Ordinary water contain one part of heavy water per 6000 parts by weight. The number of heavy water molecules present in drop of water of volume 0.01 ml is (Density of water is 1gm/ml)

Options

A. `2.5xx10^(16)`
B. `2.5xx10^(17)`
C. `5xx10^(16)`
D. `7.5xx10^(16)`

Explanation

To solve the problem of finding the number of heavy water (D2O) molecules present in a drop of ordinary water of volume 0.01 ml, we can follow these steps:

### Step 1: Calculate the mass of the water drop
Given:
- Volume of water drop = 0.01 ml
- Density of water = 1 g/ml

Using the formula for mass:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
\[ \text{Mass} = 1 \, \text{g/ml} \times 0.01 \, \text{ml} = 0.01 \, \text{g} \]

### Step 2: Determine the amount of heavy water in the mass of ordinary water
According to the problem, ordinary water contains 1 part of heavy water per 6000 parts by weight. This means:
- For every 6000 g of ordinary water, there is 1 g of heavy water.

To find the amount of heavy water in 0.01 g of ordinary water:
\[ \text{Heavy Water} = \frac{1 \, \text{g of heavy water}}{6000 \, \text{g of ordinary water}} \times 0.01 \, \text{g of ordinary water \]
\[ \text{Heavy Water} = \frac{0.01}{6000} \, \text{g} = 1.6667 \times 10^{-6} \, \text{g} \]

### Step 3: Convert the mass of heavy water to moles
The molecular weight of heavy water (D2O) is approximately 20 g/mol. To find the number of moles of heavy water:
\[ \text{Moles of Heavy Water} = \frac{\text{Mass of Heavy Water}}{\text{Molecular Weight}} \]
\[ \text{Moles of Heavy Water} = \frac{1.6667 \times 10^{-6} \, \text{g}}{20 \, \text{g/mol}} = 8.3335 \times 10^{-8} \, \text{mol} \]

### Step 4: Calculate the number of molecules of heavy water
Using Avogadro's number (approximately \(6.022 \times 10^{23} \, \text{molecules/mol}\)):
\[ \text{Number of Molecules} = \text{Moles} \times \text{Avogadro's Number} \]
\[ \text{Number of Molecules} = 8.3335 \times 10^{-8} \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \]
\[ \text{Number of Molecules} \approx 5.02 \times 10^{16} \]

### Final Answer
The number of heavy water molecules present in a drop of water of volume 0.01 ml is approximately \(5 \times 10^{16}\).

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