Ice crystallises in hexagonal lattice having volume of unit cell is `132times10^(-24)cm^(3)`.If density is 0.92g `cm^(3)`at a given temperature, then number of water molecules per unit cell is

Options

A. 1
B. 2
C. 3
D. 4

Answer

To find the number of water molecules per unit cell in ice, we can follow these steps:

### Step 1: Calculate the Mass of the Unit Cell
We know the formula for density:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
From this, we can rearrange to find the mass:
\[ \text{Mass} = \text{Density} \times \text{Volume} \]
Given:
- Volume of the unit cell = \(132 \times 10^{-24} \, \text{cm}^3\)
- Density = \(0.92 \, \text{g/cm}^3\)

Substituting the values:
\[ \text{Mass} = 0.92 \, \text{g/cm}^3 \times 132 \times 10^{-24} \, \text{cm}^3 \]
Calculating this:
\[ \text{Mass} = 121.44 \times 10^{-24} \, \text{g} \]

### Step 2: Calculate the Number of Moles of Water
To find the number of moles, we use the molar mass of water (ice), which is approximately \(18 \, \text{g/mol}\):
\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{121.44 \times 10^{-24} \, \text{g}}{18 \, \text{g/mol}} \]
Calculating this gives:
\[ \text{Number of moles} = 6.747 \times 10^{-24} \, \text{mol} \]

### Step 3: Calculate the Number of Molecules
Using Avogadro's number (\(N_A = 6.022 \times 10^{23} \, \text{molecules/mol}\)), we can find the number of molecules:
\[ \text{Number of molecules} = \text{Number of moles} \times N_A \]
Substituting the values:
\[ \text{Number of molecules} = 6.747 \times 10^{-24} \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol} \]
Calculating this gives:
\[ \text{Number of molecules} \approx 4 \]

### Conclusion
Thus, the number of water molecules per unit cell in ice is **4**.

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