Question

Write the formula equation, the overall ionic equation, and the net ionic equation for the neutralization reaction involving aqueous solutions of \(\mathrm{H}_{3} \mathrm{PO}_{4}\) and \(\mathrm{Mg}(\mathrm{OH})_{2}\) . Assume that the solutions are sufficiently dilute so that no precipitates form.

Short answer

Balanced chemical equation: \[ 2 H_3PO_4 (aq) + 3 Mg(OH)_2 (aq) \rightarrow Mg_3(PO_4)_2 (aq) + 6 H_2O (l) \]; Net ionic equation: \[ H^+ (aq) + OH^- (aq) \rightarrow H_2O (l) \].

Step-by-step solution

- Write the Balanced Chemical Equation

The neutralization reaction between phosphoric acid \(H_3PO_4\) and magnesium hydroxide \(Mg(OH)_2\) produces water (H2O) and a salt (Mg3(PO4)2). Write the balanced equation for the reaction:\[ 2 H_3PO_4 (aq) + 3 Mg(OH)_2 (aq) \rightarrow Mg_3(PO_4)_2 (aq) + 6 H_2O (l) \]

- Split into Ions for the Overall Ionic Equation

Represent each reactant and product that is aqueous as ions for the overall ionic equation. Remember that the coefficients from the balanced chemical equation will also apply here:\[ 6 H^+ (aq) + 2 PO_4^{3-} (aq) + 3 Mg^{2+} (aq) + 6 OH^- (aq) \rightarrow 3 Mg^{2+} (aq) + 2 PO_4^{3-} (aq) + 6 H_2O (l) \]

- Identify and Cancel Spectator Ions to Find the Net Ionic Equation

Remove the spectator ions from both sides of the overall ionic equation. Spectator ions appear unchanged on both sides of the equation:Spectator ions: \( Mg^{2+} \) and \( PO_4^{3-} \)Net ionic equation:\[ 6 H^+ (aq) + 6 OH^- (aq) \rightarrow 6 H_2O (l) \]

- Simplify the Net Ionic Equation

Divide every term by 6 to simplify the net ionic equation: \[ H^+ (aq) + OH^- (aq) \rightarrow H_2O (l) \]

Key concepts

Ionic Equations

When learning about chemical reactions, especially those involving neutralization, it is essential to understand ionic equations. These equations show the ions that take part in the reaction, providing a more detailed view compared to the complete balanced equation.

In the given problem, the complete balanced chemical equation for the reaction between phosphoric acid \(\text{H}_3\text{PO}_4\) and magnesium hydroxide \(\text{Mg(OH)}_2\) is:\[ \text{2 H}_3\text{PO}_4(\text{aq}) + 3 \text{Mg(OH)}_2(\text{aq}) \rightarrow \text{Mg}_3(\text{PO}_4)_2(\text{aq}) + 6 \text{H}_2\text{O}(\text{l}) \]This is essentially the formula equation. It highlights the reactants and the products formed.

Next, you represent the dissociated ions of each aqueous compound in what's called the overall ionic equation. Dissociation in water means the compound separates into cations (positively charged ions) and anions (negatively charged ions). Here’s what it looks like for our reaction:\[6 \text{H}^+(\text{aq}) + 2 \text{PO}_4^{3-}(\text{aq}) + 3 \text{Mg}^{2+}(\text{aq}) + 6 \text{OH}^-(\text{aq}) \rightarrow 3 \text{Mg}^{2+}(\text{aq}) + 2 \text{PO}_4^{3-}(\text{aq}) + 6 \text{H}_2\text{O}(\text{l}) \]This representation helps students visualize the particle-level interactions during the reaction.

Net Ionic Equation

To delve deeper into the core of the reaction, we use the net ionic equation. This equation only includes the ions and molecules directly involved in the reaction, excluding spectator ions. Spectator ions do not participate in the actual chemical change. They remain in the same form on both sides of the equation.

In the previous overall ionic equation, look for ions present on both sides without any change. These are our spectator ions:

• \( \text{Mg}^{2+} \)
• \( \text{PO}_4^{3-} \)

Removing these ions, we get the net ionic equation:

\[6 \text{H}^+(\text{aq}) + 6 \text{OH}^-(\text{aq}) \rightarrow 6 \text{H}_2\text{O}(\text{l}) \]This simplifies the reaction to its essentials. The net ionic equation shows simply that acid \( \text{H}^+ \) reacts with base \( \text{OH}^- \) to form water.After simplifying, we get: \(\text{H}^+(\text{aq}) + \text{OH}^-(\text{aq}) \rightarrow \text{H}_2\text{O}(\text{l}) \)” This tells us the fundamental interaction happening during neutralization.

Phosphoric Acid

Phosphoric acid (\( \text{H}_3\text{PO}_4 \) ) is a common triprotic acid, meaning it has three acidic hydrogen atoms that can dissociate. In aqueous solutions, dissociation happens in steps, but in many neutralization reactions, we view it as fully dissociated:

\[ \text{H}_3\text{PO}_4(\text{aq}) \rightarrow 3 \text{H}^+(\text{aq}) + \text{PO}_4^{3-}(\text{aq}) \]Phosphoric acid reacts with bases like magnesium hydroxide (\( \text{Mg(OH)}_2\) ). Magnesium hydroxide is a strong base that dissociates fully in water: \[ \text{Mg(OH)}_2(\text{aq}) \rightarrow \text{Mg}^{2+}(\text{aq}) + 2 \text{OH}^-(\text{aq}) \] When they react, it’s primarily the hydrogen ions (\( \text{H}^+ \) ) from the acid and hydroxide ions (\( \text{OH}^- \) ) from the base that neutralize each other to form water. Understanding the behavior of phosphoric acid in these reactions is key for mastering neutralization concepts.

In summary, focusing on these main ideas will give a comprehensive understanding of neutralization reactions, ionic equations, and the role of specific acids, like phosphoric acid, in such processes.