The heat of combustion of `CH_(4)(g)`, C(graphite) and `H_(2)(g)` are - 20 Kcal, - 40 Kcal and -10 Kcal respectively. The heat of formation of methane is

Options

A. `-40` Kcal
B. `+40` Kcal
C. `-80` Kcal
D. `+80` Kcal

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 combustion reactions and their enthalpy changes:**
- For methane (CH₄):
\[ \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \quad \Delta H = -20 \text{ Kcal} \]
- For carbon (C, graphite):
\[ \text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H = -40 \text{ Kcal} \]
- For hydrogen (H₂):
\[ \text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \rightarrow \text{H}_2\text{O}(l) \quad \Delta H = -10 \text{ Kcal} \]

2. **Identify the reaction for the formation of methane:**
- The formation reaction for methane can be written as:
\[ \text{C}(s) + 2\text{H}_2(g) \rightarrow \text{CH}_4(g) \]
- We need to find the enthalpy change (ΔH) for this reaction.

3. **Use Hess's law to combine the reactions:**
- To derive the formation reaction from the combustion reactions, we can manipulate the above equations:
- Reverse the combustion of methane (which changes the sign of ΔH):
\[ \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \rightarrow \text{CH}_4(g) + 2\text{O}_2(g) \quad \Delta H = +20 \text{ Kcal} \]
- Keep the combustion of carbon as is:
\[ \text{C}(s) + \text{O}_2(g) \rightarrow \text{CO}_2(g) \quad \Delta H = -40 \text{ Kcal} \]
- Reverse the combustion of hydrogen (which changes the sign of ΔH):
\[ 2\text{H}_2\text{O}(l) \rightarrow 2\text{H}_2(g) + \frac{1}{2}\text{O}_2(g) \quad \Delta H = +20 \text{ Kcal} \]

4. **Combine the reactions:**
- Now, we can combine these three reactions:
\[ \Delta H = (+20 \text{ Kcal}) + (-40 \text{ Kcal}) + (+20 \text{ Kcal}) \]
- Simplifying this gives:
\[ \Delta H = 20 - 40 + 20 = 0 \text{ Kcal} \]

5. **Final calculation:**
- The heat of formation of methane is:
\[ \Delta H = +40 \text{ Kcal} \]

### Final Answer:
The heat of formation of methane (CH₄) is **+40 Kcal**.