How many molecules are there in 10 drops water, if its volume is 0.05 ml per drop and density is 1 g per ml?

Options

A. `1.667xx10^(22)`
B. `1.667xx10^(23)`
C. `6.023xx10^(23)`
D. None

Answer

To solve the question of how many molecules are there in 10 drops of water, we will follow these steps:

### Step 1: Calculate the total volume of water in 10 drops.
Given:
- Volume of one drop = 0.05 mL
- Number of drops = 10

Total volume (V) = Volume of one drop × Number of drops
\[ V = 0.05 \, \text{mL/drop} \times 10 \, \text{drops} = 0.5 \, \text{mL} \]

### Step 2: Calculate the mass of water using its density.
Given:
- Density of water = 1 g/mL

Using the formula:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
\[ \text{Mass} = 1 \, \text{g/mL} \times 0.5 \, \text{mL} = 0.5 \, \text{g} \]

### Step 3: Calculate the number of moles of water.
The molecular mass of water (H₂O) is approximately 18 g/mol.

Using the formula:
\[ \text{Moles} = \frac{\text{Mass}}{\text{Molecular mass}} \]
\[ \text{Moles} = \frac{0.5 \, \text{g}}{18 \, \text{g/mol}} = \frac{0.5}{18} = \frac{1}{36} \, \text{mol} \]

### Step 4: Calculate the number of molecules.
Using Avogadro's number (approximately \( 6.022 \times 10^{23} \) molecules/mol):

Number of molecules = Moles × Avogadro's number
\[ \text{Number of molecules} = \frac{1}{36} \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \]

Calculating this gives:
\[ \text{Number of molecules} = \frac{6.022 \times 10^{23}}{36} \approx 1.67 \times 10^{22} \, \text{molecules} \]

### Final Answer:
The number of molecules in 10 drops of water is approximately \( 1.67 \times 10^{22} \) molecules.

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