Problem 37 - Chemistry: The Central Science in SI Units, Global Edition

Question

The Henry's law constant for hydrogen gas \(\left(\mathrm{H}_{2}\right)\) in water at \(25^{\circ} \mathrm{C}\) is \(7.7 \times 10^{-6} \mathrm{M} / \mathrm{kPa}\) and the constant for argon (Ar) at \(25^{\circ} \mathrm{C}\) is \(1.4 \times 10^{-5} \mathrm{M} / \mathrm{kPa}\). If the two gases are each present at \(253 \mathrm{kPa}\) pressure, calculate the solubility of each gas.

Step-by-Step Solution

Answer

The solubilities of hydrogen gas and argon at 25°C and 253 kPa are approximately \(1.95 \times 10^{-3} M\) and \(3.54 \times 10^{-3} M\), respectively.

Step 1: Write down the given information

We are given the following: - Henry's law constant for hydrogen gas (H₂) = \(7.7 \times 10^{-6} M/kPa\) - Henry's law constant for argon (Ar) = \(1.4 \times 10^{-5} M/kPa\) - Pressure of hydrogen and argon = 253 kPa

Step 2: Apply Henry's law formula for hydrogen gas

Using the Henry's law formula, we can calculate the solubility of hydrogen in water: \(C_{H_{2}} = k_{H_{2}} \cdot P_{H_{2}}\) Plugging in the values: \(C_{H_{2}} = (7.7 \times 10^{-6} M/kPa) \cdot (253 kPa)\)

Step 3: Calculate the solubility of hydrogen gas

By performing the calculation: \(C_{H_{2}} \approx 1.95 \times 10^{-3} M\) So, the solubility of hydrogen gas is approximately \(1.95 \times 10^{-3} M\).

Step 4: Apply Henry's law formula for argon

Similarly, we can calculate the solubility of argon in water: \(C_{Ar} = k_{Ar} \cdot P_{Ar}\) Plugging in the values: \(C_{Ar} = (1.4 \times 10^{-5} M/kPa) \cdot (253 kPa)\)

Step 5: Calculate the solubility of argon

By performing the calculation: \(C_{Ar} \approx 3.54 \times 10^{-3} M\) So, the solubility of argon is approximately \(3.54 \times 10^{-3} M\). Therefore, the solubilities of hydrogen gas and argon at 25°C and 253 kPa are approximately \(1.95 \times 10^{-3} M\) and \(3.54 \times 10^{-3} M\), respectively.

Key Concepts

Gas Solubility

The solubility of gases in liquids is an important topic in chemistry, especially when studying Henry's Law. When a gas dissolves in a liquid, it spreads evenly throughout the solution. This characteristic is influenced by several factors, such as temperature and pressure.
To quantify how well a gas dissolves in a liquid, often pressure-dependent, Henry's Law is used. It states that the concentration of a dissolved gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. This relationship serves as a guiding principle to understand gas solubility. The formula for Henry's Law is:

• \[ C = k_H \cdot P \]

• Where \( C \) is the concentration (or solubility) of the gas, \( k_H \) is Henry's Law constant specific to the gas and solvent, and \( P \) is the pressure of the gas.

When we applied this to calculate the solubility of hydrogen and argon in the exercise, we used their respective constants and pressures to determine how much of each gas can dissolve in water under given conditions. This principle demonstrates how varying the pressure can alter solubility in predictable ways. This is crucial for applications like designing carbonated beverages or predicting the behavior of gases in ecological systems.

Chemical Equilibrium

Chemical equilibrium refers to the state in a chemical reaction where the forward and reverse reactions occur at the same rate. This balance point is established when there is no net change in the concentration of reactants and products over time. While Henry's Law specifically deals with gas-liquid systems at equilibrium under constant conditions, understanding chemical equilibrium more broadly helps clarify how gases dissolve in and come out of solution.
In the context of Henry’s Law, equilibrium is achieved when the rate at which gas molecules enter the solution equals the rate at which they escape back into the gas phase. Thus, equilibrium plays a vital role in determining how and when solubility levels are maintained. Understanding this equilibrium is crucial for industries like environmental engineering, where careful balance of gas concentration is required to manage pollution levels.

Solution Concentration

Solution concentration is a measure of the amount of solute present in a given volume or mass of solvent. In the context of Henry's Law and gas solubility, it represents the concentration of dissolved gas in the liquid. Concentration is typically expressed in molarity (M), which is moles of solute per liter of solution.
The calculations for hydrogen and argon solubility in the exercise utilized concentration as the end result, expressed in molarity. High concentration implies a large amount of gas is dissolved in the solution. Multiple factors, including solute interactions, temperature, and pressure, affect concentration.
In practical terms, understanding solution concentration is key when considering the gas content in beverages, the behavior of gases in biological systems, and even in quantifying pollutants in water bodies. It is an essential concept in both everyday applications and advanced scientific research.