In the combustion of 0.4 g. of `CH_(4)` 0.25 Kcal. Of heat is liberated. The heat of combustion of `CH_(4)` is

Options

A. `-20` K. Cals.
B. `-10` K. Cals.
C. `-2.5` K. Cals.`
D. `-5` K. Cals.

Explanation

To find the heat of combustion of methane (CH₄), we can follow these steps:

### Step 1: Determine the molecular weight of methane (CH₄).
The molecular weight of CH₄ is calculated as follows:
- Carbon (C) has an atomic weight of 12 g/mol.
- Hydrogen (H) has an atomic weight of 1 g/mol, and there are 4 hydrogen atoms in methane.

Thus, the molecular weight of CH₄ = 12 + (4 × 1) = 16 g/mol.

### Step 2: Calculate the heat liberated per gram of CH₄.
We know that the combustion of 0.4 g of CH₄ liberates 0.25 Kcal of heat. To find the heat liberated per gram, we can use the formula:
\[ \text{Heat per gram} = \frac{\text{Heat liberated}}{\text{mass of CH₄}} = \frac{0.25 \text{ Kcal}}{0.4 \text{ g}} = 0.625 \text{ Kcal/g} \]

### Step 3: Calculate the heat of combustion for 16 g of CH₄.
Since we have calculated the heat liberated per gram, we can now find the total heat liberated for 16 g of CH₄:
\[ \text{Heat of combustion for 16 g} = \text{Heat per gram} \times 16 \text{ g} = 0.625 \text{ Kcal/g} \times 16 \text{ g} = 10 \text{ Kcal} \]

### Step 4: Include the sign for heat of combustion.
The heat of combustion is typically expressed as a negative value because it represents the heat released during the reaction. Therefore, the heat of combustion of CH₄ is:
\[ \text{Heat of combustion of CH₄} = -10 \text{ Kcal} \]

### Final Answer:
The heat of combustion of CH₄ is -10 Kcal.

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