To find the net ionic equation, we need to follow these steps:
1. Write the balanced molecular equation:
[tex]\[ Mg(OH)_2 + 2 HNO_3 \rightarrow Mg(NO_3)_2 + 2 H_2O \][/tex]
2. Separate the strong electrolytes into their ions:
[tex]\[ Mg(OH)_2(s) + 2 H^+(aq) + 2 NO_3^-(aq) \rightarrow Mg^{2+}(aq) + 2 NO_3^-(aq) + 2 H_2O(l) \][/tex]
Note that [tex]\( Mg(OH)_2 \)[/tex] is a slightly soluble compound, so it will be represented in its solid form.
3. Identify and cancel the spectator ions:
Spectator ions are those ions that appear unchanged on both sides of the equation. In this case, [tex]\( NO_3^- \)[/tex] and [tex]\( Mg^{2+} \)[/tex] appear on both sides.
[tex]\[ Mg(OH)_2(s) + 2 H^+(aq) + 2 NO_3^-(aq) \rightarrow Mg^{2+}(aq) + 2 NO_3^-(aq) + 2 H_2O(l) \][/tex]
4. Write the net ionic equation:
Remove the spectator ions:
[tex]\[ Mg(OH)_2(s) + 2 H^+(aq) \rightarrow Mg^{2+}(aq) + 2 H_2O(l) \][/tex]
However, we often write simpler net ionic equations for reactions involving hydroxide and hydrogen ions (acids and bases) because the primary reaction between them is the formation of water. Hence, for the reaction involving [tex]\( H^+ \)[/tex] and [tex]\( OH^- \)[/tex]:
[tex]\[ H^+(aq) + OH^-(aq) \rightarrow H_2O(l) \][/tex]
Thus, the net ionic equation is:
[tex]\[ H^+ + OH^- \rightarrow H_2O \][/tex]
So, the correct answer is:
[tex]\[ H^+ + OH^- \longrightarrow H _2 O \][/tex]
