36 mL of pure water takes 100 sec to evaporate from a vessel when a heater of 806 watt is used. The `DeltaH_("vaporisation")` of `H_(2)O` is (density of water `=1g//c c)`
(a)`40.3 kJ//mol`
(b)`43.2 kJ//mol`
(c)`4.03 kJ//mol`
(d)None of these

Options

A. `40.3 kJ//mol`
B. `43.2 kJ//mol`
C. `4.03 kJ//mol`
D. None of these

Explanation

To solve the problem, we need to calculate the enthalpy of vaporization (\( \Delta H_{vaporization} \)) of water based on the given data. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the Heat Energy (H)
We know that power (P) is related to heat (H) and time (t) by the formula:
\[ H = P \times t \]
Given:
- Power, \( P = 806 \, \text{W} \)
- Time, \( t = 100 \, \text{s} \)

Substituting the values:
\[ H = 806 \, \text{W} \times 100 \, \text{s} = 80600 \, \text{J} \]

### Step 2: Calculate the Mass of Water
We know that mass (m) can be calculated using the formula:
\[ m = \text{density} \times \text{volume} \]
Given:
- Density of water = \( 1 \, \text{g/cm}^3 \)
- Volume = \( 36 \, \text{mL} = 36 \, \text{cm}^3 \)

Substituting the values:
\[ m = 1 \, \text{g/cm}^3 \times 36 \, \text{cm}^3 = 36 \, \text{g} \]

### Step 3: Convert Mass to Moles
To find the number of moles (n) of water, we use the formula:
\[ n = \frac{m}{M} \]
Where \( M \) is the molar mass of water, which is approximately \( 18 \, \text{g/mol} \).

Substituting the values:
\[ n = \frac{36 \, \text{g}}{18 \, \text{g/mol}} = 2 \, \text{mol} \]

### Step 4: Calculate the Enthalpy of Vaporization
The enthalpy of vaporization (\( \Delta H_{vaporization} \)) can be calculated using the formula:
\[ \Delta H_{vaporization} = \frac{H}{n} \]
Substituting the values:
\[ \Delta H_{vaporization} = \frac{80600 \, \text{J}}{2 \, \text{mol}} = 40300 \, \text{J/mol} \]

### Step 5: Convert to kJ/mol
To convert joules to kilojoules, we divide by 1000:
\[ \Delta H_{vaporization} = \frac{40300 \, \text{J/mol}}{1000} = 40.3 \, \text{kJ/mol} \]

### Final Answer
Thus, the enthalpy of vaporization of water is:
\[ \Delta H_{vaporization} = 40.3 \, \text{kJ/mol} \]
The correct option is (a) \( 40.3 \, \text{kJ/mol} \).

---