To determine the number of molecules of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] in a 100 mL solution of [tex]\( 0.02 \, M \text{H}_2\text{SO}_4 \)[/tex], we can follow these steps:
1. Convert the volume from mL to liters:
The volume of the solution is given as 100 mL. To convert this to liters, we use the fact that [tex]\( 1 \)[/tex] liter [tex]\( = 1000 \)[/tex] mL.
[tex]\[
\text{Volume in liters} = \frac{100 \, \text{mL}}{1000} = 0.1 \, \text{L}
\][/tex]
2. Determine the number of moles of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] in the solution:
The molarity (M) of the solution is [tex]\( 0.02 \, M \)[/tex], which means there are [tex]\( 0.02 \)[/tex] moles of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] per liter of solution. So, for [tex]\( 0.1 \, \text{L} \)[/tex] of solution:
[tex]\[
\text{Moles of } \text{H}_2\text{SO}_4 = 0.02 \, \text{mol/L} \times 0.1 \, \text{L} = 0.002 \, \text{mol}
\][/tex]
3. Calculate 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. Therefore, to find the number of molecules in [tex]\( 0.002 \, \text{mol} \)[/tex] of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]:
[tex]\[
\text{Number of molecules} = 0.002 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol}
\][/tex]
[tex]\[
\text{Number of molecules} = 1.2044 \times 10^{21} \, \text{molecules}
\][/tex]
Therefore, the number of molecules of [tex]\( \text{H}_2\text{SO}_4 \)[/tex] in 100 mL of a [tex]\( 0.02 \, M \text{H}_2\text{SO}_4 \)[/tex] solution is [tex]\( 1.2044 \times 10^{21} \)[/tex].
Among the choices provided, this corresponds to option (i):
[tex]\[
(i) \; 12.044 \times 10^{20} \, \text{molecules}
\][/tex]
Thus, the correct answer is:
[tex]\[
(i) \; 12.044 \times 10^{20} \, \text{molecules}
\][/tex]
