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

\(\Delta _{mix}H\text{ = positive}\); \(\Delta _{mix}V\text{ = positive}\)

The correct answer is option 1. \(\Delta _{mix}H\text{ = positive}\); \(\Delta _{mix}V\text{ = positive}\).

When a solution exhibits positive deviation from Raoult's Law, it means that the observed vapor pressure of the solution is higher than what is expected based on Raoult's Law. This typically occurs when the intermolecular forces between the molecules of the components in the mixture are weaker than the forces between like molecules. In other words, the interactions between unlike molecules are weaker than expected.

Now, let's consider the signs of enthalpy change (\(\Delta_{mix}H\)) and volume change (\(\Delta_{mix}V\)) during the mixing of the components in the solution:

\(\Delta_{mix}H\) (enthalpy change):  This refers to the heat absorbed or released during the mixing process. For a positive deviation, the interactions between unlike molecules are weaker, so less energy is required to break these interactions. Therefore, \(\Delta_{mix}H\) is typically positive.

\(\Delta_{mix}V\) (volume change):  This refers to the change in volume during the mixing process. In the case of positive deviation, the molecules in the mixture may have larger sizes or experience a decrease in the strength of attractive forces, leading to an increase in the overall volume. Therefore, \(\Delta_{mix}V\) is typically positive.

So, the correct option is: (1) \(\Delta_{mix}H = \text{positive}\); \(\Delta_{mix}V = \text{positive}\)