The heat of combustion of sucrose `(C_12H_22O_11)` is 1350 kcal/mol. How much of heat will be liberated when 161 g of sucrose is burnt ?

Options

A. 26.8 kcal
B. 57.63 kcal
C. 635.5 kcal
D. 52.87 kcal

Explanation

To solve the problem of how much heat will be liberated when 161 g of sucrose is burnt, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the heat of combustion**:
The heat of combustion of sucrose (C₁₂H₂₂O₁₁) is given as 1350 kcal/mol. This means that for every mole of sucrose that is combusted, 1350 kilocalories of heat are released.

2. **Calculate the molar mass of sucrose**:
The molar mass of sucrose can be calculated as follows:
- Carbon (C): 12 g/mol × 12 = 144 g/mol
- Hydrogen (H): 1 g/mol × 22 = 22 g/mol
- Oxygen (O): 16 g/mol × 11 = 176 g/mol
- Total molar mass = 144 + 22 + 176 = 342 g/mol

3. **Determine the number of moles of sucrose in 161 g**:
To find the number of moles of sucrose in 161 g, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{161 \text{ g}}{342 \text{ g/mol}} \approx 0.470 \text{ moles} \]

4. **Calculate the heat released for 161 g of sucrose**:
Now, we can calculate the heat released using the number of moles:
\[ \text{Heat released} = \text{Number of moles} \times \text{Heat of combustion per mole} \]
Substituting the values:
\[ \text{Heat released} = 0.470 \text{ moles} \times 1350 \text{ kcal/mol} \approx 634.5 \text{ kcal} \]

5. **Final result**:
The heat liberated when 161 g of sucrose is burnt is approximately **634.5 kcal**.