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 of calculating the change in internal energy (ΔE) per mole when 0.1 g of methane is burnt in a bomb calorimeter, we can follow these steps:

### Step 1: Calculate the heat released (q) using the heat capacity of the calorimeter.
The formula to calculate the heat released is:
\[ q = C \times \Delta T \]
Where:
- \( C \) is the heat capacity of the calorimeter (500 J/°C).
- \( \Delta T \) is the change in temperature (2 °C).

Substituting the values:
\[ q = 500 \, \text{J/°C} \times 2 \, \text{°C} = 1000 \, \text{J} \]

### Step 2: Determine the amount of heat released per gram of methane.
We know that 0.1 g of methane releases 1000 J of energy. To find the energy released per gram, we can use the following calculation:
\[ \text{Energy per gram} = \frac{1000 \, \text{J}}{0.1 \, \text{g}} = 10000 \, \text{J/g} \]

### Step 3: Calculate the energy released per mole of methane.
The molar mass of methane (CH₄) is calculated as follows:
- Carbon (C) = 12 g/mol
- Hydrogen (H) = 1 g/mol × 4 = 4 g/mol
- Total = 12 + 4 = 16 g/mol

Now, we can find the energy released for 1 mole (16 g) of methane:
\[ \text{Energy for 1 mole} = 10000 \, \text{J/g} \times 16 \, \text{g} = 160000 \, \text{J} \]

### Step 4: Convert the energy from joules to kilojoules.
Since 1 kJ = 1000 J, we can convert the energy:
\[ \text{Energy in kJ} = \frac{160000 \, \text{J}}{1000} = 160 \, \text{kJ} \]

### Final Result
Thus, the value of ΔE per mole of methane is:
\[ \Delta E = -160 \, \text{kJ/mol} \]
(Note: The negative sign indicates that energy is released during combustion.)