Question

H2O

5.537

5.465

0.0305

Use the van der Waals equation of state to calculate the pressure of 3.00 mol of H2O at 463 K in a 3.60 L vessel. Van der Waals constants can be found here.Use the ideal gas equation to calculate the pressure under the same conditions. Use Atm

Answer 1

Answer – We are given, number of moles 3.00 mol , temperature K = 463 K , volume V = 3.60 L, Van der Waals constant for water , a = 5.465 atm.L²/ mol² ,

b = 0.0305 L/mol

Pressure by Van der Waals equation –

We know the equation –

(P + an² / V² ) ( V- nb) = nRT

( P + 5.465 atm.L²/ mol² *(3.00 mol)² / (3.60 L)² ) ( 3.60 L – 3.00 mol * 0.0305 L) = 3.00 mole * 0.0821L.atm/mol.K *463 K

( P + 3.79 ) (3.508) = 114.03

3.50 P + 13.31 = 114.03

3.50 P = 114.03 + 13.31

          = 127.35

P = 36.3 atm

Pressure using the Ideal gas law –

We know equation

PV = nRT

P = nRT / V

   = 3.0 mol * 0.0821 L.atm.mol^-1.K^-1 *463 K / 3.60 L

= 31.7 atm