Henry's Law and the Henry's Law Constant

Henry's Law states that the solubility of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. The mathematical expression of Henry's Law is:

C = k * P

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

The Henry's Law constant (k) is specific for each gas and solvent pair at a given temperature. It represents the proportionality constant relating the concentration of the gas in the liquid to its partial pressure. The larger the value of k, the more soluble the gas is in the liquid.

Calculating the Moles of N2 Dissolved in Water

Given:
Henry's Law constant (k) for N2 in water at 298 K = 10^5 atm
Mole fraction of N2 in air = 0.8
Pressure of N2 = 5 atm
Moles of water = 10 moles

To calculate the moles of N2 dissolved in water, we need to use Henry's Law equation and the given information.

1. Calculate the partial pressure of N2:
Since the mole fraction of N2 in air is given as 0.8, we can assume that the partial pressure of N2 is also 0.8 times the total pressure of air.

Partial pressure of N2 = 0.8 * 5 atm = 4 atm

2. Use Henry's Law equation to find the concentration of N2 in water:
C = k * P

C = (10^5 atm) * (4 atm) = 4 * 10^5

This means that the concentration of N2 in water is 4 * 10^5 moles per liter.

3. Calculate the moles of N2 dissolved in 10 moles of water:
To find the moles of N2, we need to multiply the concentration by the volume of water.

Moles of N2 = (4 * 10^5 moles/L) * (10 L) = 4 * 10^6 moles

Therefore, the number of moles of N2 dissolved in 10 moles of water at 298 K and 5 atm pressure is 4 * 10^6 moles.