To determine the net ionic equation for the given chemical reaction [tex]\( Mg(OH)_2 + 2 HNO_3 \longrightarrow Mg(NO_3)_2 + 2 H_2O \)[/tex], we first need to break down each compound into its constituent ions and identify the spectator ions.
1. Write the complete ionic equation:
Dissociate all strong electrolytes (soluble ionic compounds, strong acids, and strong bases) into their ions:
[tex]\[
Mg(OH)_2 (s) + 2 HNO_3 (aq) \rightarrow Mg^{2+} (aq) + 2 NO_3^- (aq) + 2 H_2O (l)
\][/tex]
However, because [tex]\( Mg(OH)_2 \)[/tex] is slightly soluble, it should not be completely dissociated. For the purposes of finding the net ionic equation, we'll focus on the major dissociated species.
2. Identify and remove the spectator ions:
Spectator ions appear on both sides of the equation without undergoing any change. In this case, [tex]\( Mg^{2+} \)[/tex] and [tex]\( NO_3^- \)[/tex] ions are spectators:
[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]
Remove the spectator ions:
[tex]\[
Mg(OH)_2 (s) + 2 H^+ (aq) \rightarrow Mg^{2+} (aq) + 2 H_2O (l)
\][/tex]
3. Simplify to the net ionic equation:
The focus should be on the ions that change during the reaction. Upon further consideration, since [tex]\( Mg(OH)_2 \)[/tex] does not completely dissociate, we simplify to:
[tex]\[
2OH^- (aq) + 2H^+ (aq) \rightarrow 2 H_2O (l)
\][/tex]
Dividing by 2 for simplicity:
[tex]\[
H^+ (aq) + OH^- (aq) \rightarrow H_2O (l)
\][/tex]
So, the net ionic equation is:
[tex]\[
H^+ (aq) + OH^- (aq) \rightarrow H_2O (l)
\][/tex]
Thereby, the correct net ionic equation matches the given option:
[tex]\[
\boxed{H^+ + OH^- \rightarrow H_2O}
\][/tex]
Thus, "H^+ + OH^- \longrightarrow H_2O" is the correct net ionic equation.
