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 from the combustion of methane (CH₄). Here’s how to do it step by step:

### Step 1: Write the balanced equation for the combustion of methane (CH₄).
The combustion reaction 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 combustion.
The heat of combustion of methane (CH₄) is given as -400 kJ/mol. This means that when 1 mole of CH₄ is combusted, 400 kJ of energy is released.

### Step 3: Determine 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 molar mass of H₂O = 2 + 16 = 18 g/mol

### Step 4: Calculate the number of moles of water (H₂O) in 40 grams.
To find the number of moles of water, use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
\[ \text{Number of moles of H}_2\text{O} = \frac{40 \text{ g}}{18 \text{ g/mol}} \approx 2.22 \text{ moles} \]

### Step 5: Relate the moles of water produced to the heat released.
From the balanced equation, we see that 2 moles of H₂O are produced for every 1 mole of CH₄ combusted. The heat released for the formation of 2 moles of H₂O is -400 kJ.

### Step 6: Calculate the heat released for 2.22 moles of H₂O.
Since 2 moles of H₂O correspond to -400 kJ, we can set up a proportion to find the heat released for 2.22 moles:
\[ \text{Heat released} = \left( \frac{-400 \text{ kJ}}{2 \text{ moles}} \right) \times 2.22 \text{ moles} \]
\[ \text{Heat released} = -400 \times \frac{2.22}{2} \]
\[ \text{Heat released} = -444.4 \text{ kJ} \]

### Final Answer
The heat released when 40 grams of H₂O is formed upon combustion of methane is approximately **-444.4 kJ**.

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