A gas has a Henry's law constant of 6.10 * 10 - 4 M/atm at 21.1 °C. What volume of solution is needed to completely dissolve 4.56 L of the gas at 1335 torr and 21.1 °C?

311 L

Explanation:

Henry's law states that the solubility of a gas is directly proportional to the pressure of that gas done above the liquid that it's dissolved:

S = H*P

Where S is the concentration (mol/L), H is Henry's law constant, and P is the pressure.

P = 1335 torr * 1atm/760torr = 1.76 atm

S = 6.10x10⁻⁴ * 1.76

S = 1.07x10⁻³ M

By the ideal gas law:

PV = nRT

Where P is the pressure, V is the volume of the gas, n is the number of moles, R is the ideal gas constant (0.082 atm. L/mol. K), and T is the temperature (21.1°C = 294.25 K)

1.76*4.56 = n*0.082*294.25

24.1285n = 8.0256

n = 0.33262 mol

The concentration (S) is the number of moles (n) divided by the volume of the solution (Vl) so:

S = n/Vl

Vl = n/S

Vl = 0.33262/1.07x10⁻³

Vl = 311 L