To identify the spectator ions in the complete ionic equation, we need to look at the ions that are present on both sides of the equation without undergoing any change. Let's analyze the given complete ionic equation step by step:
[tex]\[
H^+(aq) + Br^-(aq) + K^+(aq) + OH^-(aq) \rightarrow H_2O(l) + K^+(aq) + Br^-(aq)
\][/tex]
1. Identify all ions on both sides:
- On the reactant side: [tex]\( H^+(aq) \)[/tex], [tex]\( Br^-(aq) \)[/tex], [tex]\( K^+(aq) \)[/tex], [tex]\( OH^-(aq) \)[/tex]
- On the product side: [tex]\( K^+(aq) \)[/tex], [tex]\( Br^-(aq) \)[/tex]
2. Identify the species that do not change from reactants to products:
- [tex]\( K^+(aq) \)[/tex] is present on both sides and does not change.
- [tex]\( Br^-(aq) \)[/tex] is also present on both sides and does not change.
These ions ([tex]\( K^+ \)[/tex] and [tex]\( Br^- \)[/tex]) are the spectator ions because they remain unchanged and do not participate directly in the formation of the product.
3. Review the provided options and determine the correct answer:
- [tex]\( H_2O \)[/tex]
- [tex]\( OH^- \)[/tex]
- [tex]\( K^+ \)[/tex]
- none of the answers are correct
- [tex]\( H^+ \)[/tex]
Among these options, [tex]\( K^+ \)[/tex] matches one of the spectator ions we identified.
Therefore, the correct answer is:
[tex]\[ \boxed{K^+} \][/tex]
