Ths standard heat of formation of `CH_(4), CO_(2)` and `H_(2)O_(l)` are -76.2, -394.8, and - 285.82 kJ `mol^(-1)` respectively. Heat of vaporization of water is `44 kJ mol^(-1)`. Calculate the amount of heat evolved when 22.4 L to `CH_(4)` kept under normal conditions is oxidized into its gaseous products.

Options

A. 802 kJ
B. 878.4 kJ
C. 702 kJ
D. 788.4 kJ

Explanation

To calculate the amount of heat evolved when 22.4 L of methane (CH₄) is oxidized under normal conditions, we can follow these steps:

### Step 1: Determine the number of moles of CH₄
At normal conditions (NTP), 1 mole of any ideal gas occupies 22.4 L. Therefore, the number of moles of CH₄ in 22.4 L is:

\[ \text{Number of moles of CH₄} = \frac{22.4 \, \text{L}}{22.4 \, \text{L/mol}} = 1 \, \text{mol} \]

### Step 2: Write the balanced chemical equation for the combustion of methane
The balanced equation for the combustion of methane is:

\[ \text{CH}_4(g) + 2 \text{O}_2(g) \rightarrow \text{CO}_2(g) + 2 \text{H}_2\text{O}(g) \]

### Step 3: Determine the standard heat of formation for the reaction
The standard heats of formation for the reactants and products are given as follows:
- ΔHf (CH₄) = -76.2 kJ/mol
- ΔHf (CO₂) = -394.8 kJ/mol
- ΔHf (H₂O) = -285.82 kJ/mol

### Step 4: Calculate the ΔH for the reaction
Using Hess's Law, we can calculate the ΔH for the combustion reaction:

\[ \Delta H = [\Delta Hf (\text{products})] - [\Delta Hf (\text{reactants})] \]

Substituting the values:

\[ \Delta H = [\Delta Hf (\text{CO}_2) + 2 \times \Delta Hf (\text{H}_2\text{O})] - [\Delta Hf (\text{CH}_4) + 2 \times \Delta Hf (\text{O}_2)] \]

Since the standard heat of formation for O₂ is 0 (as it is in its elemental form):

\[ \Delta H = [-394.8 + 2 \times (-285.82)] - [-76.2 + 0] \]

Calculating the values:

\[ \Delta H = [-394.8 - 571.64] - [-76.2] \]
\[ \Delta H = -966.44 + 76.2 = -890.24 \, \text{kJ/mol} \]

### Step 5: Calculate the heat evolved for 1 mole of CH₄
Since we have 1 mole of CH₄, the heat evolved when 22.4 L of CH₄ is oxidized is:

\[ \text{Heat evolved} = \Delta H = -890.24 \, \text{kJ} \]

### Final Result
The amount of heat evolved when 22.4 L of CH₄ is oxidized is **890.24 kJ**.

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