The number of molecules in `22.4 cm^3` of dinitrogen gas at STP is

Options

A. `6.002 xx 10^20`
B. `6.022 xx 10^23`
C. `22.4 xx 10^20`
D. `22.4 xx 10^23`

Answer

To find the number of molecules in `22.4 cm³` of dinitrogen gas at STP, we can follow these steps:

### Step 1: Convert cm³ to L
First, we need to convert the volume from cubic centimeters (cm³) to liters (L). We know that:
1 L = 1000 cm³

So,
\[ 22.4 \, \text{cm}^3 = \frac{22.4}{1000} \, \text{L} = 0.0224 \, \text{L} \]

### Step 2: Determine the number of moles
At Standard Temperature and Pressure (STP), 1 mole of any gas occupies 22.4 L. We can use this information to find the number of moles in 0.0224 L.

Using the unitary method:
\[ \text{Number of moles} = \frac{0.0224 \, \text{L}}{22.4 \, \text{L/mole}} = 0.001 \, \text{moles} \]

### Step 3: Calculate the number of molecules
We know that 1 mole of any substance contains Avogadro's number of molecules, which is approximately \( 6.022 \times 10^{23} \) molecules/mole.

To find the number of molecules in 0.001 moles:
\[ \text{Number of molecules} = 0.001 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \]

Calculating this gives:
\[ \text{Number of molecules} = 6.022 \times 10^{20} \, \text{molecules} \]

### Final Answer
The number of molecules in `22.4 cm³` of dinitrogen gas at STP is \( 6.022 \times 10^{20} \) molecules.

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