If 1 mL of water contains 20 drops, what is the number of water molecules in the one drop of water?
(A=Avogadro number)

Options

A. `(0.5)/18 A`
B. 0.05 A
C. `(0.05)/18 A`
D. 0.5 A

Answer

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

### Step 1: Understand the relationship between volume and mass
We know that 1 mL of water has a mass of approximately 1 gram.

### Step 2: Determine the number of drops in 1 mL
According to the problem, 1 mL of water contains 20 drops.

### Step 3: Calculate the mass of one drop of water
Since 1 mL of water has a mass of 1 gram and contains 20 drops, the mass of one drop of water can be calculated as:
\[ \text{Mass of one drop} = \frac{1 \text{ gram}}{20 \text{ drops}} = 0.05 \text{ grams} \]

### Step 4: Use the molar mass of water to find the number of moles in one drop
The molar mass of water (H₂O) is approximately 18 grams per mole. To find the number of moles in one drop of water, we can use the formula:
\[ \text{Number of moles} = \frac{\text{mass of one drop}}{\text{molar mass}} = \frac{0.05 \text{ grams}}{18 \text{ grams/mole}} \approx 0.00278 \text{ moles} \]

### Step 5: Convert moles to molecules using Avogadro's number
Avogadro's number (A) is approximately \(6.022 \times 10^{23}\) molecules/mole. Therefore, the number of molecules in one drop of water can be calculated as:
\[ \text{Number of molecules} = \text{Number of moles} \times A = 0.00278 \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mole} \]

### Step 6: Calculate the number of molecules
Calculating this gives:
\[ \text{Number of molecules} \approx 1.67 \times 10^{21} \text{ molecules} \]

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

---