Question

A certain gaseous solute dissolves in water, evolving \(12.0 \mathrm{~kJ}\) of heat. Its solubility at \(25^{\circ} \mathrm{C}\) and \(4.00\) atm is \(0.0200 M .\) Would you expect the solubility to be greater or less than \(0.0200 M\) at (a) \(5^{\circ} \mathrm{C}\) and 6 atm? (b) \(50^{\circ} \mathrm{C}\) and 2 atm? (c) \(20^{\circ} \mathrm{C}\) and 4 atm? (d) \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm} ?\)

Short answer

Question: Based on the given analysis of the effects of temperature and pressure on the solubility of a gaseous solute, determine whether its solubility will be greater or less than 0.0200 M at the following conditions: (a) At 5°C and 6 atm (b) At 50°C and 2 atm (c) At 20°C and 4 atm (d) At 25°C and 1 atm Answer: (a) The solubility will be greater than 0.0200 M. (b) The solubility will be less than 0.0200 M. (c) The solubility will be greater than 0.0200 M. (d) The solubility will be less than 0.0200 M.

Step-by-step solution

Analyze the effect of temperature on solubility

In an exothermic reaction, as the temperature increases, the equilibrium will shift towards the side that absorbs heat, which in this case is the side with less dissolution of the gaseous solute. Therefore, the solubility of the gas will be lower at higher temperatures.

Analyze the effect of pressure 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. Therefore, when the pressure increases, the solubility of the gas will also increase.

Compare solubility at different temperatures and pressures

(a) At \(5^{\circ} \mathrm{C}\) and 6 atm, the temperature is lower and the pressure is higher compared to the given conditions. The lower temperature will cause an increase in solubility due to the exothermic nature of the reaction, and the higher pressure will also cause an increase in solubility according to Henry's law. Therefore, the solubility will be greater than \(0.0200 M\). (b) At \(50^{\circ} \mathrm{C}\) and 2 atm, the temperature is higher and the pressure is lower compared to the given conditions. The higher temperature will lead to a decrease in solubility due to the exothermic nature of the reaction, and the lower pressure will lead to a decrease in solubility according to Henry's law. Therefore, the solubility will be less than \(0.0200 M\). (c) At \(20^{\circ} \mathrm{C}\) and 4 atm, the temperature is lower compared to the given conditions, while the pressure remains the same. The lower temperature will lead to an increase in solubility due to the exothermic nature of the reaction. Since pressure is the same, it won't affect the solubility. Therefore, the solubility will be greater than \(0.0200 M\). (d) At \(25^{\circ} \mathrm{C}\) and 1 atm, the temperature is the same as the initial conditions, while the pressure is lower. Since the temperature remains the same, it won't affect the solubility. However, the lower pressure will lead to a decrease in solubility according to Henry's law. Therefore, the solubility will be less than \(0.0200 M\).

Key concepts

Henry's Law

Henry's law is an important principle that helps us understand the behavior of gases dissolved in liquids. It states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid.
This means that if we increase the pressure of the gas above the liquid, more gas will dissolve in the liquid.
Think of it like a sponge soaking up water; the more pressure applied, the more liquid it can absorb. Henry’s law can be expressed with the formula:
\( C = kH \times P \), where:

• \( C \) is the solubility of the gas,
• \( kH \) is the Henry's law constant for the specific gas-liquid pair,
• \( P \) is the partial pressure of the gas.

Increasing pressure works very effectively to dissolve more gas until equilibrium is reached with the liquid.

Exothermic Reactions

Exothermic reactions release heat as the reaction proceeds.
A simple way to visualize this is to think of burning wood, which releases heat as it burns. In chemical processes like the dissolution of a gas, the system releases heat.
This behavior affects how solubility changes with temperature as well.
When the dissolution of a gas is exothermic, you can expect the reaction to release heat. If you cool down the system, it actually promotes the dissolving of more gas as the system doesn’t have to release as much heat.
As a result, lower temperatures will generally lead to higher solubility in exothermic reactions.
This is a useful thing to remember: cooling an exothermic system helps it dissolve better in liquids.

Temperature Effect on Solubility

Temperature has a significant impact on the solubility of gases in liquids, particularly because of the nature of the reaction involved.
For exothermic reactions, increasing the temperature causes the solubility to decrease.
This is because the reaction will tend toward absorbing energy from its surroundings, effectively pushing the gas out of the solution.
If you heat the liquid, you add energy to the gas molecules, and they tend to escape from the liquid.
For example, think about a carbonated drink. When it's warm, more carbon dioxide escapes, making the drink flat. But when cold, more gas stays dissolved, keeping your drink fizzy.
Therefore, at higher temperatures, expect less gaseous solute in your liquid, while lower temperatures will have the opposite effect.

Pressure Effect on Solubility

Pressure also plays a critical role in determining how much gas can dissolve in a liquid. If you increase the pressure, the solubility of the gas increases, according to Henry's law.
This is because higher pressure means more gas molecules are present over the liquid, creating a larger driving force to push the gas molecules into the liquid.
Let's break it down further:

• If you have a sealed bottle of soda, the pressure inside is fairly high. This keeps carbon dioxide in the liquid, making the soda fizzy.
• When you open the bottle, the pressure decreases, and the gas starts to escape, leading to a reduction in solubility.
• By increasing the pressure again, you can drive more gas back into the solution.

Understanding the relationship between pressure and solubility is vital for predicting and controlling how gases dissolve in liquids.