Question

Tartaric acid, \(\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}\), has two acidic hydrogens. The acid is often present in wines and precipitates from solution as the wine ages. A solution containing an unknown concentration of the acid is titrated with \(\mathrm{NaOH}\). It requires \(24.65 \mathrm{~mL}\) of \(0.2500 \mathrm{M} \mathrm{NaOH}\) solution to titrate both acidic protons in \(50.00 \mathrm{~mL}\) of the tartaric acid solution. Write a balanced net ionic equation for the

Short answer

The balanced net ionic equation for the reaction between tartaric acid and sodium hydroxide is: \(2\mathrm{H}^{+} + 2\mathrm{OH}^{-} \rightarrow 2\mathrm{H}_{2}\mathrm{O}\)

Step-by-step solution

Write the balanced chemical equation

Begin by determining the products of the reaction between tartaric acid (\(\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}\)) and sodium hydroxide (\(\mathrm{NaOH}\)). Tartaric acid will donate two protons to sodium hydroxide, resulting in the formation of sodium tartrate (\(\mathrm{Na}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6}\)) and water (\(\mathrm{H}_{2}\mathrm{O}\)). So, the balanced chemical equation is: $$\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6} + 2\mathrm{NaOH} \rightarrow \mathrm{Na}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{6} + 2\mathrm{H}_{2}\mathrm{O}$$

Identify the net ionic equation

Now, we can write the complete ionic equation for this reaction: $$2\mathrm{H}^{+} + \mathrm{C}_{4}\mathrm{H}_{4}\mathrm{O}_{6}^{2-} + 2\mathrm{Na}^{+} + 2\mathrm{OH}^{-} \rightarrow 2\mathrm{Na}^{+} + \mathrm{C}_{4}\mathrm{H}_{4}\mathrm{O}_{6}^{2-} + 2\mathrm{H}_{2}\mathrm{O}$$ Next, we identify the spectator ions, which are ions that do not participate in the reaction. In this case, the spectator ions are the sodium cations (\(2\mathrm{Na}^{+}\)) and the tartrate anions (\(\mathrm{C}_{4}\mathrm{H}_{4}\mathrm{O}_{6}^{2-}\)). We can now eliminate them to obtain the net ionic equation.

Write the balanced net ionic equation

After removing the spectator ions, the balanced net ionic equation becomes: $$2\mathrm{H}^{+} + 2\mathrm{OH}^{-} \rightarrow 2\mathrm{H}_{2}\mathrm{O}$$ The net ionic equation represents the reaction between the acidic protons of tartaric acid and the hydroxide ions from sodium hydroxide, resulting in the formation of water.

Key concepts

Acid-Base Titration

Titration is a common laboratory method of quantitative chemical analysis that is used to determine the unknown concentration of an analyte, in this case, tartaric acid (\( \text{H}_2\text{C}_4\text{H}_4\text{O}_6 \)). During an acid-base titration, a base of known concentration is slowly added to an acid of unknown concentration (or vice versa) until the chemical reaction between the acid and base is complete. This point of completion is known as the equivalence point and can often be determined by a color change from an indicator or by using a pH meter.

In the example of tartaric acid titration with sodium hydroxide (\( \text{NaOH} \)), the goal is to completely neutralize the acidic protons of the tartaric acid. This is measured by the volume of the base (\( \text{NaOH} \)) needed to reach the equivalence point, which helps in calculating the concentration of the tartaric acid solution.

Net Ionic Equations

Net ionic equations are simplified chemical equations that show only the reacting ions in a chemical reaction. These equations exclude spectator ions, which are ions that do not participate in the reaction but are present to maintain charge balance. Net ionic equations thus provide a more clear depiction of the actual chemical changes occurring in a solution.

To derive the net ionic equation of the reaction between tartaric acid and sodium hydroxide, one should first write the balanced complete ionic equation. From there, spectator ions can be identified and removed. As shown in the exercise, after removing the spectator ions, the net ionic equation for the neutralization reaction simplifies to the formation of water from hydrogen and hydroxide ions: \[2\text{H}^{+} + 2\text{OH}^{-} \rightarrow 2\text{H}_2\text{O}\]

Stoichiometry

Stoichiometry is the section of chemistry that pertains to the quantitative relationships between the reactants and products in a chemical reaction. By using the coefficients from a balanced chemical equation, stoichiometry allows chemists to predict the amount of products produced or reactants needed in a given reaction.

In the context of tartaric acid titration, stoichiometry helps to calculate the concentration of the acid based on the volumes and concentrations of the reactants. Since the stoichiometry of the reaction tells us that one molecule of tartaric acid reacts with two hydroxide ions, and we know the volume and molarity of the sodium hydroxide solution used, we can determine the molarity of the unknown tartaric acid solution using the formula: \[ \text{Molarity of Tartaric Acid} = \frac{\text{Moles of NaOH}}{\text{Volume of Tartaric Acid in Liters}} \]

Chemical Equilibrium

Chemical equilibrium refers to the state in which the forward and reverse reactions occur at the same rate, resulting in a stable ratio of products to reactants. In the process of titrating tartaric acid with sodium hydroxide, equilibrium is not the focus because the aim is to drive the reaction to completion.

However, understanding equilibrium principles is important in other contexts, such as predicting the extent of reactions or understanding acid-base dissociation in solutions. The reaction of tartaric acid in wine to form crystals over time is a real-world example where chemical equilibrium principles are at play. These concepts are closely related to Le Chatelier's principle, which predicts how the position of the equilibrium will shift if changes in concentration, pressure, or temperature are applied to the system.