How much heat is evolved if 3.2 g of methane is burnt and if the heat of combustion of methane is `-880" kJ mol"^(-1)` ?

Options

A. 88 kJ
B. 264 kJ
C. 176 kJ
D. 440 kJ

Explanation

To solve the problem of how much heat is evolved when 3.2 g of methane (CH₄) is burned, given that the heat of combustion of methane is -880 kJ/mol, follow these steps:

### Step 1: Calculate the number of moles of methane in 3.2 g.
- The molar mass of methane (CH₄) is calculated as follows:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol × 4 = 4 g/mol
- Total molar mass of CH₄ = 12 g/mol + 4 g/mol = 16 g/mol

- Now, calculate the number of moles of methane in 3.2 g:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{3.2 \text{ g}}{16 \text{ g/mol}} = 0.2 \text{ moles} \]

### Step 2: Calculate the heat evolved for 0.2 moles of methane.
- The heat of combustion for 1 mole of methane is -880 kJ. Therefore, for 0.2 moles:
\[ \text{Heat evolved} = \text{moles} \times \text{heat of combustion per mole} = 0.2 \text{ moles} \times (-880 \text{ kJ/mol}) \]
\[ = -176 \text{ kJ} \]

### Step 3: Present the final answer.
- Since the question asks for the heat evolved, we can express the answer as a positive value:
\[ \text{Heat evolved} = 176 \text{ kJ} \]

Thus, the final answer is **176 kJ**.

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