What is the pH at the equivalence point in the titration of 10.0 mL of 0.56 M HZ with 0.200 M NaOH? Ka = 6.6 × 10−5 for HZ.

To determine the pH at the equivalence point in the titration, you need to understand the concept of acid-base titration and the stoichiometry of the reaction between the acid (HZ) and the base (NaOH).

The equation for the reaction between HZ and NaOH is:

HZ + NaOH -> NaZ + H2O

In this reaction, one mole of HZ reacts with one mole of NaOH to form one mole of NaZ (the salt) and one mole of water. Since the reaction proceeds in a 1:1 ratio, the number of moles of HZ initially present will be equal to the number of moles of NaOH added at the equivalence point.

Given that 10.0 mL of 0.56 M HZ is used, we can calculate the number of moles of HZ using the formula:

moles of solute = (volume of solution in liters) * (molarity)

moles of HZ = (10.0 mL / 1000 mL/L) * (0.56 M) = 0.0056 moles

At the equivalence point, all of the HZ will have reacted with the NaOH, leaving only the salt NaZ (which is a neutral species) in solution. Therefore, the number of moles of HZ will be completely consumed, and the remaining solution will contain only the salt NaZ.

Now, let's find the concentration of NaOH at the equivalence point. Since the reaction proceeds in a 1:1 ratio, the number of moles of NaOH at the equivalence point will also be 0.0056 moles.

To find the volume of NaOH needed to reach the equivalence point, we can use the equation:

moles of solute = (volume of solution in liters) * (molarity)

0.0056 moles of NaOH = (volume of NaOH / 1000 mL/L) * (0.200 M)

volume of NaOH = (0.0056 moles) / (0.200 M) * (1000 mL/L) = 28 mL

Therefore, it takes 28 mL of 0.200 M NaOH to reach the equivalence point.

Now, let's determine the concentration of NaZ at the equivalence point. Since the number of moles of NaZ is equal to the number of moles of NaOH at the equivalence point, we can use the formula:

concentration = (moles of solute) / (volume of solution in liters)

concentration of NaZ = (0.0056 moles) / (28 mL / 1000 mL/L) = 0.200 M

Since NaZ results from the complete neutralization of HZ with NaOH, the dissolved NaZ will not contribute to any additional acid or base reactions.

In order to calculate the pH at the equivalence point, we need to determine whether the NaZ salt will have a hydrolysis reaction that will affect the pH. This depends on the acid-base properties of the salt NaZ.

Using the Ka value given for HZ (6.6 × 10^-5), we can calculate the Kb value for NaZ, which will determine if there is hydrolysis. The relationship between the Ka and Kb values is given by:

Kw = Ka * Kb

Kw is the ionization constant for water and is equal to 1.0 × 10^-14 at 25°C.

Therefore:

(1.0 × 10^-14) = (6.6 × 10^-5) * Kb

Solving for Kb:

Kb = (1.0 × 10^-14) / (6.6 × 10^-5) ≈ 1.52 × 10^-10

Since the Kb value for NaZ is very small, it indicates that the salt NaZ undergoes only a slight hydrolysis. This means the concentration of hydroxide ions (OH-) produced during hydrolysis will be very low. Consequently, the concentration of hydrogen ions (H+) will also be very low.

As a result, the pH at the equivalence point of the titration will be close to neutral, approximately 7.

Approach this problem as in the NH3/HCl problem below and see where you are on the titration curve. Post your work if you need addition assistance.