To find the total ionic equation for the given reactions, we need to analyze each reaction and identify the ions involved, along with understanding which ions are the spectators (those which do not participate in the actual reaction).
Let's break it down one by one:
1. Equation 1: [tex]\(H^+ + OH^- \rightarrow H_2O\)[/tex]
This equation directly shows the ions involved in the formation of water:
[tex]\[ H^+ + OH^- \rightarrow H_2O \][/tex]
This equation already represents the ionic form showing the reactant ions combining to form water.
2. Equation 2: [tex]\(HNO_3 + NaOH \rightarrow NaNO_3 + H_2O\)[/tex]
When we write this reaction in ion form, we have:
[tex]\[ H^+ + NO_3^- + Na^+ + OH^- \rightarrow Na^+ + NO_3^- + H_2O \][/tex]
Notice that [tex]\( Na^+ \)[/tex] and [tex]\( NO_3^- \)[/tex] are present on both sides of the equation and do not change during the reaction. They are spectator ions.
3. Equation 3: [tex]\(H^+ + NO_3^- + Na^+ + OH^- \rightarrow Na^+ + NO_3^- + H_2O\)[/tex]
This is essentially the ion form of the second reaction. After canceling out the spectator ions ([tex]\( Na^+ \)[/tex] and [tex]\( NO_3^- \)[/tex]):
[tex]\[ H^+ + OH^- \rightarrow H_2O \][/tex]
It simplifies to the exact same form as the first equation.
4. Equation 4: [tex]\(H^+ + NO_3^- + OH^- \rightarrow NO_3^- + H_2O\)[/tex]
Here, [tex]\( NO_3^- \)[/tex] is present on both sides of the reaction as well, indicating it as a spectator ion.
After analyzing these options step-by-step, we find that the equation that represents the total ionic reaction—excluding spectator ions and focusing only on those participating in the formation of products—is:
[tex]\[ H^+ + OH^- \rightarrow H_2O \][/tex]
Thus, the correct equation representing the total ionic equation is:
[tex]\( H^+ + OH^- \rightarrow H_2O \)[/tex]
Therefore, the answer is:
[tex]\[ \boxed{1} \][/tex]
