Calculate Moles and Molecules of Sulfur Dioxide Gas at STP

To find the number of moles and the number of molecules present in $1.4187\text{ L}$ of $\text{SO}_2$ gas at standard temperature and pressure (STP):

1. Calculate the number of moles ($n$): At STP, $1\text{ mole}$ of any ideal gas occupies a molar volume ($V_m$) of $22.4\text{ L}$. The formula relating volume ($V$) and molar volume ($V_m$) is: $n = \frac{V}{V_m}$

Substitute the given volume: $n = \frac{1.4187\text{ L}}{22.4\text{ L mol}^{-1}} \approx 0.06333\text{ mol} \approx 0.0633\text{ mol}$

1. Calculate the number of molecules ($N$): The number of molecules is related to the number of moles by Avogadro's constant ($N_A = 6.022 \times 10^{23}\text{ molecules mol}^{-1}$): $N = n \times N_A$

Substitute the values: $N = 0.06333\text{ mol} \times 6.022 \times 10^{23}\text{ molecules mol}^{-1} \approx 3.812 \times 10^{22}\text{ molecules}$

Therefore, the number of moles and the number of molecules in $1.4187\text{ L}$ of $\text{SO}_2$ gas at STP are $0.0633$ and $3.812 \times 10^{22}$, respectively.

This corresponds to Option B.