If 1 ml of water contains 20 drops. Then no. of molecules in a drop of water is

Options

A. `6.023 xx 10^(23)` molecules
B. `1.376 xx 10^(26)` molecules
C. `1.667 xx 10^(21)` molecules
D. `4.346 xx 10^(20)` molecules

Explanation

To find the number of molecules in a drop of water, we can follow these steps:

### Step 1: Understand the volume and mass relationship
1 ml of water is equivalent to 1 gram of water at 4 degrees Celsius.

### Step 2: Determine the mass of water in one drop
Since 1 ml of water contains 20 drops, the mass of water in one drop can be calculated as:
\[ \text{Mass of water in one drop} = \frac{1 \text{ gram}}{20 \text{ drops}} = 0.05 \text{ grams} \]

### Step 3: Use the molar mass of water
The molar mass of water (H₂O) is approximately 18 grams/mol. This means that 18 grams of water contains Avogadro's number of molecules, which is \(6.022 \times 10^{23}\) molecules.

### Step 4: Calculate the number of molecules in 0.05 grams of water
To find the number of molecules in 0.05 grams of water, we can set up a proportion based on the molar mass:
\[ \text{Number of molecules in 0.05 grams} = \left(\frac{0.05 \text{ grams}}{18 \text{ grams}}\right) \times 6.022 \times 10^{23} \text{ molecules} \]

### Step 5: Perform the calculation
Calculating the number of molecules:
\[ \text{Number of molecules} = \left(\frac{0.05}{18}\right) \times 6.022 \times 10^{23} \approx 1.67 \times 10^{21} \text{ molecules} \]

### Conclusion
Thus, the number of molecules in a drop of water is approximately \(1.67 \times 10^{21}\) molecules.

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