How many water molecules are there in one drop of water (volume 0.0018 ml) at room temperature?

Options

A. `6.023xx10^(19)`
B. `1.084xx10^(18)`
C. `6.023xx10^(23)`
D. `4.84xx10^(17)`

Explanation

To find out how many water molecules are in one drop of water with a volume of 0.0018 ml, we can follow these steps:

### Step 1: Determine the mass of water in the drop
We know that the density of water at room temperature is approximately 1 gram per milliliter (g/ml).

Using the formula for density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
we can rearrange this to find the mass:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]

Substituting the values:
\[ \text{Mass} = 1 \, \text{g/ml} \times 0.0018 \, \text{ml} = 0.0018 \, \text{g} \]

### Step 2: Calculate the number of moles of water
Next, we need to convert the mass of water into moles. The molecular mass of water (H₂O) is calculated as follows:
- Hydrogen (H) has an atomic mass of approximately 1 g/mol, and there are 2 hydrogen atoms in water.
- Oxygen (O) has an atomic mass of approximately 16 g/mol.

Thus, the molecular mass of water is:
\[ \text{Molecular mass of H₂O} = 2 \times 1 + 16 = 18 \, \text{g/mol} \]

Now we can calculate the number of moles using the formula:
\[ \text{Moles} = \frac{\text{Mass}}{\text{Molecular mass}} \]
Substituting the values:
\[ \text{Moles} = \frac{0.0018 \, \text{g}}{18 \, \text{g/mol}} = 0.0001 \, \text{mol} \]

### Step 3: Calculate the number of water molecules
To find the number of molecules, we use Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules/mol.

Using the formula:
\[ \text{Number of molecules} = \text{Moles} \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Number of molecules} = 0.0001 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \]
Calculating this gives:
\[ \text{Number of molecules} = 6.022 \times 10^{19} \, \text{molecules} \]

### Final Answer
Thus, the number of water molecules in one drop of water (0.0018 ml) is approximately \(6.022 \times 10^{19}\) molecules.

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