At a total atmospheric pressure of 1.00 atm, the partial pressure of CO₂ in air is approximately 4.0 × 10^-4atm. Using the data in Problem 9.4, what is the solubility of CO₂ in an open bottle of seltzer water at 20 °C?

Verified step by step guidance

1. Identify the relationship between gas solubility and partial pressure using Henry's Law: \( C = k_H \cdot P \), where \( C \) is the solubility of the gas (in mol/L), \( k_H \) is the Henry's Law constant (in mol/L·atm), and \( P \) is the partial pressure of the gas (in atm).
2. From Problem 9.4, determine the Henry's Law constant \( k_H \) for CO₂ at 20 °C. If not provided, consult a reliable source or reference table for the value of \( k_H \) at this temperature.
3. Substitute the given partial pressure of CO₂, \( P = 4.0 \times 10^{-4} \ \text{atm} \), and the Henry's Law constant \( k_H \) into the equation \( C = k_H \cdot P \).
4. Perform the multiplication to calculate the solubility \( C \) of CO₂ in the seltzer water. Ensure the units are consistent (e.g., mol/L).
5. Interpret the result: The calculated solubility represents the concentration of CO₂ dissolved in the seltzer water at equilibrium under the given conditions of temperature and pressure.

Key Concepts

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 principle is crucial for understanding how gases like CO₂ behave in solutions, particularly in carbonated beverages, where the pressure of CO₂ influences its solubility.

Solubility

Solubility refers to the maximum amount of a substance that can dissolve in a solvent at a specific temperature and pressure. In the context of the question, it pertains to how much CO₂ can be dissolved in seltzer water at 20 °C, which is influenced by both temperature and the partial pressure of CO₂.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a mixture of gases. In this scenario, the partial pressure of CO₂ in the air is given, and it is essential for calculating the solubility of CO₂ in seltzer water using Henry's Law, as it directly affects how much CO₂ can be dissolved in the liquid.