Calculate the pressure of a 2.975 mol sample of N2 in a 0.7500 L flask at 300.0

Question

Calculate the pressure of a 2.975 mol sample of N2 in a 0.7500 L flask at 300.0 ?C using the van der Waals equation and then repeat the calculation using the ideal gas equation. Within the limits of the significant figures justified by these parameters will the ideal gas equation overestimate or underestimate the pressure, and if so by how much? For N2, a = 1.39 L2atm/mol2 and b = 0.0391 L/mol.

Overestimate by 21.87 atm

the correct answer mastering chemistry gave is underestimate 0.06atm but i dont know how to get that answer could anyone help?

Overestimate by 21.87 atm

the correct answer mastering chemistry gave is underestimate 0.06atm but i dont know how to get that answer could anyone help?

Explanation / Answer

Using Ideal gas law, PV =nRT

P = nRT/V

P = 2.975 mol * 0.0821 L.atm/mol.K * 573.15 K / 0.75 L

P = 186.564 atm

Using Vander Wall's equation:

(P + an2/V2)(V - nb) = nRT.

P = {2.975 mol * 0.0821 L.atm/mol.K * 573.15 K / 0.75 L - (2.975 mol * 0.0391 L/mol) } - {(2.975 mol)2* 1.39 L2atm/mol2} / (0.75L)2

P = {140 L.atm / 0.75L - 0.1163L} - {12.3 L2atm / 0.5625 L2}

P = (140 L.atm / 0.6337 L ) - 21.87 atm

P = 220.925 atm - 21.87 atm

P = 199.055 atm

P from Ideal gas law = 186.564 atm

difference = 199.055 - 186.564 = 12.5 atm

ideal gas equation underestimate the pressure by 12.5 atm.

The ratio is

12.5 atm / 186.564 atm = 0.067

Answer : UNDERESTIMATE BY 0.067.

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