Question

Consider an atmosphere where the mole fractions of \( N_2 \), \( Ar \), and \( CO_2 \) are \( 7.81 \times 10^{-1} \), \( 9.34 \times 10^{-3} \), and \( 4.05 \times 10^{-4} \), respectively. This atmosphere exchanges gases with sea water below having temperature and salinity of 20°C and 35 psu, respectively. In the absence of biological and chemical activity, relative concentrations of dissolved gases in the surface sea water at equilibrium are ordered as:

• A. ( [N_2]>[Ar]>[CO_2] \)
• B. ( [CO_2]>[N_2]>[Ar] \)
• C. ( [N_2]>[CO_2]>[Ar] \)
• D. ( [Ar]>[CO_2]>[N_2] \)

Hint:

At equilibrium, gases like \( CO_2 \) are more soluble in water compared to \( N_2 \) and \( Ar \), which influences their relative concentrations in the sea water.

Answer 1

The Correct Option is C

This question is related to the exchange of gases between the atmosphere and the ocean. We are given the mole fractions of gases in the atmosphere and are asked to determine the relative concentrations of dissolved gases in sea water at equilibrium.
Understanding the Concept:
1. Gas Solubility in Water: The solubility of gases in water depends on several factors, including the partial pressure of the gas, temperature, and salinity. At equilibrium, the concentration of dissolved gases in water is directly proportional to the partial pressure of the gas in the atmosphere, assuming temperature and salinity are constant.
2. Henry's Law: According to Henry’s law, the concentration of a gas dissolved in a liquid at equilibrium is proportional to its partial pressure in the gas phase. The relationship can be written as:
\[ C = k_H \cdot P \] where \( C \) is the concentration of the gas in the liquid (in this case, sea water), \( P \) is the partial pressure of the gas in the atmosphere, and \( k_H \) is the Henry's law constant for the gas.
3. Gas Solubility Order: - CO\(_2\) is highly soluble in water compared to N\(_2\) and Ar. This is because CO\(_2\) reacts with water to form carbonic acid, which enhances its solubility. - N\(_2\) and Ar are relatively insoluble in water. However, N\(_2\) is more soluble than Ar due to its lower molecular weight and better ability to dissolve in water.
4. Relative Solubility at Equilibrium: - Given the mole fractions in the atmosphere and their corresponding solubility in water, the relative concentrations of dissolved gases in the surface sea water at equilibrium would follow the order:
\[ [CO_2]>[N_2]>[Ar]. \] This is because CO\(_2\) has the highest solubility, followed by N\(_2\), and then Ar.
Conclusion:
Based on the solubility of gases and their partial pressures, the correct answer is (B): \( [CO_2]>[N_2]>[Ar] \).