(a) Equilibrium constant (Kc) = $\frac{[S{O}_3]}{[SO{]}^2\times [O_2]}$
(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.