The number of molecules present in `1.12xx10^(-7)c c ` of a gas at STP is

Options

A. `6.02xx10^(23)`
B. `3.01xx10^(12)`
C. `6.02xx10^(22)`
D. `3.01xx10^(23)`

Explanation

To find the number of molecules present in \(1.12 \times 10^{-7} \, \text{cm}^3\) of a gas at STP (Standard Temperature and Pressure), we can follow these steps:

### Step 1: Understand the volume of one mole of gas at STP
At STP, one mole of an ideal gas occupies a volume of \(22.4 \, \text{L}\) or \(22400 \, \text{cm}^3\).

### Step 2: Calculate the number of moles in the given volume
To find the number of moles (\(n\)) in the given volume (\(V\)), we can use the formula:

\[ n = \frac{V}{V_m} \]

where \(V_m\) is the molar volume at STP.

Given:
- \(V = 1.12 \times 10^{-7} \, \text{cm}^3\)
- \(V_m = 22400 \, \text{cm}^3\)

Substituting the values:

\[ n = \frac{1.12 \times 10^{-7} \, \text{cm}^3}{22400 \, \text{cm}^3} = 5 \times 10^{-12} \, \text{moles} \]

### Step 3: Calculate the number of molecules
To find the number of molecules (\(N\)), we can use Avogadro's number (\(N_A\)), which is approximately \(6.022 \times 10^{23} \, \text{molecules/mole}\).

The formula to calculate the number of molecules is:

\[ N = n \times N_A \]

Substituting the values:

\[ N = 5 \times 10^{-12} \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \]

Calculating this gives:

\[ N \approx 3.01 \times 10^{12} \, \text{molecules} \]

### Final Answer
The number of molecules present in \(1.12 \times 10^{-7} \, \text{cm}^3\) of gas at STP is approximately \(3.01 \times 10^{12}\) molecules.

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