The volume of a gas at `0^(@)C` and 760 mm pressure is 22.4 c c. The no . Of molecules present in this volume is

Options

A. `10^(-3)N_(A)`
B. `10^(-4)N_(A)`
C. `10^(-5)N_(A)`
D. `10^(-2)N_(A)`

Answer

To solve the problem of finding the number of molecules present in a volume of gas at 0°C and 760 mm pressure, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Data:**
- Volume (V) = 22.4 cm³
- Pressure (P) = 760 mm Hg = 1 atm
- Temperature (T) = 0°C = 273 K

2. **Convert Volume to Liters:**
- Since the volume is given in cm³, we need to convert it to liters.
- 1 liter = 1000 cm³
- Therefore, \( V = \frac{22.4 \, \text{cm}^3}{1000} = 0.0224 \, \text{L} \)

3. **Use the Ideal Gas Equation:**
- The ideal gas equation is given by:
\[ PV = nRT \]
- Where:
- P = pressure in atm
- V = volume in liters
- n = number of moles
- R = ideal gas constant = 0.0821 L·atm/(K·mol)
- T = temperature in Kelvin

4. **Rearranging the Ideal Gas Equation to Find Moles (n):**
- Rearranging gives:
\[ n = \frac{PV}{RT} \]

5. **Substituting the Values:**
- Substitute P = 1 atm, V = 0.0224 L, R = 0.0821 L·atm/(K·mol), and T = 273 K into the equation:
\[ n = \frac{(1 \, \text{atm}) \times (0.0224 \, \text{L})}{(0.0821 \, \text{L·atm/(K·mol)}) \times (273 \, \text{K})} \]

6. **Calculating the Number of Moles:**
- Calculate the denominator:
\[ 0.0821 \times 273 \approx 22.4143 \]
- Now, calculate n:
\[ n \approx \frac{0.0224}{22.4143} \approx 0.001 \, \text{moles} \]

7. **Calculating the Number of Molecules:**
- To find the number of molecules, use Avogadro's number (\( N_A \approx 6.022 \times 10^{23} \, \text{molecules/mole} \)):
\[ \text{Number of molecules} = n \times N_A = (0.001) \times (6.022 \times 10^{23}) \approx 6.022 \times 10^{20} \, \text{molecules} \]

### Final Answer:
The number of molecules present in the volume of gas is approximately \( 6.022 \times 10^{20} \) molecules.