Question

7.36‡ Suppose that an iron catalyst at a particular manufacturing plant produces ammonia in the most cost–effective manner at 450°C when the pressure is such that ΔrG for the reaction ½ N2(g) + 3/2 H2(g) ® NH3(g) is equal to –500 J mol–1. (a) What pressure is needed? (b) Now suppose that a new catalyst is developed that is most cost-effective at 400°C when the pressure gives the same value of ΔrG. What pressure is needed when the new catalyst is used? What are the advantages of the new catalyst? Assume that (i) all gases are perfect gases or that (ii) all gases are van der Waals gases. Isotherms of ΔrG(T, p) in the pressure range 100 atm £ p £ 400 atm are needed to derive the answer. (c) Do the isotherms you plotted confirm Le Chatelier’s principle concerning the response of equilibrium changes in temperature and pressure?

Answer 1

a) This particular haber process, as we have used iron as a catlyst, calculation of pressure accordingly is given below

ΔG∘=−RTlnK (1)

-500 JMol^-1=- 8.314 JMol^-1K^-1 723 K 2.303 log K_p

K_p= Antilog (0.03611933)

K_p= 1.032 atm ( 1 atm =101325 pascal)

b) when different catalyst is being used, pressure of the partcular reaction increased slightly i.e 1.03889 atm calculated by equation 1. the advantages of the new catalyst is reaction occurs at low temperature and there is no such much amout of pressure is required.

c) Yeah its confirm response regarding of equilibrium changes in temperature and pressure.