1. More practice with the important concept of differentials. The Gibbs free energy (G, which
you have seen in the form ∆G) can be determined for a perfect gas. It is a function of T, p,
G(p, T, n) = nRT
ln p +
ln T + a
where a is a constant.
(i) Write the differential for G
(ii) Evaluate the partial derivatives
T,p and then use the perfect gas
law to show that the first partial derivative is the volume V and then use the definition of G
from above to show that the third partial derivative is G
(iii) Write the differential for G using the partial derivatives from (ii)
2. BF3 is a gas with van der Waals parameters a = 3.98 × 10−1 P a m6 mol−2 and b = 0.05443 ×
10−3 m3 mol−1
. Calculate the pressure in Pa according to the perfect gas law and then
according to the van der Waals equation for a molar volume Vm = 1.00 × 10−3 m3 and a
temperature T = 300. K.
3. 2.50 moles of a perfect gas undergoes an isothermal expansion from 0.00215 m3
to 0.00468 m3
at 300. K and constant number of moles. Calculate the work, the heat, and the change in
internal energy ∆U for this proces
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