To determine how many moles of [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex] are present in 200.0 mL of a 0.500 M solution of [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex], we need to follow these steps:
1. Convert the volume from milliliters (mL) to liters (L):
[tex]\[
200.0 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.200 \text{ L}
\][/tex]
2. Use the definition of molarity (M) which is moles of solute per liter of solution:
[tex]\[
\text{Molarity} (M) = \frac{\text{moles of solute}}{\text{liters of solution}}
\][/tex]
3. Calculate the number of moles of [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex]:
Given the molarity of the solution is 0.500 M, and the volume of the solution is 0.200 L, the number of moles of [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex] is:
[tex]\[
\text{moles of } \text{Al}_2(\text{SO}_4)_3 = 0.500 \text{ M} \times 0.200 \text{ L} = 0.100 \text{ moles}
\][/tex]
Therefore, there are 0.100 moles of [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex] present in 200.0 mL of a 0.500 M solution.
