The volume of water molecule is
(Take, density of water is `10^(3) kg m^(-3)` and Avogadro' number `=6 X 10^(23) mole^(-1))

Options

A. `3xx10^(-28)m^(3)`
B. `3xx10^(-29)m^(3)`
C. `1.5xx10^(-28)m^(3)`
D. `1.5xx10^(-29)m^(3)`

Explanation

To find the volume of a water molecule, we will use the relationship between density, mass, and volume. Here’s a step-by-step solution:

### Step 1: Understand the relationship between mass, volume, and density
The formula for density (ρ) is given by:
\[ \rho = \frac{mass}{volume} \]
From this, we can rearrange the formula to find volume:
\[ volume = \frac{mass}{density} \]

### Step 2: Determine the mass of one water molecule
The molar mass of water (H₂O) can be calculated as follows:
- Hydrogen (H) has a molar mass of approximately 1 g/mol, and there are 2 hydrogen atoms in water.
- Oxygen (O) has a molar mass of approximately 16 g/mol.

Thus, the molar mass of water is:
\[ \text{Molar mass of H₂O} = 2 \times 1 + 16 = 18 \text{ g/mol} \]
Converting this to kilograms:
\[ \text{Molar mass of H₂O} = 18 \text{ g/mol} = 0.018 \text{ kg/mol} \]

### Step 3: Calculate the mass of a single water molecule
Using Avogadro's number (\(N_A = 6 \times 10^{23} \text{ molecules/mol}\)), the mass of one water molecule (m) can be calculated as:
\[ m = \frac{0.018 \text{ kg}}{6 \times 10^{23}} = 3 \times 10^{-26} \text{ kg} \]

### Step 4: Substitute the values into the volume formula
Now that we have the mass of one water molecule, we can substitute it into the volume formula. The density of water is given as \(10^3 \text{ kg/m}^3\):
\[ volume = \frac{mass}{density} = \frac{3 \times 10^{-26} \text{ kg}}{10^3 \text{ kg/m}^3} \]

### Step 5: Perform the calculation
Calculating the volume:
\[ volume = 3 \times 10^{-26} \text{ kg} \div 10^3 \text{ kg/m}^3 = 3 \times 10^{-29} \text{ m}^3 \]

### Final Answer
The volume of one water molecule is:
\[ \text{Volume} = 3 \times 10^{-29} \text{ m}^3 \]

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