Question

The compressibility Factor, Z, of a gas is plotted as a function of inverse molar volume, 1/V_m, in the figure. The data was collected at T = 300K.middotThe data is fit to a quadratic line with the results given as: Z = 0.98925 - 0 1.5105 times 10^-2/V_m + 1.1887 times 10^-3/V^2_m Determine the van der Waals' a and b constants and the Boyle Temperature, T_B, from the given information. Remember: if b/V_m < < 1, then (1 - b/V_m)^-1 may be expanded in a power series in terms of b/V_m: (1 - b/V_m)^-1 = 1 + b/V_m + (b/V_m)^2 + (b/V_m)^3 +

Answer 1

From the given equation of Z where molar volume=5. (from graph 1/V=0.2),. Z =0.986, since Z=1-a/RTV,.  

Molar volume V=3b,

b=V/3, b=5/3=1.66

Boyle temperature (T) = a/bR = 12.72k.

Hence. a= RTV-Z(RTV)=1.73,