Question

Select the correct option:
\(2CO (g) + O_2 (g) → 2CO_2 (g) ; ΔH = -x KJ/mol\)
\(C (graphite) + O_2(g) → CO_2 (g) ; AH = -y KJ/mol\)
Then AH for, \(C(graphite) + \frac{1}{2} O_2 (g) → CO (g):\)

• A. \(x-\frac{y}{2}\)
• B. \(\frac{x-2y}{2}\)
• C. \(x+\frac{2y}{2}\)
• D. \(\frac{x-y}{2}\)

Hint:

Hess’s Law is a powerful tool for calculating enthalpy changes. Manipulate the given equations (reverse, multiply/divide) so that when added, they result in the target equation. Remember to adjust the enthalpy changes accordingly.

Answer 1

The Correct Option is B

Step 1: Equations and Their Enthalpy Changes

We are given:

1. \( 2CO(g) + O_2(g) \rightarrow 2CO_2(g) \, \, \Delta H_1^\circ = -x \)
2. \( C(\text{graphite}) + O_2(g) \rightarrow CO_2(g) \, \, \Delta H_2^\circ = -y \)

The target equation is:

\[ C(\text{graphite}) + \frac{1}{2}O_2(g) \rightarrow CO(g) \]

Step 2: Manipulate the Given Equations

Reverse and divide equation (1) by 2:

\[ CO_2(g) \rightarrow CO(g) + \frac{1}{2}O_2(g) \, \, \Delta H = \frac{x}{2} \]

Keep equation (2) as is:

\[ C(\text{graphite}) + O_2(g) \rightarrow CO_2(g) \, \, \Delta H = -y \]

Step 3: Add the Modified Equations

Combine the two equations:

\[ C(\text{graphite}) + O_2(g) + CO_2(g) \rightarrow CO_2(g) + CO(g) + \frac{1}{2}O_2(g) \]

Cancel out \( CO_2(g) \):

\[ C(\text{graphite}) + \frac{1}{2}O_2(g) \rightarrow CO(g) \]

Step 4: Calculate the Enthalpy Change

Add the enthalpy changes of the modified equations:

\[ \Delta H^\circ = \frac{x}{2} - y \]

Reorganize the terms:

\[ \Delta H^\circ = \frac{x - 2y}{2} \]

Final Answer:

The enthalpy change for the reaction is:

\( \Delta H^\circ = \frac{x - 2y}{2} \)