How many number of molecules and atoms respectively are present in 2.8 liters of a diatomic gas at STP ?

Options

A. `6.023xx10^23, 7.5xx10^23`
B. `6.023xx10^23, 15xx10^22`
C. `7.5xx10^22, 15xx10^22`
D. `15xx10^22, 7.5xx10^23`

Explanation

To find the number of molecules and atoms in 2.8 liters of a diatomic gas at STP (Standard Temperature and Pressure), we can follow these steps:

### Step 1: Determine the number of moles of the gas
At STP, 1 mole of any gas occupies 22.4 liters. We can calculate the number of moles (n) in 2.8 liters using the formula:

\[ n = \frac{\text{Volume}}{\text{Molar Volume at STP}} = \frac{2.8 \, \text{liters}}{22.4 \, \text{liters/mole}} \]

Calculating this gives:

\[ n = \frac{2.8}{22.4} \approx 0.125 \, \text{moles} \]

### Step 2: Calculate the number of molecules
Using Avogadro's number (N_A), which is approximately \(6.022 \times 10^{23}\) molecules/mole, we can find the number of molecules (N):

\[ N = n \times N_A = 0.125 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \]

Calculating this gives:

\[ N \approx 0.125 \times 6.022 \approx 0.75 \times 10^{23} \, \text{molecules} \]

### Step 3: Determine the number of atoms
Since the gas is diatomic (A2), each molecule contains 2 atoms. Therefore, the total number of atoms (A) can be calculated as:

\[ A = N \times 2 = (0.75 \times 10^{23}) \times 2 \]

Calculating this gives:

\[ A \approx 1.5 \times 10^{23} \, \text{atoms} \]

### Final Answer
Thus, in 2.8 liters of a diatomic gas at STP, there are approximately:
- **Number of molecules**: \(0.75 \times 10^{23}\)
- **Number of atoms**: \(1.5 \times 10^{23}\)