NaOH is a strong base, so if the acid were a strong acid, the pH at equivalence would be 7. The graph, however, shows that the pH at equivalence is greater than 7, which means the acid being titrated is a weak acid.

We can also find the approximate pK_a value from the half equivalence point. In the graph, the equivalence point occurs at a pH around 8.9, corresponding to the addition of about 22mL of NaOH. The half equivalence point will thus be after the addition of approximately 11mL of NaOH, giving a pH of 5.0. The pH at the half equivalence is equal to the pK_a, meaning that the K_a value must be around 10^-5.

This leads to our answer, .

For a strong acids and strong base, the equivalence pH will be 7.0. We can see that our equivalence pH is less than 7.0, meaning that the acidic component is prevailing. Hence, we must be working with an acid that is stronger than our base. HNO₃ is a strong acid, and NH₃ is a weak base, meaning that the acid will prevail, and the pH will be acidic (<7.0).

The other answer choices show a strong acid and strong base (HCl and NaOH), a weak acid and strong base (HF and KOH, HCN and LiOH), and a weak acid and weak base (H₂S and C₅H₈O₂). Though the equivalence pH of a weak acid and weak base may not be 7.0, we do not have enough information to choose this answer. The best answer choice is HNO₃ and NH₃

The equivalence point is the point during a titration when there are equal equivalents of acid and base in the solution. Since a strong acid will have more effect on the pH than the same amount of a weak base, we predict that the solution's pH will be acidic at the equivalence point. 5.2 and 1.3 are both acidic, but 1.3 is remarkably acidic considering that there is an equal amount of base in the solution. As a result, 5.2 is a more appropriate answer.

The equivalence point for a strong acid and strong base will be 7.0. When one of the compounds is weak, however, it will dissociate less than its strong counterpart. In our case, the base will dissociate less than the acid. The acid, thus, contributes more to the pH character of the solution.

At the half equivalence point, the concentration of acid in the solution is equal to the concentration of the conjugate base in solution. At this point, the graph shows a line that is near horizontal. This means that base or acid could be added and the pH of the solution would change very slowly.

Remember that pH is on the y-axis of the titration curve; thus a near-horizontal line will signify a region where pH is most stable. At the half equivalence point, pH = pK_a.

Since we are adding acid to a base, the pH must decrease. The initial base will have a high pH, while the final acid will have a low pH; the right of the curve must be lower than the left. In addition, the pH does not change very rapidly until the equivalence point is reached, hence the curve must show little initial change followed by a rapid change.

A titrant is added to a solution being studied. In this scenario, the base is the titrant and the equivalence point is reached when all of the acid has been neutralized by the base. The equivalence point is defined as the point at which moles of added titrant equal the moles of initial solute in solution.

The equimolar concentration of acid and conjugate base happens at a point known as the half-equivalence point, which can be confusing.

For any titration curve the equivalence point corresponds to the steepest part of the curve. In this case, the question indicates that the pH at equivalence was 8.9, which would correspond to a volume between 20.0 and 24.0 on the x-axis of the graph. This leads to our approximate answer of 21.8mL.

The pK_a corresponds to the pH when half of the acid has been neutralized. In this case, that would correspond to when half of the 0.5M NaOH has been added. We can see in the curve that the equivalence point is at around 22mL of NaOH, as this is the steepest change in pH. The half equivalence point will be found at approximately 11mL of NaOH addition. On the graph, 11mL of NaOH results in a pH of approximately 5.0, giving us our pK_a value.

H₂CO₃ will have two equivalence points and two half equivalence points, one set corresponding to each of its two protons.

After the first equivalence point, all of the acid is in the form HCO₃^-. When an acid is at a half equivalence point, the acid's concentration will be equal to the concentration of the conjugate base. For the second half equivalence point, the acid is in the  HCO₃^- form, and the conjugate base is CO₃^2-. As a result, at the second half equivalence point, the concentrations of HCO₃^- and CO₃^2- will be equal.