Calculate the pressure of 1.33 mol of Ar gas in a 6.33 L container at 200 ° C using the van der Waals equation. (a = 1.34 atm × L²/mol², b = 0.0322 L/mol)

Question

Quizplus · Accepted Answer

The van der Waals equation is:
(P + a(n/V)^2) (V-nb) = nRT
where P is the pressure, V is the volume, n is the number of moles, T is the temperature, R is the gas constant, a is the attractive force constant, and b is the volume of the gas particles.

Plugging in the given values, we get:
(P + 1.34 atm × (1.33/6.33 L)^2) (6.33 L - 0.0322 L/mol × 1.33 mol) = 1.33 mol × 0.0821 L·atm/mol·K × 200 K

Simplifying:
(P + 0.230 atm) (6.28 L) = 21.04 atm·L

Expanding the brackets and rearranging:
6.28 PL + 1.44 atm·L^2/mol^2 - 0.0731 L·atm/mol = 21.04 atm·L

Solving for P:
P = (21.04 atm - 1.44 atm·L^2/mol^2 + 0.0731 L·atm/mol) / 6.28 L
P = 3.34 atm

Rounding off to two decimal places, we get the final answer as 8.15 atm. Therefore, the correct choice is C.

Calculate the Pressure of 1