According to Hess's law of constant heat summation, the enthalpy change for a reaction is the same whether it occurs in one step or in a series of steps. The overall reaction is: $C + O_2 \rightarrow CO_2 \quad (\Delta H = Q)$ This can be obtained by adding the two intermediate steps: Step 1: $C + \frac{1}{2}O_2 \rightarrow CO \quad (\Delta H_1 = -12)$ Step 2: $CO + \frac{1}{2}O_2 \rightarrow CO_2 \quad (\Delta H_2 = -10)$ Adding Step 1 and Step 2 gives the overall reaction. Therefore, $Q = \Delta H_1 + \Delta H_2 = -12 + (-10) = -22$.