Calculate the pressure of 5.33 mol of CO₂ gas in a 2.33 L container at 500 ° C using the van der Waals equation. (a = 3.59 atm × L²/mol², b = 0.0427 L/mol)

Question

Quizplus · Accepted Answer

The van der Waals equation is:

(P + a(n/V)\^2)(V - nb) = nRT

where P is pressure, V is volume, n is the number of moles, R is the gas constant, T is temperature, a is the attractive force constant, and b is the volume excluded by one mole of gas particles.

Plugging in the given values: 
n = 5.33 mol 
V = 2.33 L 
T = 500 °C + 273.15 = 773.15 K 
a = 3.59 atm × L/mol 
b = 0.0427 L/mol 
R = 0.08206 L·atm/(mol·K)

Solving for P:

(P + (3.59 atm × L/mol) × (5.33 mol/2.33 L)\^2)(2.33 L - 0.0427 L × 5.33 mol) = 5.33 mol × 0.08206 L·atm/(mol·K) × 773.15 K

P = (5.33 × 0.08206 × 773.15) / (2.33 - 0.15266) - 5.33 × 3.59 × (5.33 / 2.33)\^2 / (2.33 - 0.15266) / 154.28735

P = 142 atm

Therefore, the answer is B, 142 atm.

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