The heat capacity of a bomb calorimeter is `500J//^@C.` When 0.1 g of a methane was burnt in this calorimeter, the temperature rose by `2^@C` . The value of `DeltaE` per mole will be

Options

A. `+10kJ`
B. `-10kJ`
C. `+160kJ`
D. `-160kJ`

Answer

To solve the problem, we need to find the value of ΔE (change in internal energy) per mole when 0.1 g of methane is burnt in a bomb calorimeter.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Heat capacity of the bomb calorimeter, \( C = 500 \, \text{J/°C} \)
- Mass of methane burnt, \( m = 0.1 \, \text{g} \)
- Temperature rise, \( \Delta T = 2 \, \text{°C} \)

2. **Calculate the Heat Released (q)**:
The heat released by the combustion can be calculated using the formula:
\[ q = C \times \Delta T \]
Substituting the values:
\[ q = 500 \, \text{J/°C} \times 2 \, \text{°C} = 1000 \, \text{J} \]

3. **Determine the Heat Released per Gram of Methane**:
Since 0.1 g of methane releases 1000 J, we can find the heat released per gram:
\[ \text{Heat released per gram} = \frac{1000 \, \text{J}}{0.1 \, \text{g}} = 10000 \, \text{J/g} \]

4. **Calculate the Heat Released per Mole of Methane**:
The molar mass of methane (CH₄) is approximately 16 g/mol. Therefore, the heat released per mole is:
\[ \text{Heat released per mole} = 10000 \, \text{J/g} \times 16 \, \text{g/mol} = 160000 \, \text{J/mol} \]

5. **Convert to Kilojoules**:
To convert joules to kilojoules, we divide by 1000:
\[ \text{Heat released per mole} = \frac{160000 \, \text{J/mol}}{1000} = 160 \, \text{kJ/mol} \]

6. **Determine the Sign of ΔE**:
Since heat is released in the process, ΔE will be negative:
\[ \Delta E = -160 \, \text{kJ/mol} \]

### Final Answer:
\[ \Delta E = -160 \, \text{kJ/mol} \]