Passage:
Solubility of gases in liquids is greatly affected by pressure and temperature. Henry gave the quantitative relationship between pressure and solubility of gas in a solvent. According to Henry’s law, partial pressure of a gas above a liquid is directly proportional to its mole fraction in solution and is expressed as \(P = K_H.x\), where \(K_H\) is Henry’s constant and x is mole fraction of gas. \(K_H\) is a function of nature of gas.
F M Raoult gave a quantitative relationship between partial pressures and mole fractions in the binary solution of volatile liquids. Raoult’s law states that for a binary solution of volatile liquids, the partial pressure of each component in the solution is directly proportional to its mole fraction. Thus for a solution of component \(1\) and \(2\), partial pressure of each component \(P_1 = p_1^0x_1\), where \(p_1^0\) is the vapour pressure of pure component \(1\) at the same temperature. Similarly \(P_2 = p_2^0x_2\)
If a solution exhibits positive deviation from Raoult’s Law then sign of \(\Delta _{mix}H\) and \(\Delta _{mix}V\) will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\Delta _{mix}H\text{ = positive}\); \(\Delta _{mix}V\text{ = positive}\)
For an ideal solution, ΔmixH = 0 and ΔmixV = 0: no heat is absorbed or evolved and the volume is the sum of the volumes of the components.
In a solution with positive deviation from Raoult’s law, the A–B attractions are weaker than the A–A and B–B attractions:
Energy must be supplied to break the stronger A–A and B–B attractions, and less is given back by the weaker A–B ones, so heat is absorbed: ΔmixH > 0 (endothermic).
The molecules are held less tightly in the mixture, so they occupy more space: ΔmixV > 0 (the volume expands).
For negative deviation both signs are reversed (ΔmixH < 0, ΔmixV < 0). So for positive deviation, both ΔmixH and ΔmixV are positive.