1 mole of carbon dioxide gas CO2 at 350 K is confined to a v

1 mole of carbon dioxide gas (CO_2) at 350 K is confined to a volume of 400 cm^3. The van der Waals equation of state predicts the pressure 5.87 * 10^6 Pa. The gas is now heated until 700K. The van der Waals equation of state predicts the pressure 14.01 * 10^6 Pa. Boltzmann constant k = 1.38*10^-23 J/K, Avogadro number N_A = 6.022*10^23 mol^-1, The universal gas constant R = 8.314 J/(K*mol) Determine the van der Waals constant a of the gas Determine the van der Waals constant b of the gas At what limit the van der Waals equation of state is equivalent to ideal gas equation of state?

Solution

VDW eqn ( P+a/V²)( V-b) =RT

( 5.87 Mpa + a/.4*.4) (.4-b) =R* 350

( 14.01 MPa + a/.4*.4)(.4-b) =700R

where V is const at .4 litre

dividing thru, ( 14.01 *10⁶ +a/.16) /( 5.87*10⁶ + a/.16) = 2

14.01 * 10 ⁶ + a/.16 = 2( 5.87 * 10⁶ + a/.16)

a/.16 = 2.27*10⁶, ==> a =.3632 *10^6

b) substitute a for either of the eqns and calculate b

c) a=0, b=0