Problem 52 - Chemistry The Science in Context

Question

Which term, \(k_{\mathrm{H}}\) or \(P\), in Henry's law is affected by temperature?

Step-by-Step Solution

Answer

Answer: In Henry's Law equation, the term that is directly affected by temperature is the Henry's Law constant, \(k_{\mathrm{H}}\).

Step 1: Henry's Law Equation

Henry's Law equation is given by: Solubility = \(k_{\mathrm{H}}\) × \(P\) Here, we need to determine if temperature affects the Henry's Law constant, \(k_{\mathrm{H}}\), the partial pressure \(P\), or both.

Step 2: Effect on Partial Pressure, \(P\)

Partial pressure, \(P\), depends on the total pressure and the molar concentration of the gas. It is not affected by temperature directly. However, the molar concentration of a gas can be affected by temperature through the ideal gas law equation: \(PV = nRT\) where: - \(P\) represents pressure, - \(V\) represents volume, - \(n\) represents the amount of substance (in moles), - \(R\) represents the ideal gas constant, and - \(T\) represents temperature in Kelvin. From this equation, we can see that the temperature only has an indirect effect on the partial pressure of a gas.

Step 3: Effect on Henry's Law Constant, \(k_{\mathrm{H}}\)

Henry's Law constant, \(k_{\mathrm{H}}\), is a proportionality constant that relates the solubility of a gas to its partial pressure. It is dependent on factors like the nature of the gas, the solvent, and the temperature. The value of \(k_{\mathrm{H}}\) changes with temperature. At higher temperatures, the solubility of gases in liquids generally decreases. As a result, the value of \(k_{\mathrm{H}}\) decreases with increasing temperature. Hence, \(k_{\mathrm{H}}\) is directly affected by temperature.

Step 4: Conclusion

In Henry's Law equation: Solubility = \(k_{\mathrm{H}}\) × \(P\) The term that is directly affected by temperature is the Henry's Law constant, \(k_{\mathrm{H}}\). The partial pressure, \(P\), is not directly affected by temperature but instead can be indirectly affected through its relationship with the ideal gas law equation.

Key Concepts

Solubility of Gases

Solubility of gases refers to how well a gas can dissolve in a liquid. This is an important concept in chemistry, especially when dealing with solutions. Some key factors affect the solubility of gases:

• Type of Gas and Solvent: Different gases have varying abilities to dissolve in different liquids. For example, oxygen dissolves well in water, making it ideal for aquatic life.
• Pressure: The solubility of a gas increases with an increase in pressure. This is explained by Henry's Law, which states that the solubility of a gas is directly proportional to its partial pressure above the liquid.
• Temperature: Typically, as the temperature increases, the solubility of gases decreases. Warmer water holds less dissolved oxygen, which can affect fish and aquatic life.

Understanding these factors helps us predict how gases behave in different environments, such as our atmosphere or the oceans.

Partial Pressure

Partial pressure is the pressure exerted by a single type of gas in a mixture of gases. It plays a crucial role in determining how gases dissolve in liquids. The total pressure of a mixture is the sum of the partial pressures of all the gases present.

• Role in Henry's Law: In Henry's Law, solubility is proportional to the partial pressure of the gas. Higher partial pressure means more gas molecules are available to dissolve in the liquid.
• Independent Influence: Although partial pressure directly affects gas solubility, changes in temperature do not directly alter the partial pressure itself. This is mainly influenced by the concentration and the total pressure.
• Applications: Understanding partial pressure is essential in fields like medicine and environmental science. For instance, it's crucial for calculating oxygen levels in blood and carbon dioxide levels in the atmosphere.

Partial pressure helps us understand the behavior of gases in various mixtures and their interactions with liquids.

Temperature Effect on Solubility

Temperature has a significant impact on the solubility of gases in liquids. This effect is mainly due to changes in energy and molecular interactions.

• Energy Influence: At higher temperatures, molecules move faster, increasing the energy of the gas molecules. This results in the gas tending to escape from the liquid, thus reducing solubility.
• Impact on Henry's Law Constant: Henry's Law constant, \(k_{\mathrm{H}}\), is directly affected by temperature. As temperature rises, the constant typically decreases, indicating a lower solubility for gases.
• Practical Implications: This concept explains why cold soda holds more carbon dioxide, making it fizzier than when it's warm. It's also why aquatic life can suffer during hot weather when dissolved oxygen levels drop.

Understanding how temperature affects gas solubility is crucial for applications ranging from environmental monitoring to beverage production.