The heat of combustion of `CH_(4) is -400 KJ mol^(-1)`. Calculate the heat released when 40g of `H_(2)O` is formed upon combustion :-

Options

A. `+444.4 KJ`
B. `+888.8 KJ`
C. `-444.4 KJ`
D. `-888.8 KJ`

Explanation

To solve the problem, we need to calculate the heat released when 40 grams of water (H₂O) is formed during the combustion of methane (CH₄), given that the heat of combustion of CH₄ is -400 kJ/mol.

### Step-by-Step Solution:

**Step 1: Write the balanced chemical equation for the combustion of methane.**

The balanced equation for the 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 amount of water produced in the reaction.**

From the balanced equation, we see that 1 mole of CH₄ produces 2 moles of H₂O.

**Step 3: Calculate the molar mass of water (H₂O).**

The molar mass of water (H₂O) is calculated as follows:
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Oxygen (O): 16 g/mol × 1 = 16 g/mol
- Total: 2 + 16 = 18 g/mol

**Step 4: Determine how many moles of water are in 40 grams.**

To find the number of moles of water in 40 grams, we use the formula:
\[ \text{Moles of H}_2\text{O} = \frac{\text{mass}}{\text{molar mass}} \]
\[ \text{Moles of H}_2\text{O} = \frac{40 \text{ g}}{18 \text{ g/mol}} \approx 2.22 \text{ moles} \]

**Step 5: Calculate the heat released for the formation of 2.22 moles of water.**

From the heat of combustion, we know that the combustion of 1 mole of CH₄ releases -400 kJ, which corresponds to the formation of 2 moles of H₂O. Therefore, the heat released for the formation of 2 moles of H₂O is -400 kJ.

To find the heat released for 1 mole of H₂O:
\[ \text{Heat released per mole of H}_2\text{O} = \frac{-400 \text{ kJ}}{2} = -200 \text{ kJ} \]

Now, we can calculate the heat released for 2.22 moles of H₂O:
\[ \text{Heat released} = -200 \text{ kJ/mole} \times 2.22 \text{ moles} \approx -444.4 \text{ kJ} \]

### Final Answer:
The heat released when 40 grams of water is formed upon combustion is approximately -444.4 kJ.

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