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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, and n: G(p, T, n) = nRT  ln p + 5 2 ln T + a  where a is a constant. (i) Write the differential for G (ii) Evaluate the partial derivatives  ∂G ∂p  T,n , ∂G ∂T  p,n , ∂G ∂n  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 n (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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