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Chapter 1: Problem 9

\(\begin{array}{ll}{\mathrm{C}(s)+2 \mathrm{H}_{2}(g) \rightarrow \mathrm{CH}_{4}(g)} & {\Delta H^{\circ}=x} \\\ {\mathrm{C}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)} & {\Delta H^{\circ}=y} \\ {\mathrm{H}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(l)} & {\Delta H^{\circ}=\mathrm{z}}\end{array}\) Based on the information given above, what is \(\Delta H^{\circ}\) for the following reaction? \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) (A) \(x+y+z\) (B) \(x+y-z\) (C) \(z+y-2 x\) (D) \(2 z+y-x\)

Short Answer

Expert verified
The \(\Delta H^{\circ}\) for the target reaction \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\) is \(-x + y + 2z\). Therefore, the answer is (D) \(2 z+y-x\).

Step by step solution

01

Identify the target reaction

The target reaction here is \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)\). This is the reaction for which we want to find \(\Delta H^{\circ}\).
02

Analyze given reactions and compare with target

We have three reactions given with their respective \(\Delta H^{\circ}\) values. First, multiply the third reaction by 2 to match the number of \(\mathrm{H}_{2} \mathrm{O}(l)\) molecules in the target reaction. The new reaction becomes \(2\mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2\mathrm{H}_{2} \mathrm{O}(l)\) with \(\Delta H^{\circ}=2z\). Then comparing the three reactions with the target, we can see the first reaction needs to be reversed to match the direction in the target.
03

Execute a strategy for applying Hess's Law

Reversing the first reaction becomes \(\mathrm{CH}_{4}(g) \rightarrow \mathrm{C}(s)+2 \mathrm{H}_{2}(g)\) with \(\Delta H^{\circ}=-x\). Combining the reversed first reaction, the second, and the modified third reaction gives the target reaction. According to Hess's Law, summing up the \(\Delta H^{\circ}\) values from these reactions gives the \(\Delta H^{\circ}\) for the target reaction.
04

Calculate \(\Delta H^{\circ}\) for the target reaction

The \(\Delta H^{\circ}\) for the target reaction is therefore = \(-x + y + 2z\).

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