The heat librerated on complete combustion of 1 mole of `CH_(4)` gas to `CO_(2)(g)` and `H_(2)O(l)` is 890 kJ. Calculate the heat evolved by `2.4 L of CH_(4)` on complete combustion.

Options

A. `95.3 kJ`
B. `8900 kJ`
C. `890 kJ`
D. `8.9 kJ`

Answer

To calculate the heat evolved by the combustion of 2.4 L of methane (CH₄), we can follow these steps:

### Step 1: Understand the combustion reaction
The complete combustion of methane (CH₄) can be represented by the following balanced equation:
\[ \text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(l) \]
From this reaction, we see that 1 mole of CH₄ produces 890 kJ of heat.

### Step 2: Calculate the number of moles of CH₄ in 2.4 L
At standard temperature and pressure (STP), 1 mole of any ideal gas occupies 22.4 L. To find the number of moles of CH₄ in 2.4 L, we use the formula:
\[ \text{Number of moles} = \frac{\text{Volume of gas (L)}}{\text{Molar volume at STP (L/mol)}} \]
Substituting the values:
\[ \text{Number of moles of CH}_4 = \frac{2.4 \text{ L}}{22.4 \text{ L/mol}} = 0.1071 \text{ moles} \]

### Step 3: Calculate the heat evolved for 0.1071 moles of CH₄
Since the heat released for the combustion of 1 mole of CH₄ is -890 kJ, we can find the heat released for 0.1071 moles by using the following relationship:
\[ \text{Heat evolved} = \text{Number of moles} \times \text{Heat per mole} \]
Substituting the values:
\[ \text{Heat evolved} = 0.1071 \text{ moles} \times (-890 \text{ kJ/mole}) = -95.3 \text{ kJ} \]

### Final Answer
The heat evolved by the complete combustion of 2.4 L of CH₄ is approximately -95.3 kJ.

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