Coal, which is primarily carbon, can be converted to natural gas, primarily $\mathrm{CH}_{4}$, by this exothermic reaction.
$$
\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{4}(g)
$$
If this reaction mixture is at equilibrium, predict the effect (shift right, shift left, or no effect) of these changes.
(a) adding more $\mathrm{C}$ to the reaction mixture
(b) adding more $\mathrm{H}_{2}$ to the reaction mixture
(c) raising the temperature of the reaction mixture
(d) lowering the volume of the reaction mixture
(e) adding a catalyst to the reaction mixture