Question

A \(0.2481 \mathrm{M}\) solution of \(\mathrm{KOH}\) is used to titrate \(30.00 \mathrm{~mL}\) of \(0.269 \mathrm{M}\) hydrobromic acid. Assume that volumes are additive. (a) Write a balanced net ionic equation for the reaction that takes place during the titration. (b) What are the species present at the equivalence point? (c) What volume of \(\mathrm{KOH}\) is required to reach the equivalence point? (d) What is the \(\mathrm{pH}\) of the solution 1\. before any \(\mathrm{KOH}\) is added? 2\. halfway to the equivalence point? 3\. at the equivalence point?

Short answer

Question: Calculate the volume of KOH required to reach the equivalence point when titrated with a known volume and molarity of HBr and determine the pH at various points in the titration. Answer: The volume of KOH required to reach the equivalence point is approximately 32.56 mL. The pH before adding any KOH is approximately 0.57, the pH halfway to the equivalence point is approximately 0.87, and at the equivalence point, the pH is 7.

Step-by-step solution

Write the balanced net ionic equation for the reaction.

The balanced net ionic equation for the reaction between KOH and HBr is: \[ OH^- (aq) + H^+ (aq) \rightarrow H_2O (l) \] The hydroxide ion (OH-) from KOH reacts with the hydrogen ion (H+) from HBr to form water (H2O).

Identify the species present at the equivalence point.

At the equivalence point, the amount of OH- and H+ ions are equal, leading to a completely neutralized solution. The remaining species in the solution are the potassium ion (K+) and the bromide ion (Br-). Thus, the species present at the equivalence point are K+ and Br-.

Calculate the volume of KOH required to reach the equivalence point.

To find the volume of KOH required to reach the equivalence point, we can use the following formula: \[ M_1V_1 = M_2V_2 \] Where M1 is the molarity of HBr, V1 is its volume, M2 is the molarity of KOH, and V2 is its volume. Plugging in the given information: \[ (0.269 M)(30.00 mL) = (0.2481 M)(V_2) \] Solve for \(V_2\): \[ V_2 = \frac{(0.269)(30)}{0.2481} \approx 32.56\ \text{mL} \] The volume of KOH required to reach the equivalence point is approximately 32.56 mL.

Step 4.1: Calculate the pH before any KOH is added.

The pH before adding any KOH is determined by the concentration of the HBr solution. Use the formula: \[ pH = -\log[H^+] \] Plug in the molarity of HBr (0.269 M) as the concentration of H+ ions: \[ pH = -\log(0.269) \approx 0.57 \] The pH before adding any KOH is approximately 0.57.

Step 4.2: Calculate the pH halfway to the equivalence point.

Halfway to the equivalence point, half of the H+ ions have reacted with OH- ions. The new concentration of H+ ions is half of the initial concentration: \[ [H^+] = \frac{0.269}{2} = 0.1345\ \text{M} \] Calculate the pH using this new concentration: \[ pH = -\log(0.1345) \approx 0.87 \] The pH halfway to the equivalence point is approximately 0.87.

Step 4.3: Calculate the pH at the equivalence point.

At the equivalence point, the H+ and OH- ions have been neutralized, leaving only water. Calculate the pH of water: \[ pH = -\log[10^{-7}] = 7 \] At the equivalence point, the pH is 7.

Key concepts

Net Ionic Equation

When conducting an acid-base titration, the net ionic equation provides a simplified view of the reaction, showing only the particles that participate directly in the chemical change. In the reaction between potassium hydroxide (KOH) and hydrobromic acid (HBr), the net ionic equation is expressed as:\[ OH^- (aq) + H^+ (aq) \rightarrow H_2O (l) \]This equation demonstrates that the hydroxide ion (OH-) combines with the hydrogen ion (H+) to create water (H2O). It is crucial to understand that compounds like KOH and HBr dissociate into ions when in aqueous solution. However, for net ionic equations, spectator ions such as K+ and Br- are not included because they do not directly participate in the reaction.

Equivalence Point

The equivalence point in an acid-base titration occurs when the number of moles of acid equals the number of moles of base added. It represents the moment when the neutralization is complete. In our exercise, the equivalence point is achieved when the hydroxide ions from KOH have completely reacted with the hydrogen ions from HBr, resulting in a neutral solution. At this point, the solution predominantly contains the potassium ions (K+) and bromide ions (Br-) as no more H+ or OH- ions are present in significant amounts. These remaining ions do not affect the pH, illustrating the successful neutralization at the equivalence point.

pH Calculation

The pH value measures the acidity or basicity of a solution, and calculating it is essential during titrations to determine the solution’s properties at various stages. To find the initial pH, we use the equation \( pH = -\text{log}[H^+] \), where \( [H^+] \) is the concentration of hydrogen ions. Before any KOH is added, the pH is based solely on the concentration of HBr in the solution. At the equivalence point, the pH is neutral (approximately 7) because the acid and base have neutralized each other. Understanding these calculations helps us to track changes during titration and predict the outcome of the reaction.

Molarity and Volume Relationship

Molarity and volume have a direct relationship in the context of titrations, which is captured by the formula \( M_1V_1 = M_2V_2 \). This formula allows us to determine how much volume of a titrant (in this case, KOH) is required to reach the equivalence point when we know the molarity and volume of the analyte (HBr), and vice versa. It represents the point at which the moles of acid equal the moles of base, providing a quantitative perspective on the neutralization process. Understanding this relationship is fundamental when planning a titration and ensuring accurate results.

Acid-Base Neutralization

Acid-base neutralization is the reaction wherein an acid and a base react to form water and a salt. This reaction is the heart of a titration process. In our example, KOH (a base) neutralizes HBr (an acid) to form water and the salt potassium bromide (KBr). The phenomenon of neutralization is essential in understanding the underlying chemical changes during titration and the significance of the equivalence point. By mastering the concept of neutralization, students can better grasp the aim and outcomes of acid-base titrations.