Problem 53 - Chemistry The Science in Context

Question

Air is primarily a mixture of nitrogen and oxygen. Is the Henry's law constant for the solubility of air in water the sum of \(k_{\mathrm{H}}\) for \(\mathrm{N}_{2}\) and \(k_{\mathrm{H}}\) for \(\mathrm{O}_{2} ?\) Explain why or why not.

Step-by-Step Solution

Answer

Answer: No, the sum of Henry's law constants for nitrogen and oxygen is not the same as the Henry's law constant for the solubility of air in water. The Henry's law constant for the solubility of air in water must account for the proportion of each gas in the air and its respective solubility constant.

Step 1: Understand Henry's Law

Henry's law states that the concentration of a dissolved gas in a liquid is proportional to the partial pressure of that gas above the liquid. Mathematically, it can be represented as: C = kH * P Where: - C is the concentration of the dissolved gas - kH is the Henry's law constant - P is the partial pressure of the gas Henry's law constants vary for different gases and liquids, and it is specific to a particular gas-liquid pair under constant temperature.

Step 2: Calculate the solubility of a gas using Henry's Law

The solubility of nitrogen and oxygen gases in water can be determined using their individual Henry's law constants. For nitrogen, the solubility (C_N2) is given by: C_N2 = kH_N2 * P_N2 For oxygen, the solubility (C_O2) is given by: C_O2 = kH_O2 * P_O2 Where: - kH_N2 and kH_O2 are the Henry's law constants for nitrogen and oxygen, respectively - P_N2 and P_O2 are the partial pressures of nitrogen and oxygen in the air, respectively

Step 3: Determine the solubility of air in water

As air is primarily a mixture of nitrogen and oxygen, the total concentration of dissolved air in water (C_Air) would be the sum of the concentrations of dissolved nitrogen and oxygen gases: C_Air = C_N2 + C_O2

Step 4: Examine if the sum of Henry's law constants holds true for the solubility of air in water

If the sum of Henry's law constants (kH_N2 and kH_O2) could represent the solubility of air in water, we could find an equivalent constant, kH_Air, such that: C_Air = kH_Air * P_Air However, since air is a mixture of different gases, simply adding the Henry's law constants of the individual gases would not give us an equivalent constant for the solubility of air. Henry's law constant (kH_Air) must account for the proportion of each gas in the air and its respective solubility constant. Thus, Henry's law constant for the solubility of air in water is not simply the sum of the constants for nitrogen and oxygen.

Key Concepts

Solubility

Solubility is a measure of how well a substance, such as a gas, can dissolve in a liquid, like water. When discussing gases dissolving in liquids, it's important to consider factors like temperature and pressure that influence solubility. For example:

• Higher temperatures usually decrease gas solubility in liquids.
• The solubility of a gas increases with an increase in pressure.

Henry's Law is a key principle to understand solubility of gases in liquids. It articulates that the concentration of a dissolved gas is directly proportional to the partial pressure of that gas in contact with the liquid. The proportionality constant here is known as the Henry's law constant, denoted by \(k_H\). Each gas has its own unique \(k_H\) depending on the gas-liquid interaction and environmental conditions.

Partial Pressure

Partial pressure is a concept referring to the pressure exerted by a single type of gas in a mixture of gases. In any given mixture, each type of gas contributes to the total pressure of the system.In terms of Henry's Law, partial pressure \(P\) is directly related to how much gas will dissolve in a liquid. Essentially:

• Higher partial pressure of a gas leads to greater solubility.
• Lower partial pressure results in reduced solubility.

In the case of atmospheric air, which is made up of nitrogen and oxygen primarily, each of these gases has its own partial pressure, denoted as \(P_{N_2}\) and \(P_{O_2}\). These pressures dictate how much of each gas will dissolve when in contact with water.

Gas-Liquid Interactions

Gas-liquid interactions involve the forces and behaviors that occur when a gas is in contact with a liquid surface. These interactions define how gases dissolve in liquids, governed by factors such as:

• Temperature
• Pressure
• Nature of the gas and liquid involved

Such interactions are described by Henry's Law in scientific context, allowing for prediction of solubility by simply knowing the partial pressure and the Henry's law constant. Notably, in practical situations, interactions may vary: - Different gases dissolve differently; some are more soluble than others. - Interaction at the molecular level is unique for each gas-liquid pair. For air in water, this means that we can't simply sum up the Henry's constants of nitrogen and oxygen to get the solubility of air. Instead, each constituent gas's specific interactions with water must be considered separately, highlighting the uniqueness of each gas-liquid interaction pair.