If $C + O_2 \rightarrow CO_2$, $C + \frac{1}{2}O_2 \rightarrow CO$, and $CO + \frac{1}{2}O_2 \rightarrow CO_2$

Question

If $C + O_2 \rightarrow CO_2$, $C + \frac{1}{2}O_2 \rightarrow CO$, and $CO + \frac{1}{2}O_2 \rightarrow CO_2$, the heats of reaction are $Q$, $-12$, and $-10$ respectively. Then $Q$ =

Accepted Answer

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, $Q = \Delta H_1 + \Delta H_2 = -12 + (-10) = -22$.

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