The heats of combustion for `C, H_(2)` and `CH_(4)` are `-349, -241.8` and `-906.7 kJ` respectively. The heat of formation of `CH_(4)` is

Options

A. 174.1 kJ
B. 274.1 kJ
C. 374.1 kJ
D. 74.1 kJ

Explanation

To find the heat of formation of methane (CH₄), we can use the heats of combustion of carbon (C), hydrogen (H₂), and methane (CH₄) provided in the question. The heat of formation can be determined using Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps.

### Step-by-Step Solution:

1. **Write the combustion reactions**:
- The combustion of carbon:
\[ C + O_2 \rightarrow CO_2 \quad \Delta H = -349 \, \text{kJ} \]
- The combustion of hydrogen:
\[ 2H_2 + O_2 \rightarrow 2H_2O \quad \Delta H = -241.8 \, \text{kJ} \]
- The combustion of methane:
\[ CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O \quad \Delta H = -906.7 \, \text{kJ} \]

2. **Reverse the combustion of methane**:
To find the heat of formation of methane, we need to reverse the combustion reaction of methane:
\[ CO_2 + 2H_2O \rightarrow CH_4 + 2O_2 \quad \Delta H = +906.7 \, \text{kJ} \]

3. **Multiply the combustion of hydrogen by 2**:
Since the combustion of hydrogen produces 2 moles of water, we need to multiply the reaction by 2:
\[ 2H_2 + O_2 \rightarrow 2H_2O \quad \Delta H = -241.8 \times 2 = -483.6 \, \text{kJ} \]

4. **Add the reactions**:
Now, we will add the modified reactions together:
- From step 1 (combustion of carbon):
\[ C + O_2 \rightarrow CO_2 \quad \Delta H = -349 \, \text{kJ} \]
- From step 2 (reversed combustion of methane):
\[ CO_2 + 2H_2O \rightarrow CH_4 + 2O_2 \quad \Delta H = +906.7 \, \text{kJ} \]
- From step 3 (modified combustion of hydrogen):
\[ 2H_2 + O_2 \rightarrow 2H_2O \quad \Delta H = -483.6 \, \text{kJ} \]

Adding these together:
\[ C + O_2 + 2H_2 + O_2 + CO_2 + 2H_2O \rightarrow CO_2 + 2H_2O + CH_4 + 2O_2 \]

This simplifies to:
\[ C + 2H_2 \rightarrow CH_4 \]

5. **Calculate the total enthalpy change**:
Now, we can calculate the total enthalpy change:
\[ \Delta H = (-349) + (-483.6) + 906.7 \]
\[ \Delta H = -349 - 483.6 + 906.7 = 74.1 \, \text{kJ} \]

### Final Answer:
The heat of formation of methane (CH₄) is \( +74.1 \, \text{kJ} \).