The heat of formations for `CO_(2)(g),H_(2)O(l) and CH_(4)(g)` are -400 kJ `mol^(-1),-280" kJ "mol^(-1) and -70" kJ "mol^(-1)`, respectively. The heat of combustion of `CH_(4)` in kJ `mol^(-1)` is

Options

A. 800
B. `-160`
C. `-890`
D. `-90`

Explanation

To calculate the heat of combustion of methane (CH₄), we can use the following steps:

### Step 1: Write the balanced chemical equation for the combustion of methane.
The combustion of methane can be represented by the following equation:
\[ \text{CH}_4(g) + 2 \text{O}_2(g) \rightarrow \text{CO}_2(g) + 2 \text{H}_2O(l) \]

### Step 2: Identify the heat of formation values.
From the question, we have the following heat of formation values:
- \( \Delta H_f^\circ (\text{CH}_4(g)) = -70 \, \text{kJ/mol} \)
- \( \Delta H_f^\circ (\text{O}_2(g)) = 0 \, \text{kJ/mol} \) (elements in their standard state)
- \( \Delta H_f^\circ (\text{CO}_2(g)) = -400 \, \text{kJ/mol} \)
- \( \Delta H_f^\circ (\text{H}_2O(l)) = -280 \, \text{kJ/mol} \)

### Step 3: Apply the formula for heat of combustion.
The heat of combustion (\( \Delta H_c \)) can be calculated using the formula:
\[ \Delta H_c = \sum (\Delta H_f^\circ \text{ of products}) - \sum (\Delta H_f^\circ \text{ of reactants}) \]

### Step 4: Calculate the heat of formation for the products.
For the products:
- For \( \text{CO}_2(g) \): \( -400 \, \text{kJ/mol} \)
- For \( 2 \text{H}_2O(l) \): \( 2 \times (-280 \, \text{kJ/mol}) = -560 \, \text{kJ/mol} \)

Total heat of formation for products:
\[ \Delta H_f^\circ \text{(products)} = -400 + (-560) = -960 \, \text{kJ/mol} \]

### Step 5: Calculate the heat of formation for the reactants.
For the reactants:
- For \( \text{CH}_4(g) \): \( -70 \, \text{kJ/mol} \)
- For \( 2 \text{O}_2(g) \): \( 2 \times 0 \, \text{kJ/mol} = 0 \, \text{kJ/mol} \)

Total heat of formation for reactants:
\[ \Delta H_f^\circ \text{(reactants)} = -70 + 0 = -70 \, \text{kJ/mol} \]

### Step 6: Substitute the values into the formula.
Now, substituting the values into the heat of combustion formula:
\[ \Delta H_c = (-960) - (-70) \]
\[ \Delta H_c = -960 + 70 = -890 \, \text{kJ/mol} \]

### Conclusion:
The heat of combustion of methane (CH₄) is \( -890 \, \text{kJ/mol} \).

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