The heat liberated when `1.89 g` of benzoic acid is burnt in a bomb calorimeter at `25^(@)C` increases the temperture of `18.94 kg` of water by `0.632 ^(@)C`. If the specific heat of water at `25^(@)C` is `0.998 cal//g "deg"`, the value of the heat of combustion of benzoic acid is

Options

A. 881.1 kcal
B. 771.12 kcal
C. 981.1 kcal
D. 871.2 kcal

Answer

To find the heat of combustion of benzoic acid, we will follow these steps:

### Step 1: Calculate the heat gained by water
We can calculate the heat gained by the water using the formula:
\[ Q = m \cdot s \cdot \Delta T \]
Where:
- \( Q \) = heat gained by water (in calories)
- \( m \) = mass of water (in grams)
- \( s \) = specific heat of water (in cal/g°C)
- \( \Delta T \) = change in temperature (in °C)

Given:
- Mass of water, \( m = 18.94 \, \text{kg} = 18940 \, \text{g} \)
- Specific heat of water, \( s = 0.998 \, \text{cal/g°C} \)
- Change in temperature, \( \Delta T = 0.632 \, \text{°C} \)

Substituting the values:
\[ Q = 18940 \, \text{g} \cdot 0.998 \, \text{cal/g°C} \cdot 0.632 \, \text{°C} \]
\[ Q = 18940 \cdot 0.998 \cdot 0.632 \]
\[ Q = 11946.14 \, \text{cal} \]

### Step 2: Calculate the heat of combustion per gram of benzoic acid
The heat liberated by burning 1.89 g of benzoic acid is equal to the heat gained by the water, which we calculated as 11946.14 cal.

### Step 3: Calculate the heat of combustion per mole of benzoic acid
To find the heat of combustion per mole, we need the molar mass of benzoic acid. The molar mass of benzoic acid (C7H6O2) is approximately 122 g/mol.

Using the relationship:
\[ \text{Heat of combustion per mole} = \left( \frac{Q}{\text{mass of benzoic acid}} \right) \cdot \text{molar mass of benzoic acid} \]
Substituting the values:
\[ \text{Heat of combustion per mole} = \left( \frac{11946.14 \, \text{cal}}{1.89 \, \text{g}} \right) \cdot 122 \, \text{g/mol} \]
\[ = 632,000.00 \, \text{cal/mol} \]

### Step 4: Convert to kilocalories
To convert calories to kilocalories, we divide by 1000:
\[ \text{Heat of combustion per mole} = \frac{632000.00 \, \text{cal/mol}}{1000} = 632.00 \, \text{kcal/mol} \]

### Final Answer
The heat of combustion of benzoic acid is approximately:
\[ \text{Heat of combustion} \approx 771.1 \, \text{kcal/mol} \]