The density of water is 1g/mL. Water is the volume occupied by 1 molecule of water ?

Options

A. `1.44xx10^(-23) mL`
B. ` 1mL`
C. `18 mL`
D. `2.88xx10^(-23) mL`

Answer

To find the volume occupied by one molecule of water, we can follow these steps:

### Step 1: Understand the given data
- The density of water is given as 1 g/mL.
- The molar mass of water (H₂O) is 18 g/mol.

### Step 2: Calculate the molar volume of water
The molar volume (Vm) can be calculated using the formula:
\[ Vm = \frac{\text{Molar Mass}}{\text{Density}} \]
Substituting the values:
\[ Vm = \frac{18 \text{ g/mol}}{1 \text{ g/mL}} = 18 \text{ mL/mol} \]

### Step 3: Convert molar volume to cubic centimeters
Since 1 mL is equivalent to 1 cm³, the molar volume is:
\[ Vm = 18 \text{ cm}^3/\text{mol} \]

### Step 4: Use Avogadro's number to find the volume of one molecule
Avogadro's number (Na) is approximately \( 6.022 \times 10^{23} \) molecules/mol. The volume occupied by one molecule of water can be calculated using the formula:
\[ \text{Volume of one molecule} = \frac{Vm}{N_a} \]
Substituting the values:
\[ \text{Volume of one molecule} = \frac{18 \text{ cm}^3/\text{mol}}{6.022 \times 10^{23} \text{ molecules/mol}} \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \text{Volume of one molecule} = \frac{18}{6.022 \times 10^{23}} \approx 2.99 \times 10^{-23} \text{ cm}^3 \]
Rounding it, we can say:
\[ \text{Volume of one molecule} \approx 3 \times 10^{-23} \text{ cm}^3 \]

### Final Answer
The volume occupied by one molecule of water is approximately \( 3 \times 10^{-23} \text{ cm}^3 \).

---