(a) Equilibrium constant (Kc) = \(\frac{[SO_3]}{[SO]^2 \times [O_2]}\)
(b) The reaction profile; 2SO\(_{2(g)}\) + O\(_{2(g)}\) \(\to\) 2SO\(_{3(g)}\)

(c)(i) (i) Increase in temperature low of SO\(_{3(g)}\) because the contact proc Decrease in temperature favour E more SO\(_{3(g)}\).
(ii) Increase in pressure favour the more production of SO\(_{3(g)}\) because of moles is present in the prod reactant side of the overall read process.
(iii) Removal of some of the SO\(_{3(g)}\) produced will favour the forward flow of the Chatelier's principle about Equilibrium
(iv) Presence of V\(_2\)O\(_5\), it acts as a fasten the more production SO\(_{3(g)}\) temperature.

(d) Step I: 2SO\(_{2(g)}\) + O\(_{2(g)}\) \(\to\) 2SO\(_{3(g)}\) (Contact process)
Step II: H\(_2\)SO\(_{4(aq)}\) + SO\(_{2(g)}\) \(\to\) 2H\(_2\)S\(_2\)O\(_{7(aq)}\) Oleum fuming liquid conc
Step III: H\(_2\)S\(_2\)O\(_{7(aq)}\) + 2H\(_2\)O\(_{(l)}\) \(\to\) 2H\(_2\)SO\(_{4(aq)}\) tetraoxosulphate (VI) acid

(ii) Tetraoxosulphate (IV) acid can be used for the manufacture of paints and pigment. It can also be used for making detergents and soap.