Question

Argon makes up \(0.93 \%\) by volume of air. Calculate its solubility \((\mathrm{mol} / \mathrm{L})\) in water at \(20^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm} .\) The Henry's law constant for Ar under these conditions is \(1.5 \times 10^{-3} \mathrm{~mol} / \mathrm{L} \cdot\) atm.

Short answer

The solubility of Argon in water at 20°C and 1.0 atm is approximately \( 1.395 \times 10^{-5} \) mol/L.

Step-by-step solution

- Determine the Partial Pressure of Argon

To determine the partial pressure of Argon, use the given volume percentage and the total pressure. The volume percentage of Argon is 0.93%. Thus, its partial pressure at 1.0 atm total pressure is calculated as:\[ P_{\text{Ar}} = 0.0093 \times 1.0 \text{ atm} = 0.0093 \text{ atm} \]

- Apply Henry's Law

Using Henry's Law, the solubility of a gas can be calculated by the formula:\[ C = k_H \times P_{\text{gas}} \]where \( C \) is the solubility (in mol/L), \( k_H \) is the Henry's law constant (in mol/(L·atm)), and \( P_{\text{gas}} \) is the partial pressure of the gas (in atm).

- Substitute Values into Henry's Law Equation

Substitute the values for the Henry's law constant \( 1.5 \times 10^{-3} \) mol/(L·atm) and the partial pressure of Argon \( 0.0093 \) atm into the equation:\[ C = (1.5 \times 10^{-3}) \times 0.0093 \]

- Calculate the Solubility

Perform the multiplication to find the solubility:\[ C = 1.5 \times 10^{-3} \times 0.0093 = 1.395 \times 10^{-5} \text{ mol/L} \]

Key concepts

partial pressure

Partial pressure is a crucial concept in the realm of gases. It refers to the pressure exerted by a single gas within a mixture of gases. To determine the partial pressure, you need to know the percentage composition of the gas and the total pressure of the gas mixture. For example, in our exercise, Argon gas comprises 0.93% of air. Given that the atmospheric pressure is 1.0 atm, we find the partial pressure by multiplying 0.93% (or 0.0093 as a decimal) by the total pressure. So, the partial pressure of Argon is 0.0093 atm. It's the fraction of total pressure solely due to Argon.

solubility

Solubility is the amount of a substance (solute) that can be dissolved in a solvent at a given temperature and pressure until saturation is reached. In simpler terms, it's how much of the gas can be 'mixed' or dissolved in a liquid before no more will dissolve at that specific condition. For example, in our exercise, to find how much Argon dissolves in water, we calculated the solubility using its partial pressure and Henry's law constant. Here, we discovered the solubility by using the concept that solubility directly relates to pressure at a constant temperature. Hence, solubility helps us understand the concentration of gases in liquids.

Henry's law constant

Henry's law constant (denoted as \( k_H \)) is a proportionality constant that appears in Henry's law. It signifies how readily a gas dissolves in a liquid. The value of this constant varies with temperature and the nature of the gas and liquid involved. For example, in the given exercise, the Henry's law constant for Argon at 20°C is \( 1.5 \times 10^{-3} \) mol/(L·atm). This constant helps us link the partial pressure of a gas with its solubility, providing a straightforward way to calculate the latter.

gas solubility

Gas solubility is the measure of how much a gas can dissolve in a solvent, typically a liquid. Multiple factors affect gas solubility: temperature, nature of the gas, pressure, and the solvent itself. In our exercise, Argon's solubility in water is calculated using Henry's law, which states that the solubility of a gas in a liquid is directly proportional to its partial pressure above the liquid. For instance, higher partial pressure results in greater gas solubility in the liquid. Conversely, increasing the temperature generally reduces the solubility because gases are less soluble in warmer liquids.

pressure and concentration

Pressure and concentration are interconnected concepts in chemistry. Pressure affects how much a gas will dissolve in a liquid (its concentration). According to Henry's law, as the pressure of the gas above a liquid increases, the concentration of the gas dissolved in the liquid also increases. Our exercise involving Argon gas in water illustrates this relationship. By knowing the partial pressure of Argon and using the Henry's law constant, we calculate the concentration of Argon in the water. So, greater pressure equals higher gas concentration in the solvent, indicating that these variables are directly proportional.