A bomb calorimeter is ideally suited for measuring the heat evolved during a combustion reaction. A sample of sucrose (C12H22O11(s)) in a bomb calorimeter causes the temperature of 345 mL of water to rise from 24.9 o C to 28.3 o C. The heat capacitiy of the calorimeter assembly is 4.90 kj/mol. What is the experimental molar enthalpy of combustion of sucrose in kj/mol

To determine the experimental molar enthalpy of combustion of sucrose using the bomb calorimeter, we need to break the problem into several steps.

### Step 1: Understand the data given
- The sample of sucrose undergoes combustion, which releases heat.
- The heat released raises the temperature of 345 mL (which is equivalent to 345 g, since the density of water is 1 g/mL) of water from 24.9°C to 28.3°C.
- The heat capacity of the calorimeter assembly (including the bomb and water) is 4.90 kJ/°C.
- We want to calculate the molar enthalpy of combustion of sucrose (C₁₂H₂₂O₁₁), which is in units of kJ/mol.

### Step 2: Calculate the total heat absorbed by the calorimeter
The heat absorbed by the calorimeter can be calculated using the formula:

\[
q_{\text{total}} = C_{\text{calorimeter}} \times \Delta T
\]

Where:
- \( C_{\text{calorimeter}} = 4.90 \, \text{kJ/°C} \)
- \( \Delta T \) is the change in temperature of the water, calculated as:
\[
\Delta T = 28.3^\circ \text{C} - 24.9^\circ \text{C} = 3.4^\circ \text{C}
\]

Thus:
\[
q_{\text{total}} = 4.90 \, \text{kJ/°C} \times 3.4^\circ \text{C}
\]

### Step 3: Determine the number of moles of sucrose
We cannot calculate the molar enthalpy until we know the number of moles of sucrose involved. Let's calculate that:

- Molar mass of sucrose (C₁₂H₂₂O₁₁):
\[
M = 12 \times 12.01 + 22 \times 1.008 + 11 \times 16.00 \, \text{g/mol}
\]

Once we know the number of moles of sucrose combusted, we can calculate the experimental molar enthalpy of combustion by dividing the total heat released by the number of moles of sucrose. Let me calculate these values.- The total heat absorbed by the calorimeter is \( q_{\text{total}} = 16.66 \, \text{kJ} \).
- The molar mass of sucrose is approximately \( 342.30 \, \text{g/mol} \).

### Step 4: Calculate the molar enthalpy of combustion
To calculate the molar enthalpy of combustion, we need the mass of sucrose that was combusted. If this information were provided, we would then divide the total heat released by the number of moles of sucrose to find the molar enthalpy.

The molar enthalpy \( \Delta H \) of combustion can be calculated using:

\[
\Delta H = \frac{q_{\text{total}}}{n}
\]

Where \( n \) is the number of moles of sucrose:
\[
n = \frac{\text{mass of sucrose}}{\text{molar mass of sucrose}}
\]

Could you provide the mass of sucrose combusted?

Learn how to calculate the experimental molar enthalpy of combustion of sucrose (C12H22O11) using a bomb calorimeter. This problem involves understanding thermochemistry, heat transfer calculations, and determining the molar enthalpy. Suitable for advanced high school students and chemistry enthusiasts.

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