To determine the number of molecules in 11.2 liters of gas at Standard Temperature and Pressure (STP), we can follow these steps:
1. Understand the Concept of Molar Volume at STP:
- At STP (Standard Temperature and Pressure), one mole of any ideal gas occupies a volume of 22.4 liters.
2. Determine the Number of Moles:
- To find the number of moles in a given volume of gas, we use the molar volume. The number of moles can be calculated using the formula:
[tex]\[
\text{Number of Moles} = \frac{\text{Volume of Gas}}{\text{Molar Volume}}
\][/tex]
- For our problem, the volume of gas is 11.2 liters, and the molar volume at STP is 22.4 liters per mole.
[tex]\[
\text{Number of Moles} = \frac{11.2 \, \text{liters}}{22.4 \, \text{liters/mole}} = 0.5 \, \text{moles}
\][/tex]
3. Determine the Number of Molecules:
- Avogadro's number ([tex]\(6.022 \times 10^{23}\)[/tex]) gives the number of molecules in one mole of a substance.
- To find the total number of molecules, we multiply the number of moles by Avogadro's number.
[tex]\[
\text{Number of Molecules} = \text{Number of Moles} \times \text{Avogadro's Number}
\][/tex]
- Substituting the values:
[tex]\[
\text{Number of Molecules} = 0.5 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} = 3.011 \times 10^{23} \, \text{molecules}
\][/tex]
Thus, the number of molecules in 11.2 liters of gas at STP is [tex]\(3.011 \times 10^{23}\)[/tex].
Hence, the correct answer is:
(A) [tex]\(3.01 \times 10^{23}\)[/tex]
