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We wish to determine how many moles of [tex]BaSO_4[/tex] form when 50.0 mL of 0.250 M [tex]Al_2(SO_4)_3[/tex] reacts with excess [tex]Ba(NO_3)_2[/tex].

[tex]\[
\begin{array}{l}
3 \, Ba(NO_3)_2(aq) + Al_2(SO_4)_3(aq) \rightarrow 3 \, BaSO_4(s) + 2 \, Al(NO_3)_3(aq)
\end{array}
\][/tex]

In the previous step, you determined:

[tex]\[
0.0125 \, \text{mol} \, Al_2(SO_4)_3 \, \text{react.}
\][/tex]

How many moles of [tex]BaSO_4[/tex] form during the reaction?



Answer :

GinnyAnswer
To determine how many moles of [tex]\( \text{BaSO}_4 \)[/tex] are formed during the reaction, let's follow these steps in detail:

### Step 1: Write the Balanced Chemical Equation
The balanced chemical equation for the reaction is:
[tex]\[ 3 \text{Ba(NO}_3\text{)}_2(aq) + \text{Al}_2(\text{SO}_4)_3(aq) \rightarrow 3 \text{BaSO}_4(s) + 2 \text{Al(NO}_3\text{)}_3(aq) \][/tex]

### Step 2: Calculate the Moles of [tex]\(\text{Al}_2(\text{SO}_4)_3\)[/tex]
Given:
- Volume of [tex]\(\text{Al}_2(\text{SO}_4)_3(aq)\)[/tex] = 50.0 mL
- Concentration of [tex]\(\text{Al}_2(\text{SO}_4)_3(aq)\)[/tex] = 0.250 M

First, convert the volume from mL to L:
[tex]\[ 50.0 \text{ mL} = 0.0500 \text{ L} \][/tex]

Next, use the concentration to calculate the moles of [tex]\(\text{Al}_2(\text{SO}_4)_3\)[/tex]:
[tex]\[ \text{Moles of } \text{Al}_2(\text{SO}_4)_3 = \text{Concentration} \times \text{Volume} \][/tex]
[tex]\[ \text{Moles of } \text{Al}_2(\text{SO}_4)_3 = 0.250 \text{ M} \times 0.0500 \text{ L} \][/tex]
[tex]\[ \text{Moles of } \text{Al}_2(\text{SO}_4)_3 = 0.0125 \text{ mol} \][/tex]

### Step 3: Use Stoichiometry to Determine Moles of [tex]\(\text{BaSO}_4\)[/tex]
From the balanced chemical equation, we see that 1 mole of [tex]\(\text{Al}_2(\text{SO}_4)_3\)[/tex] produces 3 moles of [tex]\(\text{BaSO}_4\)[/tex].

Thus, if we have 0.0125 mol of [tex]\(\text{Al}_2(\text{SO}_4)_3\)[/tex], we can calculate the moles of [tex]\(\text{BaSO}_4\)[/tex] formed as:
[tex]\[ \text{Moles of } \text{BaSO}_4 = 0.0125 \text{ mol} \times 3 \][/tex]
[tex]\[ \text{Moles of } \text{BaSO}_4 = 0.0375 \text{ mol} \][/tex]

### Conclusion
The number of moles of [tex]\(\text{BaSO}_4\)[/tex] that form during the reaction is:
[tex]\[ \boxed{0.0375 \text{ mol}} \][/tex]

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