Problem 42 - Chemistry: Principles and Reactions

Question

A solution of \(\mathrm{NaOH}\) with \(\mathrm{pH} 13.68\) requires \(35.00 \mathrm{~mL}\) of \(0.128 \mathrm{M}\) \(\mathrm{HClO}_{4}\) to reach the equivalence point. (a) What is the volume of the \(\mathrm{NaOH}\) solution? (b) What is the \(\mathrm{pH}\) at the equivalence point? that volumes are additive.)

Step-by-Step Solution

Answer

Answer (a): The volume of the NaOH solution at the equivalence point is 93.00 mL. Question (b): What is the pH at the equivalence point of the reaction between NaOH and HClO4? Answer (b): The pH at the equivalence point of the reaction between NaOH and HClO4 is 7.

Step 1: 1. Identify balanced reaction

Write the balanced reaction between NaOH and HClO4. NaOH + HClO4 → NaClO4 + H2O

Step 2: 2. Find moles of HClO4

Calculate the moles of HClO4 using the given volume and molarity. Moles of HClO4 = Molarity × Volume Moles of HClO4 = 0.128 M × 35.00 mL × (1 L / 1000 mL) Moles of HClO4 = 0.00448 moles

Step 3: 3. Find moles of NaOH

Since the stoichiometry of the balanced reaction is 1:1, the moles of NaOH must be equal to the moles of HClO4 at the equivalence point. Moles of NaOH = Moles of HClO4 = 0.00448 moles

Step 4: 4. Find molarity of NaOH

Using the information provided, we can calculate the molarity of NaOH using the formula: Molarity = [H+] = 10^(-pOH) pOH = 14 - pH = 14 - 13.68 = 0.32 Molarity of NaOH = 10^(-0.32) = 0.0482 M

Step 5: 5. Find volume of NaOH solution (a)

Use the moles of NaOH to calculate the volume of the NaOH solution: Volume of NaOH solution = Moles of NaOH / Molarity of NaOH Volume of NaOH solution = 0.00448 moles / 0.0482 M = 0.0930 L = 93.00 mL

Step 6: 6. Calculate the pH at the equivalence point (b)

At the equivalence point, the moles of HClO4 and NaOH are equal, and we are left with NaClO4. As NaClO4 is a salt of a strong acid and strong base, it does not hydrolyze to produce any H+ or OH- ions in the solution. Therefore, the pH at the equivalence point will be 7, as the solution is neutral.

Key Concepts

Equivalence Point

The equivalence point in an acid-base titration is a fundamental concept where the amount of acid equals the amount of base in a solution, leading to complete neutralization. It's the moment when there are no more hydronium equivalence point. For monoprotic acids and bases, which donate or accept one proton per molecule, such as equivalence point occurs when the moles of the acid equal the moles of the base. For example, in the titration of NaOH with HClO4, since NaOH and HClO4 react in a 1:1 ratio, the equivalence point is reached when the volume of HClO4 added times its molarity equals the volume of NaOH times its molarity.

pH Calculation

Calculating pH is crucial in understanding the acidity or basicity of a solution. pH is the negative logarithm (base 10) of the hydronium ion concentration, and it typically ranges from 0 to 14, where 7 is neutral, values below 7 are acidic, and those above are alkaline (basic). pH of the NaOH solution can be found by first calculating the pOH from the given pH value and then finding the molarity of NaOH. pH at the equivalence point is different depending on the nature of the reactants. In our given problem, as NaOH (a strong base) is neutralized by HClO4 (a strong acid), the pH at the equivalence point is 7, indicating a neutral solution. This is because the salt formed doesn't affect the pH of the solution.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It's based on the balanced chemical equation and the conservation of matter, ensuring that atoms are neither created nor destroyed during a reaction. In the case of the NaOH and HClO4 reaction, the stoichiometry is 1:1. This means that one mole of NaOH will react with one mole of HClO4 to produce one mole of water and one mole of NaClO4, neither of which affects the pH at the equivalence point. Understanding stoichiometry is essential for determining the volume and concentration of one reactant when the quantity of another reactant is known.

Molarity and Volume Relationship

Molarity (M) measures the concentration of a solution and is expressed as moles of solute per liter of solution. The relationship between molarity and volume is inversely proportional within the context of a titration; as the volume of the solution increases, the molarity decreases, assuming the amount of solute remains constant. In an acid-base titration, we use the relationship between molarity and volume to find the unknown concentration or volume of a solution. The problem provided requires you to calculate the volume of NaOH solution knowing the molarity and by using the number of moles calculated from the volume and molarity of the HClO4 solution. This relationship is crucial for correctly setting up and performing titration calculations.