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 solution decreases from \(20^{\circ} \mathrm{C}\) to \(10^{\circ} \mathrm{C}\). (b) The partial pressure of \(\mathrm{CO}_{2}\) decreases from \(3 \mathrm{~atm}\) to \(2 \mathrm{~atm}\).

Short answer

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

Step-by-step solution

Understanding Solubility and Temperature Change

The solubility of gases in liquids is affected by temperature. Generally, for gases, solubility decreases as temperature increases. Since the temperature is decreasing from \(20^{\circ} \mathrm{C}\) to \(10^{\circ} \mathrm{C}\), the solubility of carbon dioxide in soda will increase.

Understanding Solubility and Pressure Change

The solubility of gases in liquids is also affected by pressure, according to Henry's Law, which states that the solubility is directly proportional to the partial pressure of the gas above the liquid. Since the partial pressure of \(\mathrm{CO}_{2}\) is decreasing from \(3 \mathrm{~atm}\) to \(2 \mathrm{~atm}\), the solubility of carbon dioxide in soda will decrease.

Key concepts

Henry's Law

Henry's Law is a fundamental principle in chemistry that defines the relationship between the solubility of a gas in a liquid and the pressure of the gas above the liquid. This law can be expressed with the equation: \( C = kP \), where \( C \) is the solubility of the gas, \( k \) is Henry's Law constant, and \( P \) is the partial pressure of the gas. This means:

• As the gas pressure increases, more gas molecules are pushed into the solution, increasing solubility.
• If the pressure decreases, fewer gas molecules are available to dissolve, thus decreasing solubility.

Understanding Henry's Law is crucial for various applications, from carbonated beverages to environmental sciences. For example, reducing the pressure on a carbonated drink by opening it allows the dissolved CO2 to escape, resulting in fizzy bubbles.

Effects of Temperature on Solubility

Temperature significantly influences the solubility of gases in liquids. Generally, as the temperature increases, the solubility of gases decreases. Here's why:

• Increased temperature provides more energy for gas molecules, making them more likely to escape the liquid.
• There is decreased interaction between gas molecules and solvent at higher temperatures.

Conversely, when the temperature drops, the solubility typically increases, meaning more gas can dissolve in the liquid. This is because lower temperatures reduce the kinetic energy of gas molecules, encouraging them to remain dissolved. These principles help explain why carbonated beverages stay fizzier in cooler environments.

Effects of Pressure on Solubility

The pressure exerted on a gas in contact with a liquid is another key factor affecting solubility. As per Henry's Law, solubility is directly proportional to the gas pressure. A few things occur when pressure is applied:

• Higher pressures increase the solubility since more gas molecules are forced into solution.
• Lower pressures decrease solubility, allowing the gas to escape more readily.

Consider opening a soda can: when sealed, CO2 is under high pressure, dissolved in the liquid. Once opened, pressure decreases, and CO2 escapes as bubbles. Understanding this connection between pressure and solubility is vital for both industrial processes and everyday activities.