Question

Indicate whether the solubility of carbon dioxide gas in soda increases or decreases for each of the following changes. (a) The temperature of the soda increases from \(10^{\circ} \mathrm{C}\) to \(20^{\circ} \mathrm{C}\). (b) The partial pressure of \(\mathrm{CO}_{2}\) increases from \(1 \mathrm{~atm}\) to \(2 \mathrm{~atm}\).

Short answer

(a) Solubility decreases. (b) Solubility increases.

Step-by-step solution

Analyzing Temperature Influence on Solubility

The solubility of gases in liquids generally decreases as the temperature increases. This is because higher temperatures provide more kinetic energy to the gas molecules, causing them to escape from the liquid into the gas phase. Therefore, as the temperature of the soda increases from \(10^{\circ} \mathrm{C}\) to \(20^{\circ} \mathrm{C}\), the solubility of carbon dioxide will decrease.

Understanding Pressure Influence on Solubility

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. Increasing the partial pressure of \(\mathrm{CO}_{2}\) from \(1 \mathrm{~atm}\) to \(2 \mathrm{~atm}\) will increase the solubility of carbon dioxide in the soda. This is because higher pressure forces more gas molecules into the solution.

Key concepts

Henry's Law

Henry's Law is a fundamental principle in understanding how gases dissolve in liquids. It states that at a constant temperature, the amount of a gas that dissolves in a liquid is directly proportional to the partial pressure of that gas above the liquid. This means that if you increase the pressure of a gas over a liquid, more gas molecules will dissolve in the liquid.

• If the partial pressure of a gas above a liquid increases, more gas molecules push into the liquid, increasing solubility.
• Conversely, if the pressure decreases, fewer gas molecules dissolve, reducing solubility.

When applied to soda, increasing the pressure of carbon dioxide increases its solubility, which is why sodas are often bottled under high pressure to keep them fizzy.

Temperature and Solubility

Temperature plays a crucial role in the solubility of gases in liquids. When you increase the temperature, the solubility of gases typically decreases. This is because gases gain kinetic energy with temperature, which means they move more and tend to escape from the liquid.

• At higher temperatures, gas molecules are more energetic, leading to a decrease in solubility as they escape into the air.
• In contrast, lower temperatures slow down the molecules and enhance the gas's tendency to stay dissolved in the liquid.

For instance, warming a soda from 10°C to 20°C will result in less dissolved carbon dioxide, causing the soda to become flatter more quickly.

Partial Pressure and Solubility

The concept of partial pressure is key to understanding gas solubility. In a mixture of gases, each gas exerts pressure independently, known as its partial pressure. The partial pressure of a gas affects how much of it dissolves in a liquid, as per Henry's Law.

• Higher partial pressure of a gas increases its solubility in a liquid because more molecules are available to dissolve.
• Lower partial pressure reduces the number of gas molecules that can be dissolved.

In practical terms, increasing the partial pressure of carbon dioxide over a soda forces more of the gas to dissolve, effectively carbonating the drink. This is why pressurized CO2 is used in soda production to ensure it stays bubbly.