4: Vapour Pressure

In a binary solution containing only A and B, the mole fractions obey xA + xB = 1. Therefore, xB = 1 − xA = 1 − 0.3 = 0.7. The ideal nature of the solution is relevant to Raoult’s law but does not alter this basic mole-fraction relation. A mole fraction cannot exceed one, and 0.03 is not the complement of 0.3.

Temperature measures the average kinetic energy of particles. When temperature rises, a larger fraction of liquid molecules has enough energy to overcome intermolecular attractions and enter the vapour phase. The rate of evaporation increases, and in a closed vessel the equilibrium vapour pressure becomes higher. Molecules do not disappear, container colour is irrelevant, and temperature is directly related to molecular motion.

Strong intermolecular attractions hold liquid molecules more firmly and make it harder for them to escape into the vapour phase. Consequently, fewer molecules are present in the vapour at equilibrium, giving a lower vapour pressure at the same temperature. Easy escape, high volatility, and a low boiling point are generally associated with higher vapour pressure, so options B, C, and D describe the opposite trend.

In a closed vessel, liquid molecules continuously evaporate and vapour molecules continuously condense. When the forward and reverse rates become equal, the macroscopic amounts of liquid and vapour remain constant, although molecular motion continues. This state is dynamic equilibrium. It is not permanent boiling, freezing or chemical decomposition.

A liquid boils when its vapour pressure becomes equal to the external pressure. The normal boiling point is specifically defined under a standard external pressure of one atmosphere. Therefore, the correct condition is vapour pressure equal to one atmosphere. Zero vapour pressure would not permit boiling, and colour or the presence of solute is not the defining condition, although solutes can change a solution’s boiling point.

Relative lowering is obtained by dividing the absolute lowering of vapour pressure by the vapour pressure of the pure solvent: relative lowering = Δp/p°. The given values give Δp/p° = 5/50 = 0.10. This is a ratio without a unit, equivalent to 10%. It is not 5.0, because the lowering must be normalized by the pure-solvent pressure, and it is not 0.50 because that would be incorrect division.

Boiling begins when the vapour pressure of a liquid equals the pressure acting on its surface. If this equality is reached at a lower temperature, the temperature required for boiling is lower; therefore, the liquid has a lower boiling point. The conclusion does not imply that the boiling point must be below zero or infinite. A higher boiling point would require reaching the same external pressure only at a higher temperature.

For a mixture containing volatile components, Dalton’s law states that the total pressure is the sum of the partial pressures. Therefore, ptotal = pA + pB = 40 + 25 = 65 kPa. The total pressure cannot be found by subtracting the values; subtraction gives only their difference, 15 kPa. It also must be greater than either individual partial pressure when both components contribute positively.

For a non-volatile solute, lowering of vapour pressure increases with the effective solute mole fraction or particle concentration. A small lowering therefore indicates that the solute has a small effect, normally because its amount is small relative to the solvent. A very large amount would cause a larger lowering, while zero solvent fraction would make the stated comparison invalid.

Raoult’s law for a component is p = x p°, where p is its partial vapour pressure, x is its mole fraction, and p° is the vapour pressure of the pure component. Substituting x = 1 gives p = 1 × p° = p°. This represents the pure-component limit: when the component makes up the entire liquid phase, its solution pressure equals its pure vapour pressure, not zero or a multiple of it.

Raoult’s law predicts the ideal vapour pressure. When the observed pressure lies below that prediction, the solution shows negative deviation. The usual molecular reason is stronger attraction between unlike molecules, which keeps more molecules in the liquid phase. Positive deviation would mean a pressure above the ideal value, while no deviation means equality.

Because the solute is non-volatile, the measurable vapour pressure is due to the solvent. Raoult’s law gives psolution = xsolvent p°solvent. Hence psolution = 0.85 × 200 = 170 kPa. The pressure is lower than 200 kPa because the solvent occupies only 0.85 of the total mole fraction. The value 30 kPa is the lowering, not the solution pressure, and 235 kPa is physically inconsistent here.

Lowering of vapour pressure is a comparative quantity. It is defined as Δp = p° − p, so both the pure-solvent pressure p° and the solution pressure p must be known. Without p°, the difference and the relative lowering Δp/p° cannot be calculated. Colour, zero mass and universal solute volatility have no role in this definition.

A non-volatile solute does not enter the vapour phase appreciably. Its particles reduce the fraction of the liquid surface occupied by solvent molecules and lower the solvent's escaping tendency. Therefore fewer solvent molecules are present in equilibrium vapour, so the vapour pressure decreases. Temperature, vessel volume and solute vapour are not the stated cause.

For an ideal solution, Raoult's law is pA = xA pA°. Thus the partial pressure of component A is directly proportional to its mole fraction in the liquid, provided temperature is fixed. If the solvent mole fraction decreases, its partial vapour pressure decreases in the same relation; mass and vessel volume are not the governing quantities.

Negative deviation means that the observed vapour pressure is lower than the value calculated from Raoult's law. This occurs when unlike, solute-solvent attractions are stronger than the corresponding like-like attractions. Molecules are then held more tightly and escape less readily. Weak attraction generally produces positive, not negative, deviation.

Positive deviation occurs when the actual total vapour pressure is higher than the Raoult-law prediction. If unlike molecules attract each other less strongly than like molecules do, they escape from the liquid more easily. The increased escaping tendency raises vapour pressure. Stronger unlike attraction would instead cause negative deviation.

Both liquids are volatile, so each contributes molecules to the vapour phase. Dalton's law states that the total pressure of a gas mixture equals the sum of the partial pressures: ptotal = pA + pB. The more volatile component may contribute more, but the less volatile component still contributes; therefore neither one alone nor their difference is correct.

Raoult’s law states that the partial vapour pressure of a component in an ideal solution equals its mole fraction multiplied by the vapour pressure of that pure component. Thus, p = x × p° = 0.75 × 80 = 60 kPa. Therefore, option B is correct. The answer is lower than 80 kPa because the solvent is only 75% of the liquid-phase mole fraction.

An ideal solution obeys Raoult's law for each component throughout the composition range, not merely at one concentration. Its unlike and like intermolecular interactions are approximately similar, so enthalpy and volume changes on mixing are approximately zero. Ideal solutions are not restricted to water, high pressure, or heat-releasing mixtures.

Deviation is identified by comparing observed pressure with the ideal Raoult-law value. If pactual is smaller than pideal, the difference is negative and the solution shows negative deviation. Stronger unlike attractions commonly cause this lower pressure. Positive deviation would require an observed pressure greater than the predicted value.

At the same temperature, vapour pressure depends on how readily molecules escape from the liquid surface. Acetone has weaker overall intermolecular attraction than water, whose molecules form strong hydrogen-bond interactions. Consequently, acetone molecules escape more easily and its volatility and vapour pressure are higher. It does not mean acetone never vapourises, and water certainly does have intermolecular attraction.

Increasing temperature raises the average kinetic energy of the liquid molecules. A larger fraction of molecules then has enough energy to overcome intermolecular attractions and escape into the vapour phase. At the new equilibrium, the vapour exerts a higher pressure. The liquid’s chemical formula and the vessel’s mass do not cause this trend, and vapour molecules do not disappear; their equilibrium amount changes.

The more volatile component has the larger pure-liquid vapour pressure. In an ideal solution, increasing its liquid mole fraction increases its partial-pressure contribution, while decreasing the other component's contribution. The weighted total therefore moves toward the higher pure-component pressure and increases, although it need not double or become infinite.

For an ideal-gas vapour mixture, Dalton's law gives ptotal = Σpi and the vapour-phase mole fraction is yi = pi/ptotal. Thus a component's partial pressure divided by total pressure gives its proportion in vapour. Liquid colour, vessel mass and smell do not provide the quantitative vapour composition.