Question

use the van der Waals equation of state to calculate the pressure of 2.30 mol of Xe 481 K in 5.20 L vessel. Use the list of van der Waals constants.

P=?

Use the ideal gas equation to calculate the pressure under the same conditions.

P=?

Answer 1

(1) The van der Waals equation for Xe is given as

( P + n²a/V²)( V - nb ) = nRT

Here, P = pressure of Xe gas

n = no of moles

a and b are van der Waals constant.

V = volume of vessel

R = molar gas constant

= 0.0821 Latmmole^-1K^-1

The value of van der Waals constant are

a = 4.19 L²atm/mol² and b = 0.051 Lmol^-1

So, P = ( nRT/ V - nb) - ( n²a/V²)

= [ (2.3 mol * 0.0821 Latmmol^-1K^-1 * 481K )/ ( 5.2 L - 2.3mol * 0.051 Lmol^-1] - [ ( 2.3 mol ) ² * 4.19 L²atmmol^-2 / ( 5.2L)² ]

= (90.83 atm / 0.1173) - ( 0.819 atm)

= (774.34 - 0.819 ) atm

P= 773.5 atm.

(b) Considering Xe as ideal gas

Then pressure would be given by

PV = nRT

or, P = nRT/V

or, P = ( 2.3 mol * 0.0821 Latm mol^-1K^-1 * 481K ) / 5.2 L

P = 17.46 atm