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 \(P_2 = p_2^0x_2\)

Solubility of Carbon dioxide in soda water increases with

Increase in pressure and decrease in temperature

The correct answer is option 2. Increase in pressure and decrease in temperature.

The solubility of gases in liquids is influenced by both pressure and temperature, and Henry's Law describes this relationship. Henry's Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. In the case of carbon dioxide \((CO_2)\) dissolving in soda water, the relationship between solubility and pressure and temperature can be explained as follows:

1. Pressure Effects:
When the pressure above a liquid containing a gas (such as soda water with \(CO_2\)) increases, more gas molecules are forced into the liquid. In the case of soda water, which is carbonated, increasing the pressure will result in more carbon dioxide molecules dissolving in the water. Therefore, an increase in pressure generally leads to an increase in the solubility of carbon dioxide in soda water.

2. Temperature Effects:
The solubility of gases in liquids often decreases with an increase in temperature. This is because as temperature rises, the kinetic energy of the gas molecules also increases. Higher kinetic energy makes it easier for gas molecules to escape from the liquid phase into the gas phase, reducing the overall solubility. In the case of carbonated beverages like soda water, cooling the liquid leads to higher solubility of carbon dioxide. That's why sodas are often more carbonated and fizzy when they are cold.

So, the combined effect is that the solubility of carbon dioxide in soda water increases with an increase in pressure and decreases with an increase in temperature. This is consistent with option (2): Increase in pressure and decrease in temperature.