Henry constant for the dissolving of nitrogen in water was reported as 7e-4 mol/Latm at 20 deg Celsius. What is the value of the equilibrium constant, K, at 20 deg Celsius for the process N2(g0)=N2(aq). If the amount of nitrogen in aqueous solution is .1 mol N2 and the partial pressure of nitrogen in contant with the solution is .8 bar, what is the volume of the solution.

Question

Henry constant for the dissolving of nitrogen in water was reported as 7e-4 mol/Latm at 20 deg Celsius. What is the value of the equilibrium constant, K, at 20 deg Celsius for the process N2(g0)=N2(aq). If the amount of nitrogen in aqueous solution is .1 mol N2 and the partial pressure of nitrogen in contant with the solution is .8 bar, what is the volume of the solution.

Answer 1

To find the value of the equilibrium constant, K, at 20°C for the process N2(g) ⇌ N2(aq), we can use Henry's Law. Henry's Law states that the concentration of a gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the liquid.

The equilibrium constant K can be expressed as the ratio of the concentration of the dissolved gas to the partial pressure of the gas:

K = [N2(aq)] / P(N2)

Given:
Henry constant (H) = 7e-4 mol/Latm at 20°C
Amount of nitrogen in aqueous solution ([N2(aq)]) = 0.1 mol N2
Partial pressure of nitrogen in contact with the solution (P(N2)) = 0.8 bar.

Step 1: Convert the partial pressure from bar to atm.
1 bar = 0.9869 atm (approximately)
P(N2) = 0.8 bar * 0.9869 atm/bar ≈ 0.7895 atm

Step 2: Calculate the concentration of dissolved nitrogen using Henry's Law.
[H] = H * P(N2)
[N2(aq)] = H * P(N2) = 7e-4 mol/Latm * 0.7895 atm ≈ 5.5245e-4 mol/L

Step 3: Substitute the values into the equilibrium constant equation.
K = [N2(aq)] / P(N2) = 5.5245e-4 mol/L / 0.7895 atm ≈ 7.0009e-4 L/mol

So, the value of the equilibrium constant, K, at 20°C for the process N2(g) ⇌ N2(aq) is approximately 7.0009e-4 L/mol.

Now, to calculate the volume of the solution, we need to know the total number of moles of the solution.

Given:
Amount of nitrogen in the aqueous solution ([N2(aq)]) = 0.1 mol N2

Since N2 is diatomic, this means there are 0.1 mol N2 * 2 = 0.2 mol of N atoms in the solution.

Step 4: Calculate the volume using the ideal gas law.
PV = nRT

R is the ideal gas constant, which is 0.0821 L·atm/(mol·K)
T is the temperature in Kelvin (20°C = 20 + 273.15 K)

Volume (V) = nRT / P
Volume (V) = (0.2 mol)(0.0821 L·atm/(mol·K))(293.15 K) / (0.7895 atm)
Volume (V) ≈ 6.125 L

Therefore, the volume of the solution is approximately 6.125 liters.