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.

To find the value of the equilibrium constant, K, at 20 degrees Celsius for the process N2(g) ⇌ N2(aq), we can use Henry's Law and the definition of the equilibrium constant.

According to Henry's Law, the concentration of a gas dissolved in a liquid is directly proportional to its partial pressure. The equation is given as:

C = KH * P

Where:
C is the concentration of the gas in the liquid (mol/L)
KH is the Henry's constant for the gas in the given solvent (mol/Latm)
P is the partial pressure of the gas above the liquid (atm)

In this case, the Henry constant for dissolving nitrogen in water is reported as 7e-4 mol/Latm at 20 degrees Celsius.

Now, let's determine the concentration of nitrogen (N2) in the aqueous solution using Henry's Law.

C = KH * P

C = (7e-4 mol/Latm) * (0.8 bar)

Note: We need to convert the pressure from bar to atm.

1 bar = 0.98692 atm

C = (7e-4 mol/Latm) * (0.8 * 0.98692 atm)

C = 5.614e-4 mol/L

Now that we know the concentration of nitrogen in the aqueous solution (C = 5.614e-4 mol/L), we can use this information to calculate the equilibrium constant, K.

For the equilibrium reaction N2(g) ⇌ N2(aq), the equilibrium constant, K, is given by:

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

K = (amount of N2(aq)) / (amount of N2(g))

The amount of N2(aq) is given as 0.1 mol.

The amount of N2(g) can be calculated using the ideal gas law:

PV = nRT

Where:
P is the pressure of the gas (atm)
V is the volume of the gas (L)
n is the amount of the gas (mol)
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature (in Kelvin)

Given:
P = 0.8 bar = 0.8 * 0.98692 atm
n = ?
R = 0.0821 L·atm/(mol·K)
T = 20 °C = 273.15 + 20 K

Rearranging the ideal gas law equation to solve for n, we have:

n = PV / RT

n = (0.8 * 0.98692 atm) * V / (0.0821 L·atm/(mol·K) * 293.15 K)

n = 0.0799 * V

As the amount of N2(aq) is given as 0.1 mol, we can equate it to the amount of N2(g) and solve for V:

0.1 mol = 0.0799 * V

V = 0.1 mol / 0.0799

Now, you can calculate the volume of the solution by dividing 0.1 mol by 0.0799.