Certainly! Let's consider the given chemical equation:
[tex]\[ 2 \, \text{AgNO}_3 + \text{K}_2\text{SO}_4 \rightarrow \text{Ag}_2\text{SO}_4 + \text{ ? } \][/tex]
This is a double displacement reaction where the ions of the reacting compounds exchange their partners to form new compounds.
### Step-by-Step Solution:
1. Identify Reactants and Products:
- Reactants:
- Silver nitrate ([tex]\(\text{AgNO}_3\)[/tex])
- Potassium sulfate ([tex]\(\text{K}_2\text{SO}_4\)[/tex])
- Products:
- Silver sulfate ([tex]\(\text{Ag}_2\text{SO}_4\)[/tex])
- The other product needs to be determined.
2. Determine the Ionic Forms:
- Silver nitrate ([tex]\(\text{AgNO}_3\)[/tex]) dissociates into [tex]\(\text{Ag}^+\)[/tex] and [tex]\(\text{NO}_3^-\)[/tex].
- Potassium sulfate ([tex]\(\text{K}_2\text{SO}_4\)[/tex]) dissociates into [tex]\(\text{K}^+\)[/tex] and [tex]\(\text{SO}_4^{2-}\)[/tex].
3. Recombine the Ions:
- [tex]\(\text{Ag}^+\)[/tex] will combine with [tex]\(\text{SO}_4^{2-}\)[/tex] to form silver sulfate ([tex]\(\text{Ag}_2\text{SO}_4\)[/tex]).
- [tex]\(\text{K}^+\)[/tex] will combine with [tex]\(\text{NO}_3^-\)[/tex] to form potassium nitrate ([tex]\(\text{KNO}_3\)[/tex]).
4. Balance the Chemical Equation:
- Start by writing the unbalanced equation:
[tex]\[ \text{AgNO}_3 + \text{K}_2\text{SO}_4 \rightarrow \text{Ag}_2\text{SO}_4 + \text{KNO}_3 \][/tex]
- Balance the silver (Ag) atoms:
[tex]\[ 2 \, \text{AgNO}_3 + \text{K}_2\text{SO}_4 \rightarrow \text{Ag}_2\text{SO}_4 + \text{KNO}_3 \][/tex]
- Now balance the potassium (K) atoms by ensuring that the potassium atoms on both sides are equal:
[tex]\[ 2 \, \text{AgNO}_3 + \text{K}_2\text{SO}_4 \rightarrow \text{Ag}_2\text{SO}_4 + 2 \, \text{KNO}_3 \][/tex]
### Final Equation:
[tex]\[ 2 \, \text{AgNO}_3 + \text{K}_2\text{SO}_4 \rightarrow \text{Ag}_2\text{SO}_4 + 2 \, \text{KNO}_3 \][/tex]
Thus, the other product formed during the reaction of silver nitrate ([tex]\(\text{AgNO}_3\)[/tex]) and potassium sulfate ([tex]\(\text{K}_2\text{SO}_4\)[/tex]) is:
[tex]\[ \boxed{2 \, \text{KNO}_3} \][/tex]
So, the correct choice is [tex]\(2 \, \text{KNO}_3\)[/tex], which corresponds to option 2.
