Current Attempt in Progress Bomb calorimetry is the classic method for determining the calories in our foods. A 1.50 g sample of pure sucrose is burned in a bomb calorimeter that has a heat capacity of $$ 8.930 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} $$. The temperature of the water jacket rises from $$ 24.00^{\circ} \mathrm{C} $$ to $$ 26.77^{\circ} \mathrm{C} $$. What is $$ riangle E $$ for the combustion of 1 mol of sucrose, $$ \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11} $$ ? i i $$ \quad \mathrm{kJ} \mathrm{mol}{ }^{-1} $$

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Current Attempt in Progress Bomb calorimetry is the classic method for determining the calories in our foods. A 1.50 g sample of pure sucrose is burned in a bomb calorimeter that has a heat capacity of $$ 8.930 \mathrm{~kJ} /{ }^{\circ} \mathrm{C} $$. The temperature of the water jacket rises from $$ 24.00^{\circ} \mathrm{C} $$ to $$ 26.77^{\circ} \mathrm{C} $$. What is $$ 	riangle E $$ for the combustion of 1 mol of sucrose, $$ \mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11} $$ ? i i $$ \quad \mathrm{kJ} \mathrm{mol}{ }^{-1} $$

UpStudy AI · Accepted Answer

To calculate the change in energy ($$ \Delta E $$) for the combustion of 1 mol of sucrose, we can follow these steps:

1. **Calculate the heat absorbed by the calorimeter** using the formula:
   $$
   q = C \times \Delta T
   $$
   where:
   - $$ q $$ is the heat absorbed (in kJ),
   - $$ C $$ is the heat capacity of the calorimeter (in kJ/°C),
   - $$ \Delta T $$ is the change in temperature (in °C).

2. **Determine the number of moles of sucrose** in the 1.50 g sample.

3. **Calculate $$ \Delta E $$ per mole of sucrose** by dividing the total heat absorbed by the number of moles of sucrose.

### Step 1: Calculate the heat absorbed by the calorimeter

Given:
- $$ C = 8.930 \, \text{kJ/°C} $$
- Initial temperature $$ T_i = 24.00 \, °C $$
- Final temperature $$ T_f = 26.77 \, °C $$

Calculate $$ \Delta T $$:
$$
\Delta T = T_f - T_i = 26.77 \, °C - 24.00 \, °C = 2.77 \, °C
$$

Now calculate $$ q $$:
$$
q = C \times \Delta T = 8.930 \, \text{kJ/°C} \times 2.77 \, °C = 24.77 \, \text{kJ}
$$

### Step 2: Determine the number of moles of sucrose

The molar mass of sucrose ($$ \text{C}_{12}\text{H}_{22}\text{O}_{11} $$) is calculated as follows:
- Carbon (C): $$ 12 \times 12.01 \, \text{g/mol} = 144.12 \, \text{g/mol} $$
- Hydrogen (H): $$ 22 \times 1.008 \, \text{g/mol} = 22.176 \, \text{g/mol} $$
- Oxygen (O): $$ 11 \times 16.00 \, \text{g/mol} = 176.00 \, \text{g/mol} $$

Total molar mass of sucrose:
$$
\text{Molar mass} = 144.12 + 22.176 + 176.00 = 342.296 \, \text{g/mol}
$$

Now calculate the number of moles in the 1.50 g sample:
$$
\text{moles of sucrose} = \frac{1.50 \, \text{g}}{342.296 \, \text{g/mol}} \approx 0.00438 \, \text{mol}
$$

### Step 3: Calculate $$ \Delta E $$ per mole of sucrose

Now we can find $$ \Delta E $$ for the combustion of 1 mol of sucrose:
$$
\Delta E = \frac{q}{\text{moles of sucrose}} = \frac{24.77 \, \text{kJ}}{0.00438 \, \text{mol}} \approx 5655.68 \, \text{kJ/mol}
$$

### Final Answer

Thus, the change in energy ($$ \Delta E $$) for the combustion of 1 mol of sucrose is approximately:
$$
\Delta E \approx 5655.68 \, \text{kJ/mol}
$$
The change in energy ($$ \Delta E $$) for the combustion of 1 mol of sucrose is approximately 5655.68 kJ/mol.

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