supersaturated solution can be prepared by raising the solubility (for example by increasing the temperature) to dissolve more solute, and then lowering it (for example by cooling).

Usually, the greater the temperature of the solvent, the more of a given solid solute it can dissolve. However, most gases and some compounds exhibit solubility that decrease with increased temperature. Such behavior is a result of an exothermic enthalpy of solution. Some surfactantsexhibit this behaviour. The solubility of liquids in liquids is generally less temperature-sensitive than that of solids or gases.

The properties ideal solutions can be calculated by the linear combination of the properties of its components. If both solute and solvent exist in equal quantities (such as in a 50% ethanol, 50% water solution), the concepts of "solute" and "solvent" become less relevant, but the substance that is more often used as a solvent is normally designated as the solvent (in this example, water).

[edit]Examples

Many types of solutions exist, as solids, liquids and gases can be both solvent and solute:

Examples of solutions		Solute
Examples of solutions		Gas	Liquid	Solid
Solvent	Gas	Oxygen and other gases in nitrogen (air)
	Liquid	Carbon dioxide (CO₂) in water (carbonated water; the visible bubbles, however, are not the dissolved gas, but only aneffervescence; the dissolved gas itself is not visible in the solution) A small fraction of O₂ and CO₂ in blood plasma	Ethanol(commonalcohol) in water Varioushydrocarbonsin each other (petroleum)	Sucrose (table sugar) in water Sodium chloride (table salt) in water gold in mercury, forming anamalgam A vast majority of O₂ inblood plasma through adipolar bond^[2] tohemoglobin
	Solid	Hydrogen dissolves rather well in metals; platinum has been studied as a storage medium.	Hexane inparaffin wax Mercury in gold.	Steel Bronze Other metal alloys

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Concentration - Wikipedia, the free encyclopedia

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Solutions & Colligative Properties IIT

Colligative properties

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Colligative properties

From Wikipedia, the free encyclopedia

This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (March 2008)

Colligative properties are properties of solutions that depend on the number of molecules in a given volume of solvent and not on the properties (e.g. size or mass) of the molecules.^[1] Colligative properties include: lowering of vapor pressure; elevation of boiling point; depression of freezing point and osmotic pressure. Measurements of these properties for a dilute aqueous solution of a non-ionized solute such as urea orglucose can lead to accurate determinations of relative molecular masses. Alternatively, measurements for ionized solutes can lead to an estimation of the percentage of ionization taking place.

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[edit]Vapor pressure

The relationship between the lowering of vapor pressure and concentration is given by Raoult's law, which states that:

The vapor pressure of an ideal solution is dependent on the vapor pressure of each chemical component and the mole fraction of the component present in the solution. (For details, see the article on Raoult's law.)

[edit]Boiling point and freezing point

Both the boiling point elevation and the freezing point depression are proportional to the lowering of vapor pressure in a dilute solution

[edit]Boiling point elevation

Boiling Point_total = Boiling Point_solvent + ΔT_b

where

ΔT_b = molality * K_b * i, (K_b = ebullioscopic constant, which is 0.51°C kg/mol for the boiling point of water; i = Van 't Hoff factor)

Since boiling point is achieved in the establishment of equilibrium between liquid and gas phase, that is, the number of molecules entering the molecules of a system equals the number of vapor molecules leaving the system, then an addition of solute would cause to hinder some of the molecules to leave the system because they are covering in the surface. To compensate for this and re-attain the equilibrium, boiling point therefore is achieved at higher temperature.

[edit]Freezing point depression

Freezing Point_solution = Freezing Point_solvent - ΔT_f

where :ΔT_f = molality * K_f * i, (K_f = cryoscopic constant, which is -1.86°C kg/mol for the freezing point of water, this is very fine; i = Van 't Hoff factor)

Freezing point, or the equilibrium between a liquid and solid phase is generally lowered in the presence of a solute compared to a pure solvent. The solute particles cannot enter the solid phase, hence, less molecules participate in the equilibrium. Again, re-establishment of equilibrium is achieved at a lower temperature at which the rate of freezing becomes equal at the rate of solidifying.

[edit]Osmotic pressure

Two laws governing the osmotic pressure of a dilute solution were discovered by the German botanist W. F. P. Pfeffer and the Dutch chemist J. H. van’t Hoff:

The osmotic pressure of a dilute solution at constant temperature is directly proportional to its concentration.
The osmotic pressure of a solution is directly proportional to its absolute temperature.

These are analogous to Boyle's law and Charles's Law for gases. Similarly, the combined ideal gas law, PV = nRT, has an analog for ideal solutions:

πV = nRTi

where: π = osmotic pressure; V is the volume; T is absolute temperature; n is the number of moles of solute; R = 8.3145 J K-1 mol-1, the molargas constant; i = Van 't Hoff factor.

Raoult's law

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Raoult's law

From Wikipedia, the free encyclopedia

Established by François-Marie Raoult, Raoult's law states:

the vapor pressure of an ideal solution is dependent on the vapor pressure of each chemical component and the mole fraction of the component present in the solution.^[1]

Once the components in the solution have reached equilibrium, the total vapor pressure pof the solution is:

and the individual vapor pressure for each component is

where

p*_i is the vapor pressure of the pure component

x_i is the mole fraction of the component in solution

Consequently, as the number of components in a solution increases, the individual vapor pressures decrease, since the mole fraction of each component decreases with each additional component. If a pure solute which has zero vapor pressure (it will not evaporate) is dissolved in a solvent, the vapor pressure of the final solution will be lower than that of the pure solvent.

This law is strictly valid only under the assumption that the chemical interactions betweenthe two liquids is equal to the bonding within the liquids: the conditions of an ideal solution. Therefore, comparing actual measured vapor pressures to predicted values from Raoult's law allows information about the relative strength of bonding between liquids to be obtained. If the measured value of vapor pressure is less than the predicted value, fewer molecules have left the solution than expected. This is put down to the strength of bonding between the liquids being greater than the bonding within the individual liquids, so fewer molecules have enough energy to leave the solution. Conversely, if the vapor pressure is greater than the predicted value more molecules have left the solution than expected, due to the bonding between the liquids being less strong than the bonding within each.

The vapor pressure and composition in equilibrium with a solution can yield valuable information regarding the thermodynamic properties of the liquids involved. Raoult’s law relates the vapor pressure of components to the composition of the solution. The law assumes ideal behavior. It gives a simple picture of the situation just as the ideal gas law does. The ideal gas law is very useful as a limiting law. As the interactive forces between molecules and the volume of the molecules approaches zero, so the behavior of gases approach the behavior of the ideal gas.

Raoult’s law is similar in that it assumes that the physical properties of the components are identical. The more similar the components are, the more their behavior approaches that described by Raoult’s law. For example, if the two components differ only in isotopic content, then the vapor pressure of each component will be equal to the vapor pressure of the pure substance $P 0$ times the mole fraction in the solution. This is Raoult’s law.

Using the example of a solution of two liquids, A and B, if no other gases are present, then the total vapor pressure p above the solution is equal to the weighted sum of the "pure" vapor pressures of the two components, p_A and p_B. Thus the total pressure above solution of A and B would be

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[edit]Derivation

We define an ideal solution as a solution for which the chemical potential of component $i$ is:

where µ*_i is the chemical potential of pure i.

If the system is at equilibrium, then the chemical potential of the component i must be the same in the liquid solution and in the vapor above it. That is,

Assuming the liquid is an ideal solution, and using the formula for the chemical potential of a gas, gives:

where ƒ_i is the fugacity of the vapor of $i$ .

The corresponding equation for pure $i$ in equilibrium with its (pure) vapor is:

where * indicates the pure component.

Subtracting both equations gives us

which re-arranges to

The fugacities can be replaced by simple pressures if the vapor of the solution behaves ideally i.e.

which is Raoult’s Law.

[edit]Ideal mixing

An ideal solution can be said to follow Raoult's Law but it must be kept in mind that in the strict sense ideal solutions do not exist. The fact that the vapor is taken to be ideal is the least of our worries. Interactions between gas molecules are typically quite small especially if the vapor pressures are low. The interactions in a liquid however are very strong. For a solution to be ideal we must assume that it does not matter whether a molecule A has another A as neighbor or a B molecule. This is only approximately true if the two species are almost identical chemically. We can see that from considering the Gibbs free energy change of mixing:

This is always negative, so mixing is spontaneous. However the expression is, apart from a factor –T, equal to the entropy of mixing. This leaves no room at all for an enthalpy effect and implies that Δ_mixH must be equal to zero and this can only be if the interactions U between the molecules are indifferent.

It can be shown using the Gibbs–Duhem equation that if Raoult's law holds over the entire concentration range x = 0–1 in a binary solution then, for the second component, the same must also hold.

If the deviations from ideality are not too strong, Raoult's law will still be valid in a narrow concentration range when approaching x = 1 for the majority phase (the solvent). The solute will also show a linear limiting law but with a different coefficient. This law is known as Henry's law.

The presence of these limited linear regimes has been experimentally verified in a great number of cases.

In a perfectly ideal system, where ideal liquid and ideal vapor are assumed, a very useful equation emerges if Raoult's law is combined withDalton's Law.

[edit]Non-ideal mixing

Raoult's Law may be adapted to non-ideal solutions by incorporating two factors that will account for the interactions between molecules of different substances. The first factor is a correction for gas non-ideality, or deviations from the ideal-gas law. It is called the fugacity coefficient ( $φ$ ). The second, the activity coefficient ( $γ$ ), is a correction for interactions in the liquid phase between the different molecules.

This modified or extended Raoult's law is then written:

[edit]Real solutions

Many pairs of liquids are present in which there is no uniformity of attractive forces i.e. the adhesive & cohesive forces of attraction are not uniform between the two liquids, so that they show deviation from the raoult's law which is applied only to ideal solutions.

[edit]Negative deviation

When adhesive forces between molecules of A & B are greater than the cohesive forces between A & A or B & B, then the vapor pressure of the solution is less than the expected vapor pressure from Raoult's law. This is called as negative deviation from Raoult's law. These cohesive forces are lessened not only by dilution but also attraction between two molecules through formation ofhydrogen bonds. This will further reduce the tendency of A and B to escape.

For example, chloroform & acetone show such an attraction by formation of an H-bond.

[edit]Positive deviation

When the cohesive forces between like molecules are greater than the adhesive forces, the dissimilarities of polarity or internal pressure will lead both components to escape solution more easily. Therefore, the vapor pressure will be greater than the expected from the Raoult's law, showing positive deviation. If the deviation is large, then the vapor pressure curve will show a maximum at a particular composition, e.g. benzene & ethyl alcohol, carbon disulfide & acetone, chloroform & ethanol.

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Image results for raoult's law

Lowering of V.P.

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Vapor Pressure Lowering

Click here to review vapor pressure of pure liquids and solids.

The Macroscopic View

When a solute is added to a solvent, the vapor pressure of the solvent (above the resulting solution) is lower than the vapor pressure above the pure solvent.

The vapor pressure of the solvent above a solution changes as the concentration of the solute in the solution changes (but it does not depend on the identity of either the solvent or the solute(s) particles (kind, size or charge) in the solution).

Non-Volatile Solutes

Experimentally, we know that the vapor pressure of the solvent above a solution containing a non-volatile solute (i.e., a solute that does not have a vapor pressure of its own) is directly proportional to the mole fraction of solvent in the solution. This behavior is summed up in Raoult's Law:

P_solvent = X_solventP^o_solvent

where:

P_solvent is the vapor pressure of the solvent above the solution,
X_solvent is the mole fraction of the solvent in the solution, and
P^o_solvent is the vapor pressure of the pure solvent.

Note that

when X_solvent = 1 (pure solvent), P_solvent = P^o_solvent, and
when X_solvent <>P_solvent < P^o_solvent (i.e., the vapor pressure of the solvent above the solution is lower than the vapor pressure above the pure solvent).

The following graph shows the vapor pressure for water (solvent) at 90^oC as a function of mole fraction of water in several solutions containing sucrose (a non-volatile solute). Note that the vapor pressure of water decreases as the concentration of sucrose increases.

Volatile Solutes

A volatile solute (i.e., a solute that has a vapor pressure of its own) will contribute to the vapor pressure above a solution in which it is dissolved. The vapor pressure above a solution containing a volatile solute (or solutes) is equal to the sum of the vapor pressures of the solvent and each of the volatile solutes.

P_solvent = X_solventP^o_solvent

P_solute = X_soluteP^o_solute

P_solution = P_solvent + P_solute + ... = X_solventP^o_solvent + X_soluteP^o_solute + ...

The Microscopic View

The figure below shows a microscopic view of the surface of pure water. Note the interface between liquid water (below) and water vapor (above).

Non-Volatile Solutes

The figures below illustrate how the vapor pressure of water is affected by the addition of the non-volatile solute, NaCl.

Note that:

there are fewer water molecules in the vapor (i.e., lower vapor pressure) above the NaCl solution than in the vapor above pure water, and
there are no sodium ions or chloride ions in the vapor above the NaCl solution.


Pure water - microscopic view.	1.0 M NaCl solution - microscopic view. Note that the ionic solid, NaCl, produces Na⁺ ions (blue) and Cl^- ions (green) when dissolved in water.

Volatile Solutes

The figures below illustrate how the vapor pressure of liquid xenon is affected by the addition of the volatile solute, liquid krypton.

Note that:

there are fewer xenon atoms in the vapor (i.e., lower vapor pressure) above the solution than in the vapor above pure liquid xenon, and
there are krypton atoms in the vapor above the solution (i.e., both krypton and xenon contribute to the vapor pressure above the solution).


Pure liquid xenon - microscopic view.	Krypton-xenon solution - microscopic view (krypton atoms are shown in blue).

B.P.elevation

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Boiling-point elevation

From Wikipedia, the free encyclopedia

Boiling-point elevation describes the phenomenon that the boiling point of a liquid (a solvent) will be higher when another compound is added, meaning that a solution has a higher boiling point than a pure solvent. This happens whenever a non-volatile solute, such as a salt, is added to a pure solvent, such as water. The boiling point can be measured accurately using an ebullioscope.

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[edit]Explanation

The change in chemical potential of a solvent when a solute is added explains why boiling point elevation takes place.

The boiling point elevation is a colligative property, which means that it is dependent on the presence of dissolved particles and their number, but not their identity. It is an effect of the dilution of the solvent in the presence of a solute. It is a phenomenon that happens for all solutes in all solutions, even in ideal solutions, and does not depend on any specific solute-solvent interactions. The boiling point elevation happens both when the solute is an electrolyte, such as various salts, and a nonelectrolyte. In thermodynamic terms, the origin of the boiling point elevation is entropic and can be explained in terms of the vapor pressure or chemical potential of the solvent. In both cases, the explanation depends on the fact that many solutes are only present in the liquid phase and do not enter into the gas phase (except at extremely high temperatures).

Put in vapor pressure terms, a liquid boils at the temperature when its vapor pressure equals the surrounding pressure. For the solvent, the presence of the solute decreases its vapor pressure by dilution. A non-volatile solute has a vapor pressure of zero, so the vapor pressure of the solution is the same as the vapor pressure of the solvent. Thus, a higher temperature is needed for the vapor pressure to reach the surrounding pressure, and the boiling point is elevated.

Put in chemical potential terms, at the boiling point, the liquid phase and the gas (or vapor) phase have the same chemical potential (or vapor pressure) meaning that they are energetically equivalent. The chemical potential is dependent on the temperature, and at other temperatures either the liquid or the gas phase has a lower chemical potential and is more energetically favourable than the other phase. This means that when a non-volatile solute is added, the chemical potential of the solvent in the liquid phase is decreased by dilution, but the chemical potential of the solvent in the gas phase is not affected. This means in turn that the equilibrium between the liquid and gas phase is established at another temperature for a solution than a pure liquid, i.e., the boiling point is elevated.^[1]

The phenomenon of freezing-point depression is analogous to boiling point elevation. However, the magnitude of the freezing point depression is larger than the boiling point elevation for the same solvent and the same concentration of a solute. Because of these two phenomena, the liquid range of a solvent is increased in the presence of a solute.

[edit]Calculations

The extent of boiling-point elevation can be calculated by applying Clausius-Clapeyron relation and Raoult's law together with the assumption of the non-volatility of the solute. The result is that in dilute ideal solutions, the extent of boiling-point elevation is directly proportional to the molalconcentration of the solution according to the equation:^[1]

ΔT_b = K_b · m_B

where

ΔT_b, the boiling point elevation, is defined as T_{b (solution)} - T_{b (pure solvent)}.
K_b, the ebullioscopic constant, which is dependent on the properties of the solvent. It can be calculated as K_b = RT_b²M/ΔH_v, where R is thegas constant, and T_b is the boiling temperature of the pure solvent [in K], M is the molar mass of the solvent, and ΔH_v is the heat of vaporization per mole of the solvent.
m_B is the molality of the solution, calculated by taking dissociation into account since the boiling point elevation is a colligative property, dependent on the number of particles in solution. This is most easily done by using the van 't Hoff factor i as m_B = m_solute · i. The factor iaccounts for the number of individual particles (typically ions) formed by a compound in solution. Examples:
- i = 1 for sugar in water
- i = 2 for sodium chloride in water, due to the full dissociation of NaCl into Na⁺ and Cl^-
- i = 3 for calcium chloride in water, due to dissociation of CaCl₂ into Ca²⁺ and 2Cl^-

At high concentrations, the above formula is less precise due to nonideality of the solution. If the solute is also volatile, one of the key the assumptions used in deriving the formula is not true, since it derived for solutions of non-volatile solutes in a volatile solvent. In the case of volatile solutes it is more relevant to talk of a mixture of volatile compounds and the effect of the solute on the boiling point must be determined from the phase diagram of the mixture. In such cases, the mixture can sometimes have a boiling point that is lower than either of the pure components; a mixture with a minimum boiling point is a type of azeotrope.

[edit]Ebullioscopic constants

Values of the ebullioscopic constants K_b for selected solvents:^[2]

Compound	Boiling point in °C	Ebullioscopic constant K_b in units of [(K·kg)/mol] or [K/molal]
Acetic acid	118.1	3.07
Benzene	80.1	2.53
Carbon disulfide	46.2	2.37
Carbon tetrachloride	76.8	4.95
Naphthalene	217.9	5.8
Phenol	181.75	3.04
Water	100	0.512

[edit]Uses

Together with the formula above, the boiling-point elevation can in principle be used to measure the degree of dissociation or the molar mass of the solute. This kind of measurement is called ebullioscopy (Greek "boiling-viewing"). However, since superheating is difficult to avoid, preciseΔT_b measurements are difficult to carry out,^[1] which was partly overcome by the invention of the Beckmann thermometer. Furthermore, the cryoscopic constant that determine freezing-point depression is larger than the ebullioscopic constant, and since the freezing point is often easier to measure with precision, it is more common to use cryoscopy.

A common misuse of the effect of ebullioscopic increase leads to add salt when cooking pasta, only after water has started boiling. The misconception is that otherwise it would take longer for water to boil to elevate the temperature of the water before it boils. However, at the approximate dosage of salting water for cooking (10 g of salt per 1 kg of water, or 1 teaspoon per quart), ebullioscopic increase is approximately 0.17 C (0.31 F), but it is counteracted by the fact that at that concentration salted water absorbs heat faster.

F.P.depression

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Freezing-point depression

From Wikipedia, the free encyclopedia

This article deals with melting/freezing point depression due to mixture of another compound. For depression due to small particle size, see melting point depression.

Freezing-point depression describes the phenomenon that the freezing point of a liquid (a solvent) is depressed when another compound is added, meaning that a solution has a lower freezing point than a pure solvent. This happens whenever a solute is added to a pure solvent, such as water. The phenomenon may be observed in sea water, which due to its salt content remains liquid at temperatures below 0°C, the freezing point of pure water.

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[edit]Explanation

The change in chemical potential of a solvent when a solute is added explains why freezing point depression takes place.

The freezing point depression is a colligative property, which means that it is dependent on the presence of dissolved particles and their number, but not their identity. It is an effect of the dilution of the solvent in the presence of a solute. It is a phenomenon that happens for all solutes in all solutions, even in ideal solutions, and does not depend on any specific solute-solvent interactions. The freezing point depression happens both when the solute is an electrolyte, such as various salts, and a nonelectrolyte. In thermodynamic terms, the origin of the freezing point depression is entropic and is most easily explained in terms of the chemical potential of the solvent.

At the freezing (or melting) point, the solid phase and the liquid phase have the same chemical potential meaning that they are energetically equivalent. The chemical potential is dependent on the temperature, and at other temperatures either the solid or the liquid phase has a lower chemical potential and is more energetically favourable than the other phase. In many cases, a solute does only dissolve in the liquid solvent and not in the solid solvent. This means that when such a solute is added, the chemical potential in the liquid phase is decreased by dilution, but the chemical potential of the solvent in the solid phase is not affected. This means in turn that the equilibrium between the solid and liquid phase is established at another temperature for a solution than a pure liquid; i.e., the freezing point is depressed.^[1]

The phenomenon of boiling point elevation is analogous to freezing point depression. However, the magnitude of the freezing point depression is larger than the boiling point elevation for the same solvent and the same concentration of a solute. Because of these two phenomena, the liquid range of a solvent is increased in the presence of a solute.

[edit]Calculations

The extent of freezing-point depression can be calculated by applying the Clausius-Clapeyron relation and Raoult's law together with the assumption of the non-solubility of the solute in the solid solvent. The result is that in dilute ideal solutions, the extent of freezing-point depression is directly proportional to the molal concentration of the solution according to the equation^[1]

ΔT_f = K_f · m_B

where

ΔT_f, the freezing point depression, is defined as T_{f (pure solvent)} − T_{f (solution)}, the difference between the freezing point of the pure solvent and the solution. It is defined to assume positive values when the freezing point depression takes place.
K_f, the cryoscopic constant, which is dependent on the properties of the solvent. It can be calculated as K_f = RT_m²M/ΔH_f, where R is thegas constant, T_m is the melting point of the pure solvent in kelvin, M is the molar mass of the solvent, and ΔH_f is the heat of fusion per mole of the solvent.
m_B is the molality of the solution, calculated by taking dissociation into account since the freezing point depression is a colligative property, dependent on the number of particles in solution. This is most easily done by using the van 't Hoff factor i as m_B = m_solute · i. The factor iaccounts for the number of individual particles (typically ions) formed by a compound in solution. Examples:
- i = 1 for sugar in water
- i = 2 for sodium chloride in water, due to dissociation of NaCl into Na⁺ and Cl^-
- i = 3 for calcium chloride in water, due to dissociation of CaCl₂ into Ca²⁺ and 2 Cl^-
- i = 2 for hydrogen chloride in water, due to complete dissociation of HCl into H⁺ and Cl^-
- i = 1 for hydrogen chloride in benzene, due to no dissociation of HCl in a non-polar solvent

At high concentrations, the above formula is less precise due to the approximations used in its derivation and any nonideality of the solution. If the solute is highly soluble in the solid solvent, one of the key assumptions used in deriving the formula is not true. In this case the effect of the solute on the freezing point must be determined from the phase diagram of the mixture.

[edit]Cryoscopic constants

Values of the cryoscopic constant K_f for selected solvents:^[2]^[3]

Compound	Freezes at °C	K_f at °C/m
Acetic acid	16.6	3.90
Benzene	5.5	5.12
Camphor	179.8	39.7
Carbon disulfide	−112	3.8
Carbon tetrachloride	−23	30
Chloroform	−63.5	4.68
Cyclohexane	6.4	20.2
Ethanol	−114.6	1.99
Ethyl ether	−116.2	1.79
Naphthalene	80.2	6.9
Phenol	41	7.27
Water	0	1.86

[edit]Uses

The phenomenon of freezing point depression is used in technical applications to avoid freezing. In the case of water, ethylene glycol or other forms of antifreeze is added to cooling water in internal combustion engines, making the water stay a liquid at temperatures below its normal freezing point.

The use of freezing-point depression through "freeze avoidance" has also evolved in some animals that live in very cold environments. This happens through permanently high concentration of physiologically rather inert substances such as sorbitol or glycerol to increase the molality of fluids in cells and tissues, and thus decrease the freezing point. Examples include some species of arctic-living fish, such as rainbow smelt, which need to be able to survive in freezing temperatures for a long time. In other animals, such as the spring peeper frog (Pseudacris crucifer), the molality is increased temporarily as a reaction to cold temperatures. In the case of the peeper frog, this happens by massive breakdown ofglycogen in the frog's liver and subsequent release of massive amounts of glucose.^[4]

Together with formula above, freezing-point depression can be used to measure the degree of dissociation or the molar mass of the solute. This kind of measurement is called cryoscopy (Greek "freeze-viewing") and relies on exact measurement of the freezing point. The degree of dissociation is measured by determining the van 't Hoff factor i by first determining m_B and then comparing it to m_solute. In this case, the molar mass of the solute must be known. The molar mass of a solute is determined by comparing m_B with the amount of solute dissolved. In this case, i must be known, and the procedure is primarily useful for organic compounds using a nonpolar solvent. Cryoscopy is no longer as common a measurement method as it once was. As an example, it was still taught as a useful analytic procedure in Cohen's Practical Organic Chemistry of 1910,^[5] in which the molar mass of Naphthalene is determined in a so-called Beckmann freezing apparatus.

Freezing-point depression can also be used as a purity analysis tool when analysed by Differential scanning calorimetry.^[6] The results obtained are in mol%, but the method has its place, where other methods of analysis fail.

This is also the same principle acting in the melting-point depression observed when the melting point of an impure solid mixture is measured with a melting point apparatus, since melting and freezing points both refer to the liquid-solid phase transition (albeit in different directions).

In principle, the boiling point elevation and the freezing point depression could be used interchangeably for this purpose. However, the cryoscopic constant is larger than the ebullioscopic constant and the freezing point is often easier to measure with precision, which means measurements using the freezing point depression are more precise.

2009-11-07T09:55:00.000+05:30

Image results for osmotic pressure

osmosis

2009-11-07T09:49:00.000+05:30

Osmosis

From Wikipedia, the free encyclopedia

It has been suggested that Electroneutral exchange be merged into this article or section. (Discuss)

Osmosis is the diffusion of water through a semi-permeable membrane.^[1] More specifically, it is the movement of water across a semi-permeable membrane from an area of high water potential (low solute concentration) to an area of low water potential (high solute concentration). It is a physical process in which a solvent moves, without input of energy, across a semi-permeable membrane (permeable to the solvent, but not the solute) separating two solutions of different concentrations.^[2] Osmosis releases energy, and can be made to do work^[3].

Shot of a computer simulation of the process of osmosis

Net movement of solvent is from the less-concentrated (hypotonic) to the more-concentrated (hypertonic) solution, which tends to reduce the difference in concentrations. This effect can be countered by increasing the pressure of the hypertonic solution, with respect to the hypotonic. The osmotic pressure is defined to be the pressure required to maintain an equilibrium, with no net movement of solvent. Osmotic pressure is acolligative property, meaning that the property depends on the molar concentration of the solute but not on its identity.

Osmosis is important in biological systems as many biological membranes are semipermeable. In general, these membranes are impermeable to organic solutes with large molecules, such as polysaccharides, while permeable to water and small, uncharged solutes. Permeability may depend on solubility properties, charge, or chemistry as well as solute size. Water molecules travel through the plasma cell wall, tonoplast (vacuole) or protoplast in two ways, either by diffusing across the phospholipid bilayer directly, or via aquaporins (small transmembrane proteins similar to those in facilitated diffusion and in creating ion channels). Osmosis provides the primary means by which water is transported into and out of cells. The turgor pressure of a cell is largely maintained by osmosis, across the cell membrane, between the cell interior and its relatively hypotonic environment.^[4]

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Basic explanation

Osmosis may occur when there is a partially-permeable membrane, such as a cell membrane. When a cell is submerged in water, the water molecules pass through the cell membrane from an area of low solute concentration (outside the cell) to one of high solute concentration (inside the cell), this is called osmosis. The cell membrane is selectively permeable, so only necessary materials are let into the cell and waste left out.^[4]

When the membrane has a volume of pure water on both sides, water molecules pass in and out in each direction at the exact same rate; there is no net flow of water through the membrane. However, if there is a solution on one side, and pure water on the other, the membrane is still hit by molecules from both sides at the same rate. However, some of the molecules hitting the membrane from the solution side will be solute molecules, and these will not pass through the membrane. So water molecules pass through the membrane from this side at a slower rate. This will result in a net flow of water to the side with the solution. Assuming the membrane does not break, this net flow will slow and finally stop as the pressure on the solution side becomes such that the movement in each direction is equal: dynamic equilibrium. This could either be due to the water potential on both sides of the membrane being the same, or due to osmosis being inhibited by factors such as pressure potential or Osmotic pressure.

Osmosis can also be explained using the notion of entropy, from statistical mechanics. As above, suppose a permeable membrane separates equal amounts of pure solvent and a solution. Since a solution possesses more entropy than pure solvent, the second law of thermodynamicsstates that solvent molecules will flow into the solution until the entropy of the combined system is maximized. Notice that, as this happens, the solvent loses entropy while the solution gains entropy. Equilibrium, hence maximum entropy, is achieved when the entropy gradient becomes zero, and dissolution takes place.

Pure water is more ordered than water in a solution; thus, from an entropic standpoint it takes some net energy to move water molecule from a disordered solution and "pack it in" with pure water. This is the same explanation as to why the disordered air does not spontaneously separate and order into oxygen and nitrogen, it would take energy for this to happen. Additionally, particle size has no bearing on osmotic pressure, as this is the fundamental postulate of colligative properties.^[5]

Examples of osmosis

Effect of different solutions on blood cells

Plant cell under different environments

Osmotic pressure is the main cause of support in many plants. The osmotic entry of water raises the turgor pressure exerted against the cell wall, until it equals the osmotic pressure, creating a steady state.

When a plant cell is placed in a hypertonic solution, the water in the cells moves to an area higher in solute concentration and the cell shrinks, and in doing so, becomes flaccid. (This means the cell has become plasmolysed - the cell membrane has completely left the cell wall due to lack of water pressure on it; the opposite of turgid.)

Also, osmosis is responsible for the ability of plant roots to draw water from the soil. Since there are many fine roots, they have a large surface area, and water enters the roots by osmosis.

Osmosis can also be seen when potato slices are added to a high concentration of salt solution. The water from inside the potato moves to the salt solution, causing the potato to shrink and to lose its 'turgor pressure'. The more concentrated the salt solution, the bigger the difference in size and weight of the potato slice.

In unusual environments, osmosis can be very harmful to organisms. For example, freshwaterand saltwater aquarium fish placed in water of a different salinity than that they are adapted to will die quickly, and in the case of saltwater fish, dramatically. Another example of a harmful osmotic effect is the use of table salt to killleeches and slugs.

Suppose an animal or a plant cell is placed in a solution of sugar or salt in water.

If the medium is hypotonic — a dilute solution, with a higher water concentration than the cell — the cell will gain water through osmosis.
If the medium is isotonic — a solution with exactly the same water concentration as the cell — there will be no net movement of water across the cell membrane.
If the medium is hypertonic — a concentrated solution, with a lower water concentration than the cell — the cell will lose water by osmosis.

Essentially, this means that if a cell is put in a solution which is has a solute concentration higher than its own, then it will shrivel up, and if it is put in a solution with a lesser solute concentration than its own, the cell will expand and burst.

Chemical gardens demonstrate the effect of osmosis in inorganic chemistry.

Factors

Osmotic pressure

Main article: Osmotic Pressure

As mentioned before, osmosis may be opposed by increasing the pressure in the region of high solute concentration with respect to that in the low solute concentration region. The force per unit area, or pressure, required to prevent the passage of water through a selectively-permeable membrane and into a solution of greater concentration is equivalent to the osmotic pressure of the solution, or turgor. Osmotic pressure is acolligative property, meaning that the property depends on the concentration of the solute but not on its identity.

Increasing the pressure increases the chemical potential of the system in proportion to the molar volume ( $δμ = δ P V$ ). Therefore, osmosis stops when the increase in potential due to pressure equals the potential decrease from

N/A Correction need to be affected on given incorrect equations

Osmotic gradient

The osmotic gradient is the difference in concentration between two solutions on either side of a semipermeable membrane, and is used to tell the difference in percentages of the concentration of a specific particle dissolved in a solution.

Usually the osmotic gradient is used while comparing solutions that have a semipermeable membrane between them allowing water to diffuse between the two solutions, toward the hypertonic solution(the solution with the higher concentration). Eventually, the force of the column of water on the hypertonic side of the semipermeable membrane will equal the force of diffusion on the hypotonic (the side with a lesser concentration) side, creating equilibrium. When equilibrium is reached, water continues to flow, but it flows both ways in equal amounts as well as force, therefore stabilizing the solution.

Variation

Reverse osmosis

Main article: Reverse osmosis

Reverse osmosis is a separation process that uses pressure to force a solvent through a membrane that retains the solute on one side and allows the pure solvent to pass to the other side. More formally, it is the process of forcing a solvent from a region of high solute concentration through a membrane to a region of low solute concentration by applying a pressure in excess of the osmotic pressure.

Forward osmosis

Main article: Forward osmosis

Osmosis may be used directly to achieve separation of water from a "feed" solution containing unwanted solutes. A "draw" solution of higher osmotic pressure than the feed solution is used to induce a net flow of water through a semi-permeable membrane, such that the feed solution becomes concentrated as the draw solution becomes dilute. The diluted draw solution may then be used directly (as with an ingestible solute like glucose), or sent to a secondary separation process for the removal of the draw solute. This secondary separation can be more efficient than a reverse osmosis process would be alone, depending on the draw solute used and the feedwater treated. Forward osmosis is an area of ongoing research, focusing on applications in desalination, water purification, water treatment, food processing, etc.

Van't Hoff laws

2009-11-07T09:44:00.000+05:30

THE ROLE OF OSMOTIC PRESSURE IN THE ANALOGY BETWEEN SOLUTIONS AND GASES

J.H. van `t Hoff
Zeitschrift fur physikalische Chemie
vol. 1, pp. 481-508 (1887)

In an investigation, whose essential aim was a knowledge of the laws of chemical equilibrium in solutions, it gradually became apparent that there is a deep-seated analogy-indeed, almost an identity-between solutions and gases, so far as their physical relations are concerned; provided that with solutions we deal with the so-called osmotic pressure, where with gases we are concerned with the ordinary elastic pressure. This analogy will be made as clear as possible in the following paper, the physical properties being considered first:

1. OSMOTIC PRESSURE. KIND OF ANALOGY WHICH ARISES THROUGH THIS CONCEPTION.

In considering the quantity, with which we shall chiefly have to deal in what follow, at first from the theoretical point of view, let us think of a vessel, A, completely filled for example, with an aqueous solution of sugar, the vessel being placed in water, B. If, now, the perfectly solid wall of the vessel is permeable to water, but impermeable to the dissolved sugar, the attraction of the water by the solution will, as is well known, cause the water to enter A, but this action will soon reach its limit due to the pressure produced by the water which enters (in minimal quantity). Equilibrium exists under these conditions, and the pressure exerted on the wall of the vessel we will designate in the following pages as osmotic pressure.

It is evident that this condition of equilibrium can be established in A also at the outset, that is, without previous entrance of water, by providing the vessel B with a piston which exerts a pressure equal to the osmotic pressure. We can then see that by increasing or diminishing the pressure on the piston it is possible to produce arbitrary changes in the concentration of the solution, through the walls of the vessel.

Let this osmotic pressure be described form an experimental stand-point by one of Pfeffer's experiments. An unglazed porcelain cell was used, which was provided with a membrane permeable to water, but not to sugar. This was obtained as follows: The cell, thoroughly moistened, so as to drive out the air, and filled with a solution of potassium ferrocyanide, was placed in a solution of copper sulphate. The potassium and copper salts came in contact, after a time, by diffusion, in the interior of the porous wall, and formed there a membrane having the desired property. Such a vessel was then filled with a one-per-cent. solution of sugar, and, after being closed by a cork with mano meter attached, was immersed in water. The osmotic pressure gradually makes its appearance through the entrance of some water, and after equilibrium is established it is read on the manometer. Thus, the one-per-cent. solution of sugar in question, which was diluted only an insignificant amount by the water which entered, showed at 6.8°, a pressure of 50.5 millimetres of mercury, therefore about 1/15 of an atmosphere.

The porous membrances here described will, under the name "semipermeable membranes," find extensive application in what follows, even though in some cases the practical application is, perhaps, still unrealized. They furnish a means of dealing with solutions, which bears the closest resemblance to that used with gases. This evidently arises from the fact that the elastic pressure, characteristic of the latter condition, is now introduced also for solutions as osmotic pressure. At the same time let stress be laid upon the fact that we are not dealing here with an artificially forced analogy, but with one which is deeply seated in the nature of the case. The mechanism by which, according to our present conceptions, the elastic pressure of gases is produced is essentially the same as that which gives rise to osmotic pressure in solutions. It depends, in the first case, upon the impact of the gas molecules against the wall of the vessel; in the latter, upon the impact of the molecules of the dissolved substance against the semipermeable membrance, since the molecules of the solvent, being present upon both sides of the membrane through which they pass, do not enter into consideration.

The great practical advantage for the study of solutions, which follows from the analogy upon which stress has been laid, and which leads at onece to quantitative results, is that the application of the second law of thermodynamics to solutions has now become extremely easy, since reversible processes, to which, as is well known, this law applies, can now be performed with the greatest simplicity. It has been already mentioned above that a cylinder, provided with semipermeable walls and piston, when immersed in the solvent, allows any desired change in concentration to be porduced in the solution beneath the piston by exerting a proper pressure upon the piston, just as a gas is compressed and can then expand; only that, in the first case the solvent, in these changes in volume, moves through the wall of the cylinder. Such processes can, in both cases, preserve the condition of reversibility with the same degree of ease, provided that the pressure of the piston is equal to the counter-pressure, i.e., with solutions, to the osmotic pressure.

We will now make use of this practical advantage, especially for the investigations of the laws which hold for "ideal solution," that is, for solutions which are diluted to such an extent that they are comparable with "ideal gases," and in which, therefore, the reciprocal action of the dissolved molecules can be neglected, as also the space occupied by these molecules, in comparison with the volume of the solution itself.

4.-AVOGADRO'S LAW FOR DILUTE SOLUTIONS.

While up to the present, essentially only those changes have been dealt with which the osmotic pressure in solutions undergoes due to changes in concentration and temperature, and while the agreement with the corresponding laws which hold for gases manifested itself, we must now deal with the direct comparison of the two analogous quantities, elastic pressure and osmotic pressure of one and the same substance. It is evident that this applies to gases which have also been investigated in solution; and, as a matter of fact, it will be proved that, in case the law of Henry is satisfied, the osmotic pressure in solution is exactly equal to the elastic pressure as gas, at least at the same temperature and concentration.

For the purpose of demonstration, we will perfom a reversible cycle at constant temperature, by means of semipermeable walls, and then employ the second law of thermodynamics, which, in this case, as is known, leads to an extremely simple result, that no heat is transformed into work, or work into heat, and consequently the sum of all the work done must be equal to zero.

The reversible cycle is perfomed by two similarly arranged double cylinders, with pistons, like the one already described. One cylinder is partly filled with a gas (A), say oxygen, in contact with a solution of oxygen (B), saturated under the conditions of the experiment, for example, and aqueous solution. The wall bc allows only oxygen, but no water to pass through; the wall ab, on the contrary, allows water but not oxygen to pass, and in in contact on the outside with the liquid (E) in question. A reversible transformation can be made with such a cylinder; which amounts to this, that by raising the two pistons (1) and (2) oxygen is evolved form its aqueous solution as gas, while water is removed through ab. This transformation can take place so that the concentrations of gas and solution remain the same. The only difference between the two cylinders is in the concentrations which are present in them. These we will express in the following manner:

The unit of weight of the substance in question fills, in the left vessel, as gas and as solution, the volumes v and V respectively, in the right of v + dv and V+ dV; then in order that Henry's law be satisfied, the following relation must obtain:

v : V = (v + dv) : (V + dV)

therefore:

v : V = dv : dV.

Let now the pressure and osmotic pressure of gas and solution, in case unit weight is present in unit volume, be respectively P and p (values which hereafter will be shown to be equal), the pressure in gas and solution is, then, from Boyle's law, respectively P/v and p/V.

If we now raise the pistons (1) and (2), and thus liberate a unit weight of gas from the solution, we increase, then, this gas volume v by dv, in order that it may have the concentration of the gas in the left vessel; if the gas just set free is forced into solution by lowering pistons (4) and (5), and thus the volume of the solution V+ dV diminished by dV in the cylinder with semipermeable walls, the cycle is then completed.

Six amounts of work are to be taken into consideration, whose sum, from what is stated above, must be equal to zero. We will designate these by numbers, whose meaning is self-evident. We have, then:

(1) + (2) + (3) + (4) + (5) + (6) = 0

But (2) and (4) are of equal value and opposite sign, since we are dealing with volume changes v and v + dv, in the opposite sense, which takes place at pressures which are inversely proportional to the volumes. For the same reasons the sum of (1) and (5) is zero; then , from the above relation:

(3) + (6) = 0.

The work done by the gas (3), in case it undergoes an increase in volume dv at a pressure P/v, is :

(3) = P/v dv,

while the work done by the solution (6), in case it undergoes a diminution in volume dV at an osmotic pressure p/V is:

(6) = p/V dV.

We obtain then :

P/v dv = p/V dV;

and since v : V = dv : dV, P and p must be equal, which was to be proved.

The conclusion here reached, which will be repeatedly confirmed in what follows, is, in turn, a new support to the law of Gay-Lussac applied to solutions. In case gaseous pressure and osmotic pressure are equal at the same temperature, changes in temperature must have also and equal influence on both. But, on the other hand, the relation found permits of an important extension of the law of Avogadro, which now finds application also to all solutions, if only osmotic pressure is considered instead of elastic pressure. At equal osmotic pressure and equal temperature, equal volumes of the most widely different solution's contain an equal number of molecules, and, indeed, the same number which, at the same pressure and temperature, is contained in an equal volume of a gas.

5. GENERAL EXPRESSION OF THE LAW OF BOYLE, GAY-LUSSAC, AND AVOGADRO, FOR SOLUTIONS AND GASES.

The well-known formula which expresses for gasses the two laws of Boyle and Gay-Lussac:

PV = RT,

is now, where the laws referred to are also applicable to liquids, valid also fro solutions, if we are dealing with the osmotic pressure. This holds even with the same limitaion which is also to be considered with gases, that the dilution shall be sufficiently great to allow one to disregard the reciprocal action of, and the space taken by, the dissolved particles.

If we wish to include in the above expression, also, the third, the law of Avogadro, this can be done in an exceedingly simple manner, following the suggestion of Horstmann, considering always kilogram-molecules of the substance in question; thus, 2k. hydrogen, 44 k. carbon dioxide, etc. Then R in the above equation has the same value for all gases, since at the same temperature and pressure the quantities mentioned occupy also the same volume. If this value is calculated, and the volume taken in Mr³, the pressure in K° per Mr², and if, for example, hydrogen at 0° and atmospheric pressure is chosen:

P = 10333, V = 2/0.08956, T = 273, R = 845.05.

The combined expression of the laws of Boyle, Gay-Lussac, and Avogadro is, then:

PV = 845T

and in this form it refers not only to gases, but to all solutions, P being then always taken as osmotic presure.

In order that the formula last obtained may be hereafter easily applied, we give it finally a simpler form, by observing that the number of calories, which is equal to a kilogram-metre, therefore to the equivalent of work (A =1/423), stands in a very simple relation to R, indeed, AR = 2 (more exactly, about one-thousandth less).

Therefore, the following form can be chosen:

APV = 2T

which has the great practical advantage that the work done, of which we shall often speak hereafter, finds a very simple expression, in case it is calculated in calories.

2009-11-07T09:43:00.000+05:30

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osmosis

Animation: How Osmosis Works

osmosis

Osmosis

Solutions & Colligative Properties IIT

Concentration

Solutions phase diagram

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Solution

From Wikipedia, the free encyclopedia

Contents

[edit]Introduction

[edit]Properties of solutions

[edit]Types of bonding

[edit]Bond polarity

[edit]Aqeous solutions

[edit]Non-polar solutions

[edit]Solubility

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Concentration - Wikipedia, the free encyclopedia

Colligative properties

Colligative properties

From Wikipedia, the free encyclopedia

Contents

[edit]Vapor pressure

[edit]Boiling point and freezing point

[edit]Boiling point elevation

[edit]Freezing point depression

[edit]Osmotic pressure

Raoult's law

Raoult's law

From Wikipedia, the free encyclopedia

Contents

[edit]Derivation

[edit]Ideal mixing

[edit]Non-ideal mixing

[edit]Real solutions

[edit]Negative deviation

[edit]Positive deviation

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Lowering of V.P.

B.P.elevation

Boiling-point elevation

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Contents

[edit]Explanation

[edit]Calculations

[edit]Ebullioscopic constants

[edit]Uses

F.P.depression

Freezing-point depression

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Contents

[edit]Explanation

[edit]Calculations

[edit]Cryoscopic constants

[edit]Uses

Image results for osmotic pressure

osmosis

Osmosis

From Wikipedia, the free encyclopedia

Contents

Basic explanation

Examples of osmosis

Factors

Osmotic pressure

Osmotic gradient

Variation

Reverse osmosis

Forward osmosis

Van't Hoff laws

THE ROLE OF OSMOTIC PRESSURE IN THE ANALOGY BETWEEN SOLUTIONS AND GASES