Dry air contains 79% of N2 and 21% of O2. Determine the proportion of N2 and O2(in terms of mole fractions) dissolved in water at 1 atm pressure. Henry's law constant for N2 and O2 in H2O are 8.5×10^4 atm and 4.56× 10^4 atm respectively.?

Question

Answer

Problem Statement

Dry air contains 79% of N2 and 21% of O2. Determine the proportion of N2 and O2 (in terms of mole fractions) dissolved in water at 1 atm pressure. Henry's law constant for N2 and O2 in H2O are 8.5×10^4 atm and 4.56× 10^4 atm respectively.

Solution

Step 1: Finding the mole fraction of N2 and O2 in dry air

Given that dry air contains 79% of N2 and 21% of O2.

Mole fraction of N2 in dry air = 79/100 = 0.79

Mole fraction of O2 in dry air = 21/100 = 0.21

Step 2: Applying Henry's Law

Henry's Law states that the concentration of a gas in a solution is directly proportional to the partial pressure of the gas above the solution. It is expressed as:

C = kP

where C is the concentration of the gas in the solution, k is the Henry's Law constant, and P is the partial pressure of the gas above the solution.

Step 3: Finding the concentration of N2 and O2 in water

Let x be the mole fraction of N2 dissolved in water and y be the mole fraction of O2 dissolved in water.

According to Henry's Law,

x = kN2 × PN2

y = kO2 × PO2

where PN2 and PO2 are the partial pressures of N2 and O2 in air, respectively. We know that the total pressure of air is 1 atm. Therefore,

PN2 = 0.79 atm

PO2 = 0.21 atm

Substituting the given values, we get:

x = (8.5 × 10^4 atm) × (0.79 atm) = 6.715

y = (4.56 × 10^4 atm) × (0.21 atm) = 0.95976

Step 4: Finding the proportion of N2 and O2 in water

The total mole fraction of the dissolved gases in water is:

x + y = 6.715 + 0.95976 = 7.67476

The mole fraction of N2 in water is:

mole fraction of N2 = x / (x + y) = 6.715 / 7.67476 = 0.875

The mole fraction of O2 in water is:

mole fraction of O2 = y / (x + y) = 0.95976 / 7.67476 = 0.125

Final Answer

The proportion of N2 and O2 (in terms of mole fractions) dissolved in water at 1

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