Average volume available to a molecule in a sample of ideal gas at S.T.P. is

Options

A. `3.72 xx 10^(-20) cm^(3)`
B. `2.69 xx 10^(19) cm^(3)`
C. `22400 cm^(3)`
D. `22400 xx 6.02 xx 10^(23) cm^(3)`

Explanation

To find the average volume available to a molecule in a sample of ideal gas at Standard Temperature and Pressure (S.T.P.), we can follow these steps:

### Step-by-Step Solution:

1. **Understand Standard Temperature and Pressure (S.T.P.):**
- At S.T.P., the volume of one mole of an ideal gas is 22,400 cm³ (or 22.4 liters).

2. **Use Avogadro's Number:**
- Avogadro's number (N_A) is approximately \(6.022 \times 10^{23}\) molecules/mole. This number tells us how many molecules are in one mole of any substance.

3. **Calculate the Volume per Molecule:**
- To find the average volume available to one molecule, we need to divide the total volume of one mole of gas by Avogadro's number.
- The formula is:
\[ \text{Volume per molecule} = \frac{\text{Volume of 1 mole}}{N_A} \]
- Substituting the known values:
\[ \text{Volume per molecule} = \frac{22,400 \, \text{cm}^3}{6.022 \times 10^{23}} \]

4. **Perform the Calculation:**
- First, calculate \( \frac{22,400}{6.022} \):
\[ \frac{22,400}{6.022} \approx 3.72 \times 10^{-20} \, \text{cm}^3 \]

5. **Final Answer:**
- Therefore, the average volume available to a molecule in a sample of ideal gas at S.T.P. is approximately \(3.72 \times 10^{-20} \, \text{cm}^3\).