The solubility of a gas in a liquid

Increase with decrease of temperature

The correct answer is option 4. Increase with decrease of temperature.

The solubility of a gas in a liquid is influenced by both pressure and temperature. Let's analyze each option:

1. Decrease with increase of pressure: This statement is incorrect. According to Henry's law, the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. Therefore, as pressure increases, the solubility of the gas in the liquid also increases.

2. Decrease with increase of both temperature and pressure: This statement is incorrect. While an increase in pressure typically increases the solubility of a gas in a liquid (as per Henry's law), an increase in temperature generally decreases the solubility of gases in liquids. Therefore, the combined effect of increasing pressure and temperature on the solubility of a gas in a liquid depends on the relative magnitude of the changes in pressure and temperature.

3. Increase with increase of both pressure and temperature: This statement is incorrect. While an increase in pressure tends to increase the solubility of a gas in a liquid, an increase in temperature tends to decrease the solubility of gases in liquids. Therefore, the combined effect of increasing pressure and temperature on the solubility of a gas in a liquid depends on the relative magnitude of the changes in pressure and temperature.

4. Increase with decrease of temperature: This statement is generally correct. As per Henry's law, the solubility of a gas in a liquid typically increases as temperature decreases. This is because a decrease in temperature reduces the kinetic energy of the gas molecules, leading to a greater tendency for them to dissolve in the liquid.

Therefore, the correct answer is option 4: Increase with decrease of temperature.