4: Vapour Pressure

Increasing surface area increases the rate at which evaporation can initially occur, and it may also speed up attainment of equilibrium. However, at a fixed temperature, the equilibrium vapour pressure is determined by the nature of the liquid and the temperature, provided some liquid remains. Therefore the final equilibrium pressure is unchanged, although the time to reach it may differ.

Saturated equilibrium vapour pressure is defined when liquid and vapour coexist in equilibrium. If the entire liquid evaporates, no liquid reservoir remains to maintain saturation. The pressure then depends on the amount of vapour, vessel volume, and temperature, and may be below the saturated value. Therefore it is not automatically equal to the pure-liquid equilibrium pressure.

For an ideal binary solution, p_A = x_Ap°_A and p_B = (1−x_A)p°_B. Adding them gives P = p°_B + x_A(p°_A − p°_B), which is a linear function of composition. Thus the total-pressure versus mole-fraction graph is a straight line joining the pure-component pressures. Non-ideal mixtures may curve above or below it.

For an ideal binary solution, P = x_Ap_A° + (1 − x_A)p_B°. If p_A° < p_B°, increasing x_A replaces part of the larger B contribution with the smaller A contribution. The change in total pressure is dP/dx_A = p_A° − p_B°, which is negative, so P decreases. The pressure is not zero; it simply moves downward as the less volatile component becomes more abundant in the liquid.

At a fixed temperature, the equilibrium vapour pressure of a liquid is governed mainly by its nature, including intermolecular attractions. The amount of liquid changes how long equilibrium can be maintained, but not the equilibrium pressure while liquid remains. Vapour pressure determines boiling when it equals external pressure, and a non-volatile solute generally lowers, rather than raises, solvent vapour pressure.

For an ideal solution containing a non-volatile solute, the solvent partial pressure is p_solvent = x_solvent p°_solvent. Adding solute lowers x_solvent, so the statistical fraction of solvent molecules available to escape is reduced and the partial pressure falls. Complete ionisation, a higher solute pressure, or automatic cooling is not required by the model.

For a binary ideal solution, Ptotal = xA pA° + xB pB° and xB = 1 − xA. Substitution gives a linear expression in xA, so the total vapour pressure varies along a straight line between the pure-component pressures. Curvature indicates non-ideal behaviour, while a horizontal line would occur only in a special equal-pressure case, not generally.

Positive deviation produces a vapour pressure maximum because unlike attractions are relatively weak. A mixture with higher vapour pressure reaches the external pressure at a lower temperature, producing a minimum in the boiling-temperature curve. At the azeotropic composition, liquid and vapour compositions are the same, so ordinary fractional distillation cannot separate it completely. Negative deviation instead favours maximum boiling.

Negative deviation arises from stronger unlike attractions and gives a vapour pressure minimum. The mixture must therefore be heated to a higher temperature before its pressure equals the external pressure, creating a maximum-boiling point. At the azeotropic composition, liquid and vapour have the same composition. Positive deviation is associated instead with minimum-boiling azeotropes.

For the solvent in an ideal solution, Raoult’s law is p_solvent = x_solvent p⁰_solvent. Substituting the given values gives p_solvent = 0.8 × 50 = 40 units. The result is lower than 50 because the solvent mole fraction is less than one. Dividing by 0.8 would incorrectly reverse the relation, while 0.016 does not have the correct numerical or physical basis.

For a proposed ideal solution, calculate the expected pressure from Raoult’s law using composition and pure-component pressures. Comparing this calculated value with the measured value identifies behaviour: equality indicates ideality, a higher measured value indicates positive deviation, and a lower value indicates negative deviation. The measurement does not reveal handwriting or molecular dates.

An ideal solution requires the interactions between unlike molecules to be nearly equal to those between like molecules. Liquids with similar molecular size, polarity, and intermolecular forces are therefore the best candidates. Very different polarity can cause strong positive or negative deviation, while chemical reaction changes the species present and is inconsistent with simple ideal mixing.

Raoult’s law directly relates a component’s partial pressure to its mole fraction when the solution behaves ideally, or approximately so. In a reacting, associating, dissociating, or precipitating system, the actual species and effective concentrations may differ from the simple composition, causing deviations. Thus the ideal or nearly ideal condition is the safest direct application.

For an ideal solution, pA = xA pA° and pB = xB pB°. If xA and xB are equal, the comparison of partial pressures reduces to a comparison of pA° and pB°. Since pA° is higher, pA is higher, so component A contributes more molecules to the vapour phase. The container does not contribute to the vapour composition.

For an ideal binary solution, the total pressure is p_total = x_Ap_A⁰ + x_Bp_B⁰. The less volatile component has the lower pure vapour pressure. At constant temperature and fixed total composition amount, increasing its proportion replaces some of the more volatile component, so the weighted average of the two pure pressures decreases. The total pressure remains positive; it does not increase or become negative.

During mixing, some like-molecule interactions are broken and unlike-molecule interactions are formed. In an ideal solution, the two interaction energies are nearly equal, so the energy absorbed in breaking old contacts is nearly balanced by the energy released in forming new contacts. Consequently, the enthalpy change of mixing is approximately zero. This does not mean that molecules disappear or vapour pressure vanishes.

Boiling begins when a liquid’s vapour pressure equals the surrounding external pressure. Atmospheric pressure is lower at high altitude, while the liquid’s pressure–temperature relation remains comparable. Therefore, equality is reached at a lower temperature, so water and other liquids boil sooner but below their sea-level boiling temperatures. The effect is due to pressure, not a change in mole fraction or zero vapour pressure.

For an ideal binary solution, the partial pressure of each component is its liquid mole fraction multiplied by its pure vapour pressure. Here x_A = 0.25 and x_B = 1 − 0.25 = 0.75. Thus p_A = 0.25 × 240 = 60 kPa and p_B = 0.75 × 80 = 60 kPa. The total pressure is their sum, 60 + 60 = 120 kPa. Therefore, option A is correct.

Dalton’s law states that the mole fraction of a component in the vapour phase equals its partial pressure divided by the total pressure. The total pressure is p_total = 45 + 15 = 60 kPa. Therefore, y_A = p_A/p_total = 45/60 = 0.75. The value must lie between 0 and 1, so 1.50 is impossible. Since A contributes most of the total pressure, its vapour fraction is also the larger value, 0.75.

Positive deviation means the actual vapour pressure is higher than the Raoult-law prediction. A composition with unusually high vapour pressure reaches the external pressure at a lower temperature, producing a minimum-boiling azeotrope. Negative deviation instead lowers vapour pressure and is associated with maximum boiling behaviour.

A maximum-boiling azeotrope is associated with a sufficiently strong negative deviation from Raoult’s law. Strong unlike-molecule attractions hold particles in the liquid more firmly, making the vapour pressure lower than the ideal value. Because boiling occurs when vapour pressure equals external pressure, a lower vapour pressure requires a higher temperature; hence the mixture has a maximum boiling point. Positive deviation generally leads toward minimum-boiling behaviour, so option B is correct.

Saturated vapour pressure is defined for equilibrium between a liquid and its vapour. When the last liquid disappears, that equilibrium cannot be maintained. The remaining vapour behaves approximately like a gas, so at fixed temperature its pressure may depend on the number of vapour molecules and the vessel volume, rather than only on liquid identity.

For an ideal binary solution, x_B = 1 − x_A = 1 − 0.7 = 0.3. By Raoult’s law, p_A = x_A p_A° = 0.7 × 50 = 35 kPa and p_B = x_B p_B° = 0.3 × 150 = 45 kPa. Dalton’s law then gives the total pressure as p_total = 35 + 45 = 80 kPa. Therefore, option A is correct; using only one component’s pressure would be incomplete.

For an ideal binary solution, p_total = x_A p°_A + (1 − x_A)p°_B. Since the pure-component pressures are fixed at a given temperature, this expression is linear in x_A. The total-pressure versus liquid-composition graph is therefore a straight line joining the pure-component pressures. Non-ideal interactions produce curved deviations from this line.

Equilibrium vapour pressure is the pressure established by a liquid and its vapour in a closed system at a specified temperature. Evaporation rate describes how quickly molecules leave a surface and can change with surface area, air movement, and humidity. These factors affect the rate but, at equilibrium and fixed temperature, do not determine the saturated pressure.