On the basis of thermochemical equations (a), (b) and (c), find out which of the algebric relationships given in options (i) to (iv) is correct.
(1) $ {C (graphite) + O_2(g) -> CO_2(g); \Delta_rH = x \, kJ \, mol^{-1}}$
(2) $ {C(graphite) + \frac{1}{2} O_2(g) -> CO (g); \Delta_rH = y \, kJ \, mol^{-1}}$
(3) $ {CO (g) + \frac{1}{2} O_2 (g) -> CO_2 (g); }$