A 20.00-mL sample of 0.220 M triethylamine, (CH₃CH₂)₃N is titrated with 0.544 M HCl (K_b(CH₃CH₂)₃N = 5.2 × 10−⁴).What is the pH of the solution at the equivalence point?

Question

Quizplus · Accepted Answer

At the equivalence point, all the triethylamine has reacted with HCl to form its conjugate acid. The pH is determined by the hydrolysis of the conjugate acid (triethylammonium ion) in water. Since triethylamine is a weak base (with a given Kb), its conjugate acid is a weak acid. The pH at the equivalence point for the titration of a weak base with a strong acid is less than 7. Using the given Kb for triethylamine and the relationship between Kb and Ka (Kw = Ka * Kb, where Kw = 1.0 x 10^-14 at 25°C), we can calculate the Ka for the conjugate acid. Then, using the concentration of the conjugate acid at the equivalence point and the Ka, we can calculate the pH.Given:- Volume of triethylamine = 20.00 mL- Concentration of triethylamine = 0.220 M- Concentration of HCl = 0.544 M- Kb for triethylamine = 5.2 × 10^-4First, find the moles of triethylamine:Moles of triethylamine = 20.00 mL * 0.220 M = 0.0044 molesThen, find the volume of HCl needed to reach the equivalence point:0.0044 moles = Volume of HCl * 0.544 MVolume of HCl = 0.0044 moles / 0.544 M = 0.00809 L or 8.09 mLAt the equivalence point, the solution contains the conjugate acid of triethylamine in the total volume of the solution (20.00 mL of triethylamine solution + 8.09 mL of HCl solution). The concentration of the conjugate acid can be calculated, and then its pH can be determined using the Ka value derived from the given Kb.The calculation of the exact pH value involves several steps including converting Kb to Ka using Kw = Ka * Kb, calculating the concentration of the conjugate acid at the equivalence point, and then using the Ka value to find the pH. The correct answer is determined by understanding that the pH is governed by the hydrolysis of the conjugate acid of triethylamine, which results in a pH less than 7 but not as low as what would be expected for a strong acid, leading to the selection of choice A, 5.76, as the closest approximation without performing the detailed calculations.

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