Calculate the pressure exerted by Ar for a molar volume of 0.590 L⋅mol-1 at 295 K using the van der Waals equation of state. The van der Waals parameters a and b for Ar are 1.355 bar⋅dm^6⋅mol^ (-2) and 0.0320 dm^3⋅mol^ (-1), respectively.

the pressure P = 40.03 bar

Explanation:

The Van der Waals equation states that

P = R*T / (V-b) - a/V²

where

T = absolute temperature = 295 K

V = molar volume = 0.590 L/mol

R = ideal gas constant = 0.082 atm*L/mol*K

a = van der Waals parameter = 1.355 bar⋅dm⁶/mol² * (0.987 atm/bar) * (1 L²/dm⁶) = 1.337 atm ⋅L²/mol²

b = van der Waals parameter = 0.032 dm³/mol * (1 L/dm³) = 0.032 L/mol

then replacing values

P = R*T / (V-b) - a/V² = 0.082 atm*L/mol*K*295 K / (0.590 L/mol-0.032 L/mol) - 1.337 atm ⋅L²/mol² / (0.590 L/mol) ² = 39.51 atm

P = 39.51 atm / (0.987 atm/bar) = 40.03 bar