Question

According to the ideal gas law, a 1.041 mol sample of carbon dioxide gas in a 1.016 L container at 270.0 K should exert a pressure of 22.70 atm. By what percent does the pressure calculated using the van der Waals' equation differ from the ideal pressure? For CO₂ gas, a = 3.592 L²atm/mol² and b = 4.267×10^-2 L/mol.

%

Hint: % difference = 100×(P _ideal - P_{van der Waals}) / P _ideal

Answer 1

Given n (CO₂) = 1.041 mol, V (CO₂) = 1.016 L and T (CO₂) = 270 .0 K

P_ideal = 22.70 atm

Now we will calculate pressure using van der Waals equation

(P + an²/V²) (V - nb) = nRT (Here R is gas constant)

Rearranging the equation,

P_real = (nRT/V - nb) - an²/V²

Substitute the all given values and calculate P

P_real = (1.041 x 0.08206 x 270 / 1.016 - 1.041 x 4.267×10^-2) - 3.5x(1.041)² / (1.016)²

P_real = 20.07 atm

Percentage difference = [(P_ideal - P_{van der Waals}) / P _ideal ] x 100

                                 = (22.70 - 20.07 / 22.70) x 100

                                 = 11.58 %