Given `C(s)+O_(2)(g)rarr CO_(2)(g)+94.2` Kcal
`H_(2)(g)+2O_(2)(g)rarr CO_(2)(g)+2H_(2)O(l)+210.8` Kcal
The heat of formation of methane in Kcal will be

Options

A. `-45.9`
B. `-47.8`
C. `-20.0`
D. `-47.3`

Answer

To find the heat of formation of methane (CH₄), we can use Hess's Law, which states that the total enthalpy change for a reaction is the sum of the enthalpy changes for the individual steps of the reaction.

### Step-by-Step Solution:

1. **Write the Given Reactions:**
- Reaction 1:
\[ C(s) + O_2(g) \rightarrow CO_2(g) \quad \Delta H_1 = -94.2 \text{ Kcal} \]
- Reaction 2 (corrected to include methane):
\[ CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l) \quad \Delta H_2 = -210.8 \text{ Kcal} \]
- Reaction 3 (formation of water):
\[ H_2(g) + \frac{1}{2}O_2(g) \rightarrow H_2O(l) \quad \Delta H_3 = -68.3 \text{ Kcal} \]

2. **Reverse the Second Reaction:**
To find the formation of methane, we need to reverse the second reaction:
\[ CO_2(g) + 2H_2O(l) \rightarrow CH_4(g) + 2O_2(g) \quad \Delta H_2' = +210.8 \text{ Kcal} \]

3. **Multiply the Third Reaction by 2:**
We need to produce 2 moles of water, so we multiply the third reaction by 2:
\[ 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) \quad \Delta H_3' = 2 \times (-68.3) = -136.6 \text{ Kcal} \]

4. **Add the Reactions:**
Now, we can add the modified reactions:
- From Reaction 1:
\[ C(s) + O_2(g) \rightarrow CO_2(g) \quad \Delta H_1 = -94.2 \text{ Kcal} \]
- From the reversed Reaction 2:
\[ CO_2(g) + 2H_2O(l) \rightarrow CH_4(g) + 2O_2(g) \quad \Delta H_2' = +210.8 \text{ Kcal} \]
- From the modified Reaction 3:
\[ 2H_2(g) + O_2(g) \rightarrow 2H_2O(l) \quad \Delta H_3' = -136.6 \text{ Kcal} \]

Adding these gives:
\[ C(s) + O_2(g) + CO_2(g) + 2H_2O(l) + 2H_2(g) + O_2(g) \rightarrow CH_4(g) + 2O_2(g) + 2H_2O(l) \]

5. **Calculate the Total Enthalpy Change:**
\[ \Delta H_{formation} = \Delta H_1 + \Delta H_2' + \Delta H_3' \]
\[ \Delta H_{formation} = -94.2 + 210.8 - 136.6 \]
\[ \Delta H_{formation} = -20 \text{ Kcal} \]

### Final Result:
The heat of formation of methane (CH₄) is **-20 Kcal**.