On complete combustion of 2 gm methane 26575 cals heat is generated. The heat of formation of methane will be (given heat of formation of `CO_(2)` and `H_(2)O` are - 97000 and - 68000 cais respectivvely) :

Options

A. `+20400 cal`
B. `+20600 cal`
C. `-20400 cal`
D. `-2000 cal`

Answer

To find the heat of formation of methane (CH₄) based on the given data, we will follow these steps:

### Step 1: Write the balanced equation for the complete combustion of methane.
The balanced equation for the complete combustion of methane is:
\[ \text{CH}_4 + 2 \text{O}_2 \rightarrow \text{CO}_2 + 2 \text{H}_2\text{O} \]

### Step 2: Identify the heat of formation values.
From the problem, we have:
- Heat of formation of CO₂ (ΔHf CO₂) = -97000 cal
- Heat of formation of H₂O (ΔHf H₂O) = -68000 cal
- Heat of formation of O₂ (ΔHf O₂) = 0 cal (since it is in its elemental form)

### Step 3: Write the expression for the enthalpy change (ΔH) of the reaction.
The enthalpy change for the combustion reaction can be expressed as:
\[ \Delta H = \text{(Sum of heat of formation of products)} - \text{(Sum of heat of formation of reactants)} \]

Substituting the values:
\[ \Delta H = [\Delta Hf \text{(CO₂)} + 2 \times \Delta Hf \text{(H₂O)}] - [\Delta Hf \text{(CH₄)} + 2 \times \Delta Hf \text{(O₂)}] \]

### Step 4: Substitute the known values into the equation.
Substituting the known values into the equation:
\[ \Delta H = [-97000 + 2 \times (-68000)] - [\Delta Hf \text{(CH₄)} + 0] \]

### Step 5: Calculate the total heat of formation of products.
Calculating the total heat of formation of products:
\[ \Delta H = [-97000 - 136000] - \Delta Hf \text{(CH₄)} \]
\[ \Delta H = -233000 - \Delta Hf \text{(CH₄)} \]

### Step 6: Set the enthalpy change equal to the given heat of combustion.
The problem states that the heat generated from the combustion of 2 g of methane is 26575 cal. Since combustion is an exothermic reaction, we take it as negative:
\[ -26575 = -233000 - \Delta Hf \text{(CH₄)} \]

### Step 7: Solve for ΔHf (CH₄).
Rearranging the equation to solve for ΔHf (CH₄):
\[ \Delta Hf \text{(CH₄)} = -233000 + 26575 \]
\[ \Delta Hf \text{(CH₄)} = -206225 \text{ cal} \]

### Step 8: Finalize the answer.
Thus, the heat of formation of methane (CH₄) is:
\[ \Delta Hf \text{(CH₄)} = -206225 \text{ cal} \]