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Vapour Pressure Of A Solution

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The vapour pressure of a solution is the pressure exerted by its vapour when in equilibrium with the liquid. Adding a non-volatile solute always lowers it (Raoult's law), and for a mixture of two volatile liquids the total pressure equals the sum of the partial pressures: . Ideal solutions obey Raoult's law across all compositions; non-ideal solutions show positive (repulsive) or negative (attractive) deviations that can form azeotropes - mixtures that boil at a constant composition and cannot be separated by fractional distillation.

Key Formulas - Quick Reference
  1. Raoult's law for volatile components:  and 
  2. Total vapour pressure (Dalton's law):
  3. Vapour phase composition:  and 
  4. Relative lowering of vapour pressure: (mole fraction of solute)
  5. Dilute-solution form:
  6. Ostwald-Walker:
  7. Ideal solution conditions: , ; obeys Raoult's law for all

1. What is Vapour Pressure of a Solution

Every liquid in a closed container establishes a dynamic equilibrium between its liquid and vapour phases. The pressure of the vapour at this equilibrium is called the vapour pressure of the liquid. When another substance is dissolved in the liquid, the vapour pressure typically changes.

Relative lowering of vapour pressure is the difference between the vapour pressure of the pure solvent and that of the solution, expressed relative to the pure solvent value. For example, at 20 °C the vapour pressure of pure water is 17.54 mmHg. When an aqueous solution containing 0.010 mole fraction of ethylene glycol (a non-volatile liquid) is prepared, its vapour pressure drops to 17.36 mmHg. The lowering is mmHg.

Molecular reason why a non-volatile solute lowers vapour pressure Two closed containers. In the pure solvent many solvent molecules occupy the surface and escape freely into the vapour space, so the vapour pressure is high. In the solution, non-volatile solute particles take up part of the surface, fewer solvent molecules can escape per second, and the equilibrium vapour pressure settles at a lower value. (a) pure solvent every surface site can evaporate vapour pressure = P° (b) solution with a non-volatile solute solute blocks part of the surface vapour pressure = P < P°
Figure 1: Why a non-volatile solute lowers vapour pressure. In the pure solvent every surface site can evaporate. In the solution the solute occupies part of the surface and cannot itself enter the vapour, so fewer solvent molecules escape per second and equilibrium settles at .

2. Raoult's Law

Raoult's law: at a constant temperature, the partial vapour pressure of any volatile component of a solution is equal to the vapour pressure of the pure component multiplied by its mole fraction in the solution.

where and are the vapour pressures of the pure liquids and .

If the vapour behaves as an ideal gas, Dalton's law of partial pressures gives the total vapour pressure:

Vapour pressure diagram of an ideal binary solution Partial pressure of each component and the total pressure plotted against the mole fraction of A in the liquid. The partial pressure of A is a straight line from zero at pure B up to the vapour pressure of pure A. The partial pressure of B falls the other way. The total pressure is their sum, a straight line joining the two pure vapour pressures. xA = 0 xB = 1 xA = 1 xB = 0 mole fraction of A in the liquid, xA total vapour pressure, P P°A P°B III: PT = pA + pB I: pA = xA P°A II: pB = xB P°B all three lines are STRAIGHT: this is what makes the solution ideal
Figure 2: Ideal binary solution at constant temperature. Line I is , line II is , and line III is the total . All three stay straight across the entire composition range, which is precisely what defines an ideal solution.

Raoult's law as a special case of Henry's law: Henry's law applies to a gas dissolved in a liquid. When we set (the vapour pressure of the pure component), we recover Raoult's law . So Raoult's law is Henry's law with the special value , which is exactly what happens when the "solute" is chemically similar to the solvent - i.e., in an ideal solution.

Solved Example 1
The vapour pressures of ethanol and methanol are 44.5 mmHg and 88.7 mmHg respectively at some temperature. An ideal solution is formed by mixing 60 g of ethanol with 40 g of methanol. Calculate the total vapour pressure of the solution.
Solution:

Molar masses: ethanol () = 46, methanol () = 32.

Moles of ethanol ;   moles of methanol .

Let = methanol, = ethanol (so , ).

;   .

mmHg.

Solved Example 2
The composition of the vapour over a binary ideal solution is determined by the composition of the liquid. If and are the mole fractions of in the liquid and vapour respectively, find the value of for which has a minimum. What is the total pressure at this composition?
Solution:

Vapour-phase mole fraction of :

Let . Setting and solving (algebra shown expanded):

Substituting back, the total pressure at this composition is:

(the geometric mean of the two pure vapour pressures)

Solved Example 3
What is the composition of the vapour in equilibrium at 30 °C with a benzene-toluene solution having mole fraction of benzene = 0.400? Given torr and torr (subscripts denote pure benzene B and pure toluene T).
Solution:

Partial pressures in solution: torr; torr.

Total pressure: torr.

Vapour-phase mole fraction of benzene: ;   .

The vapour is richer in benzene (the more volatile component) - . This is Konowaloff's rule: the vapour phase is always richer in the more volatile component.

Solved Example 4
The vapour pressure of a pure liquid is 100 mmHg. When a non-volatile solute is dissolved in it, the vapour pressure of the solution becomes 80 mmHg. Calculate the mole fraction of the solute in the solution.
Solution:

Applying the relative lowering formula (which is valid for a non-volatile solute):

Mole fraction of solvent .

3. Ideal Solutions

An ideal solution is one in which both components obey Raoult's law across the entire range of compositions (not just in dilute limits).

The three signatures of an ideal solution:

  • Raoult's law holds for all : and
  • No enthalpy change on mixing: (no heat absorbed or evolved)
  • No volume change on mixing: (volumes add up)

Why: ideal behaviour occurs when the A-B, A-A, and B-B intermolecular forces are all equal in strength. Then a molecule "does not know" whether its neighbours are A or B - the escape tendency of each component is unchanged by mixing, so Raoult's law holds.

Examples of near-ideal solutions: benzene () and toluene (); -hexane and -heptane; ethylene bromide and ethylene chloride; chlorobenzene and bromobenzene. Note that each pair is chemically similar - similar functional groups, similar polarity, similar shape.

4. Non-Ideal Solutions

Solutions that do not obey Raoult's law across the whole composition range are non-ideal. They fall into two categories based on the sign of the deviation.

(a) Positive Deviation

Total observed vapour pressure is higher than the ideal prediction. This happens when A-B interactions are weaker than A-A and B-B interactions - molecules escape more easily than in the pure liquids.

Positive deviation from Raoult's law Vapour pressure against liquid composition for a mixture showing positive deviation. Every observed curve lies above its dashed ideal straight line, and the total pressure curve rises to a maximum higher than both pure vapour pressures. All curves still meet the ideal lines exactly at the two pure ends. Positive deviation xA = 0 xB = 1 xA = 1 xB = 0 mole fraction of A in the liquid, xA total vapour pressure, P P°A P°B maximum in P azeotropic composition observed ideal (Raoult) A-B attraction is WEAKER than A-A and B-B, so molecules escape more easily ΔHmix > 0 (endothermic) · ΔVmix > 0 (expands) · examples: ethanol-water, acetone-CS2
Figure 3: Positive deviation from Raoult's law. Every observed curve lies above its dashed ideal line, and rises to a maximum higher than both and . Note that observed and ideal coincide exactly at the two pure ends. Cause: A-B forces weaker than A-A and B-B. Example: ethanol-water.

Signatures:

  • for both components
  • (endothermic - heat absorbed as weaker bonds form)
  • (volume expands slightly on mixing)

Examples: ethanol-water, acetone-carbon disulphide, ethanol-chloroform, cyclohexane-ethanol. Ethanol-water in particular has hydrogen bonding within pure ethanol and within pure water; on mixing, each ethanol OH is next to different chemistry, disrupting the H-bonds.

(b) Negative Deviation

Total observed vapour pressure is lower than the ideal prediction. This happens when A-B interactions are stronger than A-A and B-B - the molecules "hold on to each other" and escape less readily.

Negative deviation from Raoult's law Vapour pressure against liquid composition for a mixture showing negative deviation. Every observed curve lies below its dashed ideal straight line, and the total pressure curve dips to a minimum lower than both pure vapour pressures. All curves still meet the ideal lines exactly at the two pure ends. Negative deviation xA = 0 xB = 1 xA = 1 xB = 0 mole fraction of A in the liquid, xA total vapour pressure, P P°A P°B minimum in P azeotropic composition observed ideal (Raoult) A-B attraction is STRONGER than A-A and B-B, so molecules escape less easily ΔHmix < 0 (exothermic) · ΔVmix < 0 (contracts) · examples: acetone-chloroform, HNO3-water
Figure 4: Negative deviation from Raoult's law. Every observed curve lies below its dashed ideal line, and dips to a minimum lower than both and . Cause: A-B forces stronger than A-A and B-B. Example: acetone-chloroform, -water.

Signatures:

  • for both components
  • (exothermic - heat released as stronger bonds form)
  • (volume contracts on mixing)

Examples: acetone-chloroform (chloroform H can hydrogen-bond to acetone C=O), -water, -water, phenol-aniline.

Hydrogen bond between chloroform and acetone causing negative deviation A chloroform molecule on the left with its central carbon carrying three chlorine atoms and one hydrogen. An acetone molecule on the right with a carbonyl group and two methyl groups. The slightly acidic hydrogen of chloroform forms a hydrogen bond with the carbonyl oxygen of acetone. This attraction exists only in the mixture, not in either pure liquid, so the molecules escape less easily and the vapour pressure falls below the Raoult prediction. Why acetone and chloroform deviate negatively Cl Cl Cl C H δ+ chloroform CHCl3 three Cl pull electrons away, so H is acidic hydrogen bond absent in both pure liquids O δ- C CH3 CH3 acetone (CH3)2C=O carbonyl O carries lone pairs stronger A-B attraction → molecules escape less easily → P below the Raoult line
Figure 5: The acetone-chloroform hydrogen bond. Three chlorines pull electron density away from the chloroform , leaving that hydrogen acidic enough to hydrogen-bond to the carbonyl oxygen of acetone. This attraction exists in neither pure liquid, so escape into the vapour becomes harder and the mixture deviates negatively.
Solved Example 5
A mixture of two liquids has kJ/mol and mL/mol. Predict whether this mixture shows positive or negative deviation from Raoult's law and give one likely example.
Solution:

(exothermic) and (contraction) are both signatures of negative deviation. The A-B interactions are stronger than A-A and B-B, so mixing releases heat and packs molecules more tightly.

A likely example is acetone-chloroform: the acidic hydrogen of chloroform () forms a hydrogen bond with the carbonyl oxygen of acetone () - an attraction that does not exist in either pure liquid.

5. Measurement of Vapour Pressure Lowering - Ostwald and Walker Apparatus

The Ostwald-Walker method is a classical way to measure the relative lowering of vapour pressure. Dry air is bubbled successively through three parts of the apparatus:

  • Part 1: a set of bulbs containing the solution under study.
  • Part 2: a set of bulbs containing the pure solvent.
  • Part 3: a U-tube containing anhydrous calcium chloride, which absorbs all solvent vapour.
Ostwald and Walker apparatus for measuring relative lowering of vapour pressure Dry air enters on the left and bubbles in turn through three bulbs of solution, then three bulbs of pure solvent, and finally through a U tube packed with anhydrous calcium chloride. The solution bulbs lose a mass proportional to the vapour pressure of the solution. The solvent bulbs lose a mass proportional to the difference between the pure solvent vapour pressure and that of the solution. The calcium chloride tube gains a mass proportional to the vapour pressure of the pure solvent. Ostwald and Walker apparatus dry air in dry air out SOLUTION loses mass ∝ P PURE SOLVENT loses mass ∝ (P° − P) anhydrous CaCl2 gains mass ∝ P° loss by solvent bulbs ÷ gain by CaCl2 tube = (P° − P) ÷ P° which is exactly the relative lowering of vapour pressure, and equals xsolute
Figure 6: Ostwald-Walker apparatus. Dry air bubbles in turn through the solution, the pure solvent, and anhydrous . Dividing the mass lost by the solvent bulbs by the mass gained by the tube gives the relative lowering directly, with no pressure measurement needed.

How the mass changes work:

  • As dry air passes through the solution, it saturates with solvent vapour and picks up mass proportional to (the vapour pressure of the solution). So the solution bulbs lose mass .
  • The now-partially-saturated air passes through pure solvent. It picks up additional vapour proportional to . So the solvent bulbs lose mass .
  • The CaCl tube absorbs all solvent vapour, gaining a mass proportional to .

From the relative lowering, and using , one can calculate the molar mass of an unknown non-volatile solute.

Solved Example 6
Dry air is passed through a solution containing 20 g of a non-volatile organic solute in 250 mL of water, then through pure water, and finally through a U-tube containing anhydrous CaCl. The solution loses 26 g and the U-tube gains 26.48 g. Calculate the molar mass of the solute.
Solution:

Loss in mass of solution g. Gain in CaCl tube g.

Therefore loss in mass of solvent (pure water bulbs) g.

For dilute solution:

g/mol g/mol

6. Azeotropes

An azeotrope (or "constant-boiling mixture") is a binary liquid mixture that boils at a fixed temperature and has the same composition in liquid and vapour phases. Because , the components of an azeotrope cannot be separated by fractional distillation.

Azeotropes arise from non-ideal behaviour that produces a maximum or minimum in the vapour pressure (and hence boiling point) curve at some intermediate composition.

Minimum boiling and maximum boiling azeotropes Two boiling point against composition diagrams. On the left a mixture with positive deviation has a maximum in vapour pressure, so the boiling point curve dips to a minimum at the azeotropic composition, as for ethanol and water at about ninety five per cent ethanol. On the right a mixture with negative deviation has a minimum in vapour pressure, so the boiling point curve rises to a maximum, as for nitric acid and water at about sixty eight per cent nitric acid. (a) Minimum-boiling azeotrope from POSITIVE deviation (maximum in P) boiling point Tb composition pure A pure B azeotrope boils below both pure liquids ethanol + water 95% ethanol, boils at 78 °C (b) Maximum-boiling azeotrope from NEGATIVE deviation (minimum in P) boiling point Tb composition pure A pure B azeotrope boils above both pure liquids nitric acid + water 68% HNO3, boils at 120 °C
Figure 7: Azeotropes. (a) Positive deviation gives a maximum in and therefore a minimum in : ethanol-water at about 95% ethanol boils at 78 °C. (b) Negative deviation gives a minimum in and a maximum in : -water at about 68% acid boils at 120 °C. At the azeotrope , so distillation cannot separate the pair.

Minimum-Boiling Azeotrope

Solutions showing positive deviation from Raoult's law have a maximum in the vapour pressure curve, which corresponds to a minimum in the boiling point curve. At the azeotrope composition, the mixture boils at a lower temperature than either pure component.

Example: ethanol-water forms a minimum-boiling azeotrope at ~95% ethanol by volume, boiling at 351.15 K (78 °C), lower than either pure ethanol (78.4 °C) or pure water (100 °C). This is why fractional distillation of a fermentation mixture cannot produce 100% ethanol - it stops at the azeotropic 95%. Absolute alcohol is made by other means (e.g., addition of benzene).

Maximum-Boiling Azeotrope

Solutions showing negative deviation have a minimum in vapour pressure, which corresponds to a maximum in boiling point. The azeotrope boils at a higher temperature than either pure component.

Example: -water forms a maximum-boiling azeotrope at ~68% by mass, boiling at 393 K (120 °C), higher than either pure (86 °C) or water (100 °C). This is why "concentrated nitric acid" available commercially is 68% - fractional distillation of dilute acid cannot exceed this composition.

Solved Example 7
Liquids and form an ideal solution. The vapour pressures of pure and at 100 °C are 300 and 100 mmHg respectively. Vapour above a solution containing 1 mole of and 1 mole of is collected and completely condensed. This condensate is then heated to 100 °C and its vapours are collected and condensed again to form liquid . Find the mole fraction of in the vapour above .
Solution:

Starting solution: , ; mmHg.

in first vapour ; .

First condensate: now , ; mmHg.

in second vapour (which becomes liquid ) .

Liquid vapour composition: has , ; mmHg.

above .

Notice: each successive distillation enriches the more volatile component () further. This is the principle of fractional distillation.

Common Mistakes to Avoid

Watch out
  • Raoult's law with mole fraction of solvent gives . Do not accidentally use mole fraction of solute here.
  • The relative lowering formula is valid only when the solute is non-volatile. For volatile solutes, use instead.
  • Vapour is always richer in the more volatile component ( if ). Do not compute as the same as .
  • Positive deviation (endothermic). Negative deviation (exothermic). Do not confuse the signs.
  • Azeotropes cannot be separated by fractional distillation, but they are true mixtures, not compounds. Their composition depends on external pressure.
  • Minimum-boiling azeotrope = maximum in (positive deviation). Maximum-boiling azeotrope = minimum in (negative deviation). "Minimum" and "maximum" swap between and .

Frequently Asked Questions

Q1. Why does adding a non-volatile solute lower the vapour pressure of a solvent?

The vapour pressure of a liquid is due to solvent molecules escaping from the surface. When a non-volatile solute is added, its molecules occupy part of the surface and do not contribute to the vapour phase. Fewer solvent molecules can escape per unit time, so the vapour pressure of the solution is lower than that of pure solvent.

Q2. What is the difference between an ideal solution and a non-ideal solution?

An ideal solution obeys Raoult's law across the entire range of compositions and has zero enthalpy and volume change on mixing. Non-ideal solutions deviate from Raoult's law and show either positive deviation (A-B interactions weaker than A-A and B-B, giving endothermic mixing) or negative deviation (A-B interactions stronger, giving exothermic mixing).

Q3. Why cannot an azeotrope be separated by fractional distillation?

At the azeotropic composition, the liquid and vapour phases have identical compositions. Distillation works by exploiting differences in composition between liquid and vapour, so if they are the same, no further separation occurs no matter how many distillation stages are used. This is why concentrated is stuck at 68% and ethanol-water at 95%.

Q4. Is an azeotrope a compound or a mixture?

An azeotrope is a mixture, not a compound. It has a fixed composition only at a specific pressure. If the external pressure changes, the azeotropic composition changes too. Compounds, by contrast, have fixed compositions regardless of pressure. The azeotropic ratio also does not obey the law of definite proportions in a chemical sense.

Q5. Why does acetone-chloroform mixture show negative deviation?

In pure acetone the molecules interact via weak dipole-dipole forces. In pure chloroform there are only weak dispersion forces. When mixed, the acidic hydrogen of chloroform () forms a hydrogen bond with the carbonyl oxygen of acetone (C=O). This new attraction is stronger than the interactions in either pure liquid, so molecules escape less readily - vapour pressure drops below the Raoult prediction.

Q6. What is Konowaloff's rule?

Konowaloff's rule states that at any given liquid composition, the vapour phase is always richer in the more volatile component (the one with the higher pure vapour pressure). Mathematically, if , then . This is why repeated distillation progressively enriches the more volatile species.

Q7. Can Raoult's law be derived from Henry's law?

Yes. Henry's law says for a gas dissolved in a liquid. In an ideal solution, when one component acts as "solvent" and the other as "solute" but the two are chemically similar, the Henry constant becomes equal to the vapour pressure of the pure component . Substituting gives Raoult's law . So Raoult's law is the special case of Henry's law where .

Q8. What is the physical meaning of a maximum-boiling azeotrope having negative deviation?

In a negatively-deviating mixture, unlike molecules attract each other more strongly than like molecules do. The molecules hold on to each other tightly, making escape into the vapour phase difficult. The vapour pressure is depressed, and since boiling occurs when vapour pressure equals atmospheric pressure, the mixture needs to be heated to a higher temperature than either pure component to boil - producing a maximum on the boiling-point diagram.

Previous year questions on Vapour Pressure Of A Solution

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