Concept:

Sublimation is the direct phase transition from a solid to a gas: \( I_{2(s)} \rightarrow I_{2(g)} \). We can determine its enthalpy using Hess's Law by algebraically manipulating given reactions.

Formula:

$$ \text{Reaction 1: } H_{2(g)} + I_{2(s)} \rightarrow 2HI_{(g)} \quad (\Delta H = +51.8) $$
$$ \text{Reaction 2: } H_{2(g)} + I_{2(g)} \rightarrow 2HI_{(g)} \quad (\Delta H = -10.5) $$

Solution:

• We need \( I_{2(s)} \) on the reactant side and \( I_{2(g)} \) on the product side.



• Keep Reaction 1 as is: \( H_2 + I_{2(s)} \rightarrow 2HI \quad (\Delta H = +51.8) \).



• Reverse Reaction 2: \( 2HI \rightarrow H_2 + I_{2(g)} \quad (\Delta H = +10.5) \).



• Add the two reactions together. The \( H_2 \) and \( 2HI \) molecules completely cancel out on both sides.



• Resulting equation: \( I_{2(s)} \rightarrow I_{2(g)} \).



• Total Enthalpy = \( 51.8 + 10.5 = +62.3 \text{ kJ/mol} \).

Why other options are incorrect:

41.3 results from blindly adding the numbers without flipping the necessary equation (\( 51.8 - 10.5 \)). The other numbers are mathematically irrelevant.