Problem 146 - General Chemistry

Question

Two samples of \(1.00 \mathrm{M} \mathrm{HCl}\) of equivalent volumes are prepared. One sample is titrated to the equivalence point with a \(1.00 \mathrm{M}\) solution of sodium hydroxide, while the other sample is titrated to the equivalence point with a \(1.00 M\) solution of calcium hydroxide. a. Compare the volumes of sodium hydroxide and calcium hydroxide required to reach the equivalence point for each titration. b. Determine the \(\mathrm{pH}\) of each solution halfway to the equivalence point. c. Determine the \(\mathrm{pH}\) of each solution at the equivalence point.

Step-by-Step Solution

Answer

a. Equal volumes for NaOH; half volume for Ca(OH)2. b. Low, close to neutral halfway. c. Neutral (pH 7) at equivalence point.

Step 1: Understand the Reaction Equations

First, recognize the chemical reactions: - For HCl and NaOH, the reaction is: \[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \] This indicates a 1:1 molar ratio.- For HCl and Ca(OH)2, the reaction is: \[ 2\text{HCl} + \text{Ca(OH)}_2 \rightarrow \text{CaCl}_2 + 2\text{H}_2\text{O} \] This indicates a 2:1 molar ratio.

Step 2: Calculate Volume Ratios for Equivalence Point

For NaOH, since the reaction is 1:1, the volume of NaOH required to reach the equivalence point is equal to the volume of the HCl sample. For Ca(OH)2, since the reaction is 2:1, the volume of Ca(OH)2 required is half the volume of the HCl sample.

Step 3: Determine pH Halfway to Equivalence Point

Halfway to the equivalence point means half of the acid has been neutralized. For both titrations, when half of the HCl is neutralized, the pH is determined by the remaining concentration of HCl and is nearly neutral. Thus, the pH halfway to the equivalence point is lower than 7, but close, because of the remaining strong acid.

Step 4: Determine pH at the Equivalence Point

At the equivalence point for a strong acid with a strong base, the solution is neutral since the acid and base completely neutralize each other. Therefore, the pH at the equivalence point for both titrations is 7 as pure water remains.

Key Concepts

Equivalence Point

When we talk about the equivalence point in titrations, we're looking at a crucial moment during the process. It is where the amount of titrant added perfectly reacts with the analyte in the solution, meaning their molar amounts are equal according to the balanced chemical equation. In other words, the acid and the base have neutralized each other completely.

Specific to this exercise, we have two different titrations. For the HCl and NaOH titration, the reaction is 1:1. This means the equivalence point is reached when one mole of NaOH neutralizes one mole of HCl. Hence, the volume of NaOH needed is equal to the volume of HCl if the concentrations are the same.

For the HCl and Ca(OH)₂ titration, the stoichiometry is 2:1. Here, two moles of HCl react with one mole of Ca(OH)₂. Therefore, only half the volume of Ca(OH)₂ is needed compared to the volume of HCl. Each equivalence point represents the precise moment when amounts of acid and base match in the correct stoichiometric ratios, ensuring complete neutralization.

Neutralization Reaction

A neutralization reaction is a type of chemical reaction where an acid and a base react to form water and a salt. This is a fundamental concept in acid-base chemistry and is the basis for titration experiments.

For instance, when HCl, a strong acid, is titrated with NaOH, a strong base, they react to form water and NaCl, a neutral salt. The balanced chemical equation is: \[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]This balanced equation shows a 1:1 molar ratio of HCl to NaOH.

• The strong acid and strong base completely neutralize each other, leaving a neutral solution at the equivalence point.

Similarly, when HCl is titrated with Ca(OH)₂, the reaction equation is: \[ 2\text{HCl} + \text{Ca(OH)}_2 \rightarrow \text{CaCl}_2 + 2\text{H}_2\text{O} \], indicating a 2:1 molar ratio. This reaction showcases how two moles of HCl are needed to neutralize one mole of Ca(OH)₂, again leading to a neutral pH at the equivalence point.

pH Calculation

Calculating pH during a titration is essential for understanding the reaction progress. pH is a measure of the acidity or alkalinity of a solution. It is typically calculated using the formula:\[pH = -\log [\text{H}^+]\]At different points of titration, the pH of the solution will vary based on the extent of neutralization.

• Halfway to the equivalence point in our exercise, for both titrations, half of the HCl has reacted with the base. The At the equivalence point, since both titrations involve strong acids and bases, the reactions are completely neutralized, thus converting all reactants to products with no excess H⁺ or OH⁻ ions left in the solution. Consequently, the resulting pH at the equivalence point for both titrations will be neutral, around pH 7, signifying the formation of neutral water and salt.

Understanding pH changes at these critical points help us apply theoretical principles to predict and interpret real-life titration results effectively.