We are given the unbalanced molecular equation. So first we will have to balance it:
AgNO₃ (aq) + K₂CrO₄ (aq) ⟶ Ag₂CrO₄ (s) + KNO₃ (aq)
We have two atoms of Ag on the right side and just one atom of it on the left. So we can change the coefficient for AgNO₃ and write a 2 there.
2 AgNO₃ (aq) + K₂CrO₄ (aq) ⟶ Ag₂CrO₄ (s) + KNO₃ (aq)
Now we have 2 atoms of K on the left and 2 ions NO₃- on the left, but just one of them on the right. If we change the coefficient for KNO₃ we will balance the equation.
Molecular equation:
2 AgNO₃ (aq) + K₂CrO₄ (aq) ⟶ Ag₂CrO₄ (s) + 2 KNO₃ (aq)
Now we can split these compounds into their ions to determine the total ionic equation.
Total ionic equation:
2 Ag⁺ (aq) + 2 NO₃⁻ (aq) + 2 K⁺ (aq) + CrO₄²⁻ (aq) -----> Ag₂CrO₄ (s) + 2 K⁺ (aq) + 2 NO₃⁻ (aq)
With this equation we can find the spectator ions. They are the ones that are repeated on both sides of the equation.
If we look at the equation we will see that K⁺ and NO₃⁻ are on both sides.
Answer: the spectator ions are K⁺ and NO₃⁻.