The air is a mixture of a number of gases. The major components are oxygen and nitrogen with approximate proportion of 20% is to 79% by volume at 298 K. The water is in equilibrium with air at a pressure of 10 atm. At 298 K if the Henry’s law constants for oxygen and nitrogen at 298 K are 3.30 × 107 mm and 6.51 × 107 mm respectively, calculate the composition of these gases in water.

To determine the composition of oxygen and nitrogen in water when in equilibrium with air at 298 K and a pressure of 10 atm, we can apply Henry's Law. This law states that the concentration of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. The formula we use is:

Applying Henry's Law

According to Henry's Law, the concentration of a gas in a liquid can be expressed as:

C = kH * P

Where:

• C = concentration of the gas in the liquid (in mol/L)
• kH = Henry's law constant for the gas (in mol/(L·atm))
• P = partial pressure of the gas (in atm)

Step 1: Calculate Partial Pressures

Given that the total pressure is 10 atm and the composition of air is approximately 20% oxygen and 79% nitrogen, we can calculate the partial pressures:

• Partial pressure of oxygen (P_O2) = 0.20 * 10 atm = 2 atm
• Partial pressure of nitrogen (P_N2) = 0.79 * 10 atm = 7.9 atm

Step 2: Use Henry's Law Constants

Next, we will use the provided Henry's law constants for oxygen and nitrogen:

• k_H,O2 = 3.30 × 10⁷ mm (which we convert to atm for consistency)
• k_H,N2 = 6.51 × 10⁷ mm (also converted to atm)

To convert mm to atm, we use the conversion factor: 1 atm = 760 mm. Therefore:

• k_H,O2 = 3.30 × 10⁷ mm / 760 mm/atm ≈ 4.34 × 10⁴ mol/(L·atm)
• k_H,N2 = 6.51 × 10⁷ mm / 760 mm/atm ≈ 8.57 × 10⁴ mol/(L·atm)

Step 3: Calculate Concentrations

Now we can calculate the concentrations of oxygen and nitrogen in water:

• Concentration of oxygen (C_O2):

C_O2 = k_H,O2 * P_O2 = (4.34 × 10⁴ mol/(L·atm)) * (2 atm) ≈ 8.68 × 10⁴ mol/L

• Concentration of nitrogen (C_N2):

C_N2 = k_H,N2 * P_N2 = (8.57 × 10⁴ mol/(L·atm)) * (7.9 atm) ≈ 6.77 × 10⁵ mol/L

Step 4: Calculate Composition in Water

To find the composition of these gases in water, we can express the concentrations as a percentage of the total concentration:

• Total concentration = C_O2 + C_N2 = 8.68 × 10⁴ mol/L + 6.77 × 10⁵ mol/L ≈ 7.64 × 10⁵ mol/L
• Percentage of oxygen = (C_O2 / Total concentration) * 100 ≈ (8.68 × 10⁴ / 7.64 × 10⁵) * 100 ≈ 11.37%
• Percentage of nitrogen = (C_N2 / Total concentration) * 100 ≈ (6.77 × 10⁵ / 7.64 × 10⁵) * 100 ≈ 88.63%

Final Results

In summary, at 298 K and a pressure of 10 atm, the composition of gases in water is approximately:

• Oxygen: 11.37%
• Nitrogen: 88.63%

This calculation illustrates how the solubility of gases in water can vary significantly based on their partial pressures and Henry's law constants, providing insight into the behavior of gases in aquatic environments.