Question

A \(0.400 M\) solution of ammonia was titrated with hydrochloric acid to the equivalence point, where the total volume was \(1.50\) times the original volume. At what \(\mathrm{pH}\) does the equivalence point occur?

Short answer

At the equivalence point, the concentration of HCl, C_HCl, is \(\frac{0.400}{1.50}\) M, which is also the concentration of Cl- ions. The Kb value for ammonia is \(1.8 \times 10^{-5}\), and we find that the OH- concentration is also \(1.8 \times 10^{-5}\) M. Calculating the pOH and subtracting it from 14 gives the pH at the equivalence point.

Step-by-step solution

Calculate the concentration of NH3 at the equivalence point

Given that the total volume of the solution at the equivalence point is 1.50 times the original volume. On reaching the equivalence point, the moles of NH3 will be equal to the moles of HCl. Let V be the original volume and C_NH3 be the initial concentration of NH3. Moles of NH3 = C_NH3 * V Moles of HCl = C_HCl * 1.50V At the equivalence point, Moles of NH3 = Moles of HCl C_NH3 * V = C_HCl * 1.50V C_HCl = \(\frac{C_{NH3}}{1.50}\) Now substitute the given value of C_NH3: C_HCl = \(\frac{0.400}{1.50}\) M

Calculate the concentration of Cl- ions

The HCl completely dissociates into H+ and Cl- ions in the solution. Therefore, at the equivalence point, the concentration of Cl- ions is the same as the concentration of HCl. Concentration of Cl- = C_HCl = \(\frac{0.400}{1.50}\) M

Use the Kb value for ammonia to find the OH- concentration

The Kb value for ammonia, NH3, is \(1.8 \times 10^{-5}\). Let x be the concentration of OH- ions in the solution. Kb = \(\frac{[NH4^+][OH^-]}{[NH3]}\) At the equivalence point, [NH4+] = [Cl-] [NH3] = [Cl-] So, Kb = \(\frac{[Cl^-][x]}{[Cl^-]}\) Solve for x: x = Kb = \(1.8 \times 10^{-5}\)

Calculate the pOH and pH

Now that we have the hydroxide ion concentration, we can calculate the pOH and then the pH. pOH = -log([OH-]) pOH = -log(\(1.8 \times 10^{-5}\)) pH = 14 - pOH After calculating the pOH and subtracting it from 14, you will get the pH at the equivalence point.

Key concepts

Understanding Titrations

Titration is an analytical technique used to determine the concentration of an unknown solution by reacting it with a solution of known concentration, referred to as the titrant. The point at which the reaction is complete is known as the equivalence point, and it's where the quantity of titrant added equals the quantity needed to completely react with the analyte. For example, in an acid-base titration, at the equivalence point, the moles of acid equal the moles of base.

During a titration, a pH indicator or a pH meter can be used to monitor the reaction's progress. In our exercise example, ammonia (\( NH_3 \)), a weak base, is titrated with hydrochloric acid (\( HCl \)), a strong acid. The determination of the equivalence point's pH is crucial for understanding the acid-base neutralization and for the analytical quantification of substances in a sample.

When performing calculations related to titrations, one must consider the dilution factor—as illustrated by the total volume change—and the concentrations before and after reaching the equivalence point. By calculating the concentrations, you can figure out how much titrant was used and thus, the point of stoichiometric equivalence during the titration process.

Grasping the Chemical Equilibrium

Chemical equilibrium is a state in a chemical reaction when the rate of the forward reaction equals the rate of the reverse reaction. This implies that the concentrations of reactants and products remain constant over time, not that they are equal. Equilibrium is dynamic; the reactions are still occurring, but with no net change.

In the case of weak bases like ammonia (\( NH_3 \)) in our exercise, they partially ionize in the solution to form ammonium ions (\( NH_4^+ \)) and hydroxide ions (\( OH^- \)). The extent of ionization is represented by the base dissociation constant (\( K_b \)), which reflects how readily the base donates its electrons to form hydroxide ions.

At the equivalence point of a titration, where the analyte and titrant have reacted completely, chemical equilibrium calculations help to determine the resulting pH. For weak bases, knowing the concentration of ions at this point, as well as the base's dissociation constant, enables us to calculate the hydroxide ion concentration in the solution. This is key for determining the pH, as shown in the step-by-step solution for the given exercise, where the dissociation of ammonia in the solution post-titration is a crucial element to finding the pH at the equivalence point.

Understanding Acid-Base Reactions

Acid-base reactions are processes in which a proton (hydrogen ion, \( H^+ \)) is transferred between reactants. In the context of titrations, these reactions are typically between an acid and a base, which can be thought of as proton donors and acceptors, respectively.

A strong acid will completely dissociate in water to yield hydronium (\( H_3O^+ \)) or hydrogen ions (\( H^+ \)) and its conjugate base, whereas a strong base completely dissociates into the hydroxide ion (\( OH^- \)) and its conjugate acid. The reaction between \( NH_3 \) and \( HCl \) is an example of an acid-base reaction where the \( NH_3 \) acts as a proton acceptor and the \( HCl \) as a proton donor, resulting in the formation of ammonium chloride (\( NH_4Cl \)).

At the equivalence point of an acid-base titration, the amount of acid equals the amount of base, leading to a neutralization reaction. However, the pH at this point is not always neutral (\textsc{ph} 7). For titrations involving weak acids or bases, the pH will depend on the strength of the weak acid or base and the resulting solution's ion concentration after equilibrium is reached. This concept is fundamental to understanding the calculation performed in our exercise, where the pH at the equivalence point reflects the weak base's partial ionization and its reaction with a strong acid.