To determine how many moles of [tex]\( \text{BaSO}_4 \)[/tex] form, let’s refer to the stoichiometry of the balanced chemical equation:
[tex]\[
3 \text{Ba}(\text{NO}_3)_2(aq) + \text{Al}_2(\text{SO}_4)_3(aq) \rightarrow 3 \text{BaSO}_4(s) + 2 \text{Al}(\text{NO}_3)_3(aq)
\][/tex]
From the balanced equation, we can see that 1 mole of [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex] reacts to form 3 moles of [tex]\( \text{BaSO}_4 \)[/tex].
Given the previous calculation:
[tex]\[
0.0125 \, \text{mol} \, \text{Al}_2(\text{SO}_4)_3 \text{ react}
\][/tex]
Using the stoichiometric ratio from the balanced equation:
[tex]\[
\text{Moles of BaSO}_4 \text{ formed} = 3 \times \text{Moles of Al}_2(\text{SO}_4)_3
\][/tex]
Substituting the given moles of [tex]\( \text{Al}_2(\text{SO}_4)_3 \)[/tex]:
[tex]\[
\text{Moles of BaSO}_4 \text{ formed} = 3 \times 0.0125 \, \text{mol}
\][/tex]
[tex]\[
\text{Moles of BaSO}_4 \text{ formed} = 0.0375 \, \text{mol}
\][/tex]
Therefore, the number of moles of [tex]\( \text{BaSO}_4 \)[/tex] formed during the reaction is [tex]\( 0.0375 \, \text{mol} \)[/tex].
