If, combustion of `4g` of `CH_(4)` liberates `2.5kcal` of heat, the heat of combustion of `CH_(4)` is `:`

Explanation

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

### Step 1: Understand the given data
We know that the combustion of 4 grams of methane releases 2.5 kilocalories of heat.

### Step 2: Calculate the molar mass of methane (CH₄)
The molar mass of CH₄ can be calculated as follows:
- Carbon (C) has an atomic mass of 12 g/mol.
- Hydrogen (H) has an atomic mass of 1 g/mol, and there are 4 hydrogen atoms in methane.

Thus, the molar mass of CH₄ is:
\[ \text{Molar mass of CH}_4 = 12 + (1 \times 4) = 12 + 4 = 16 \, \text{g/mol} \]

### Step 3: Use the unitary method to find the heat of combustion per mole
We know that 4 grams of CH₄ releases 2.5 kilocalories. We need to find out how much heat is released when 1 mole (16 grams) of CH₄ is combusted.

Using the unitary method:
- If 4 grams of CH₄ releases 2.5 kilocalories, then 16 grams will release:
\[ \text{Heat from 16 g} = \frac{2.5 \, \text{kcal}}{4 \, \text{g}} \times 16 \, \text{g} \]

Calculating this gives:
\[ \text{Heat from 16 g} = 2.5 \times \frac{16}{4} = 2.5 \times 4 = 10 \, \text{kcal} \]

### Step 4: State the heat of combustion
Since heat is released during combustion, we represent it as a negative value:
\[ \text{Heat of combustion of CH}_4 = -10 \, \text{kcal/mol} \]

### Final Answer
The heat of combustion of methane (CH₄) is \(-10 \, \text{kcal/mol}\).

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