Problem 13 - A Complete Resource Book in Chemistry for JEE Main

Question

The solubility of a gas in a liquid increases with (a) increase of temperature (b) amount of liquid taken (c) decrease in temperature (d) reduction of gas pressure

Step-by-Step Solution

Answer

The solubility of a gas in a liquid increases with a decrease in temperature.

Step 1: Examine Gas Solubility and Temperature

Understand that the solubility of gases in liquids generally decreases with an increase in temperature. This phenomenon is due to the increased kinetic energy of the molecules at higher temperatures, which causes the dissolved gas molecules to escape from the liquid more readily.

Step 2: Consider Liquid Volume and Solubility

Recognize that the solubility of a gas in a liquid is generally expressed as a concentration (e.g., moles per liter). Changing the amount of liquid does not inherently increase solubility. Therefore, the absolute amount of gas dissolved might change, but the concentration will remain constant if you just increase the liquid volume.

Step 3: Evaluate the Effect of Decreasing Temperature

Acknowledge that decreasing the temperature typically increases the solubility of a gas in a liquid. At lower temperatures, the kinetic energy is reduced, leading to fewer gas molecules escaping the solution, hence solubility increases.

Step 4: Assess the Impact of Gas Pressure on Solubility

Note that according to Henry's Law, the solubility of a gas in a liquid is directly proportional to the pressure of the gas above the liquid. Therefore, reducing the gas pressure would decrease its solubility in the liquid.

Key Concepts

Temperature Effect on Gas Solubility

The solubility of gases in liquids is significantly influenced by temperature. When the temperature increases, the solubility of most gases decreases. This is because higher temperatures provide more kinetic energy to the molecules. As the gas molecules gain energy, they move faster and are more likely to escape from the liquid into the air.
Therefore, at higher temperatures, it's harder for gases to stay dissolved in liquids.

• This is why fizzy drinks lose their carbonation faster in the warmth compared to when they are cold.
• In contrast, at lower temperatures, the reduced movement of molecules means gas molecules are less likely to escape, thus increasing solubility.

Henry's Law

Henry's Law is a fundamental principle that describes the relationship between the concentration of a gas in a liquid and the partial pressure of the gas above the liquid. The law states that the solubility (also known as the concentration) of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid.
Henry's Law can be expressed with the formula: \[ C = kP \]
where:

• \( C \) is the concentration of the gas in the liquid.
• \( k \) is the Henry's law constant, specific for each gas-liquid pair at a given temperature.
• \( P \) is the partial pressure of the gas above the liquid.

If the pressure of the gas above the liquid increases, more gas will dissolve in the liquid until equilibrium is reached. If the pressure decreases, the dissolved gas will escape from the liquid until a new equilibrium is established.

Effect of Pressure on Solubility

In the context of gas solubility, pressure plays a crucial role. According to Henry's Law, when the pressure of the gas above a liquid is increased, more gas molecules are "pushed" into the liquid, enhancing the gas's solubility. Conversely, decreasing the pressure means that fewer gas molecules can be kept in the liquid, reducing solubility.
Think of how carbonated drinks are bottled under high pressure. The high pressure keeps the gas dissolved. When you open the bottle, the pressure decreases, and you can see the gas escaping as bubbles.

• Increasing the pressure "forces" more gas molecules into the solution.
• Decreasing the pressure allows the gas to escape more easily, which we observe when fizz escapes from a soda can.

Understanding these principles helps explain why gas solubility varies with temperature and pressure changes.