Given `C+ 2S rarr CS_(2), DeltaHf^(0) = +117.0 KJ mol^(-1), C + O_(2) rarr CO_(2), DeltaHf^(0)= -393.0 KJ mol^(-1) S + O_(2) rarr SO_(2), DeltaHf^(0) = -297.0 KJ mol^(-1)`. The heat of combustion of `CS_(2) + 3O_(2) rarr CO_(2) + 2SO_(2)` is

Options

A. `-807 KJ mol^(-1)`
B. `-1104 KJ mol^(-1)`
C. `+1104 KJ mol^(-1)`
D. `+807 KJ mol^(-1)`

Answer

To find the heat of combustion of the reaction \( CS_2 + 3O_2 \rightarrow CO_2 + 2SO_2 \), we will use the given standard enthalpies of formation (\( \Delta H_f^{\circ} \)) for the relevant reactions.

### Step-by-Step Solution:

1. **Write down the reactions and their enthalpies of formation:**
- \( C + 2S \rightarrow CS_2 \), \( \Delta H_f^{\circ} = +117.0 \, \text{kJ/mol} \)
- \( C + O_2 \rightarrow CO_2 \), \( \Delta H_f^{\circ} = -393.0 \, \text{kJ/mol} \)
- \( S + O_2 \rightarrow SO_2 \), \( \Delta H_f^{\circ} = -297.0 \, \text{kJ/mol} \)

2. **Invert the first reaction to express \( CS_2 \) as a reactant:**
- The inverted reaction will be:
\[ CS_2 \rightarrow C + 2S \]
- The enthalpy change for this reaction will be:
\[ \Delta H = -117.0 \, \text{kJ/mol} \]

3. **Write the second reaction as it is:**
- \( C + O_2 \rightarrow CO_2 \)
- The enthalpy change remains:
\[ \Delta H = -393.0 \, \text{kJ/mol} \]

4. **Multiply the third reaction by 2 to get \( 2SO_2 \):**
- The modified reaction will be:
\[ 2S + 2O_2 \rightarrow 2SO_2 \]
- The enthalpy change for this reaction will be:
\[ \Delta H = 2 \times (-297.0) = -594.0 \, \text{kJ/mol} \]

5. **Combine all three reactions:**
- Adding the modified reactions gives:
\[ CS_2 \rightarrow C + 2S \quad (-117.0 \, \text{kJ}) \]
\[ C + O_2 \rightarrow CO_2 \quad (-393.0 \, \text{kJ}) \]
\[ 2S + 2O_2 \rightarrow 2SO_2 \quad (-594.0 \, \text{kJ}) \]
- When we add these reactions, the \( C \) and \( 2S \) will cancel out, leading to:
\[ CS_2 + 3O_2 \rightarrow CO_2 + 2SO_2 \]

6. **Calculate the total enthalpy change for the combustion reaction:**
- The total enthalpy change is:
\[ \Delta H_{combustion} = -117.0 + (-393.0) + (-594.0) \]
- This simplifies to:
\[ \Delta H_{combustion} = -1104.0 \, \text{kJ/mol} \]

### Final Answer:
The heat of combustion of \( CS_2 + 3O_2 \rightarrow CO_2 + 2SO_2 \) is \( \Delta H_{combustion} = -1104.0 \, \text{kJ/mol} \).

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