Ch.18 - Chemistry of the Environment

Problem 78

Chapter 18, Problem 78

The Henry's law constant for CO2 in water at 25 °C is 3.1x10^-2 M atm-1. (a) What is the soubility of CO2 in water at this temperature if the soltuion is in contact with air at normal atmospheric pressure?

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Identify the given values: Henry's law constant \( k_H = 3.1 \times 10^{-2} \text{ M atm}^{-1} \) and the partial pressure of CO2 in air at normal atmospheric pressure, which is approximately 0.0004 atm (since CO2 is about 0.04% of air).

Use Henry's Law to find the solubility of CO2: \( C = k_H \times P_{\text{CO}_2} \), where \( C \) is the concentration (solubility) of CO2 in water, \( k_H \) is the Henry's law constant, and \( P_{\text{CO}_2} \) is the partial pressure of CO2.

Substitute the known values into the equation: \( C = (3.1 \times 10^{-2} \text{ M atm}^{-1}) \times (0.0004 \text{ atm}) \).

Calculate the product to find the solubility of CO2 in water at 25 °C under normal atmospheric conditions.

Interpret the result: The calculated solubility represents the concentration of CO2 in water when it is in equilibrium with air at 25 °C.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Henry's Law

Henry's Law states that the amount of gas that dissolves in a liquid at a given temperature is directly proportional to the partial pressure of that gas above the liquid. This relationship can be expressed mathematically as C = kH * P, where C is the concentration of the gas in the liquid, kH is the Henry's law constant, and P is the partial pressure of the gas.

Solubility

Solubility refers to the maximum amount of a substance that can dissolve in a given quantity of solvent at a specific temperature and pressure. In the context of gases, solubility is influenced by factors such as temperature, pressure, and the nature of the gas and solvent, with higher pressures generally leading to increased solubility.

Atmospheric Pressure

Normal atmospheric pressure at sea level is approximately 1 atm. When a solution is in contact with air, the partial pressure of the gas in the air contributes to the overall pressure exerted on the liquid, which in turn affects the solubility of the gas according to Henry's Law. At 1 atm, the solubility of CO2 can be calculated using the provided Henry's law constant.

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