The number of molecules in 8.96L of a gas at `0^(@)C` and 1 atmosphere pressure is approximately

Options

A. `6.02xx10^(23)`
B. `12.04xx10^(23)`
C. `18.06xx10^(23)`
D. `24.08xx10^(22)`

Explanation

To find the number of molecules in 8.96 L of a gas at 0°C and 1 atmosphere pressure, we can use the ideal gas law and Avogadro's number. Here’s a step-by-step solution:

### Step 1: Understand the conditions
At standard temperature and pressure (STP), which is defined as 0°C (273 K) and 1 atm pressure, 1 mole of an ideal gas occupies 22.4 L.

### Step 2: Calculate the number of moles
To find the number of moles of gas in 8.96 L, we can use the formula:
\[ \text{Number of moles} = \frac{\text{Volume of gas}}{\text{Molar volume at STP}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{8.96 \, \text{L}}{22.4 \, \text{L/mol}} \approx 0.4 \, \text{moles} \]

### Step 3: Use Avogadro's number to find the number of molecules
Avogadro's number tells us that 1 mole of any substance contains approximately \(6.022 \times 10^{23}\) molecules. Therefore, the number of molecules in 0.4 moles is calculated as follows:
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Number of molecules} = 0.4 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \approx 2.41 \times 10^{23} \, \text{molecules} \]

### Final Answer
The approximate number of molecules in 8.96 L of gas at 0°C and 1 atmosphere pressure is \(2.41 \times 10^{23}\) molecules.

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