Concept:

Hess's Law of Constant Heat Summation states that if a reaction can take place by more than one route, the total enthalpy change is identical regardless of the route taken, provided initial and final states are the same.

Formula:

$$ \Delta H_{\text{total}} = \Delta H_1 + \Delta H_2 $$

Solution:

• The direct, single-step route is: \( C + O_2 \rightarrow CO_2 \) with \( \Delta H = -393.7 \text{ kJ/mol} \).



• The two-step indirect route is: Step 1 (forming \( CO \) with \( \Delta H_1 \)) + Step 2 (burning \( CO \) to \( CO_2 \) with \( \Delta H_2 = -283 \text{ kJ/mol} \)).



• Applying Hess's Law: \( -393.7 = \Delta H_1 + (-283) \).



• Solve for \( \Delta H_1 \):
  \( \Delta H_1 = -393.7 - (-283) \)
  \( \Delta H_1 = -393.7 + 283 = -110.7 \text{ kJ/mol} \).



• Rounding to the nearest whole number given in the options yields \( -110 \text{ kJ mol}^{-1} \).

Why other options are incorrect:

Option B has a positive sign, incorrectly implying the partial combustion of carbon is endothermic. Options C and D result from incorrectly adding the two values (\( -393.7 - 283 \)) instead of substituting them properly into the algebraic sum.