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Chapter 14: Problem 34

A buffer is prepared using the propionic acid/propionate \(\left(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{2} /\right.\) \(\left.\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{2}^{-}\right)\) acid-base pair for which the ratio \(\left[\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}\right] /\left[\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{2}^{-}\right]\) is \(4.50 .\) \(K_{\mathrm{a}}\) for propionic acid is \(1.4 \times 10^{-5}\). (a) What is the \(\mathrm{pH}\) of this buffer? (b) Enough strong base is added to convert \(27 \%\) of \(\mathrm{HC}_{3} \mathrm{H}_{5} \mathrm{O}_{2}\) to \(\mathrm{C}_{3} \mathrm{H}_{5} \mathrm{O}_{2}^{-} .\) What is the \(\mathrm{pH}\) of the resulting solution? (c) Strong base is added to increase the \(\mathrm{pH}\). What must the acid/base ratio be so that the \(\mathrm{pH}\) increases by exactly one unit (e.g., from 2 to 3 ) from the answer in (a)?

Short Answer

Expert verified
Question: Calculate the initial pH of the buffer, the new pH after adding a strong base that converts 27% of propionic acid to propionate, and the new acid/base ratio required to increase the pH by 1 unit. Given the ratio of acid to conjugate base as 4.50 and the \(K_a\) value for propionic acid as \(1.4 \times 10^{-5}\).

Step by step solution

01

Calculate the pKa of propionic acid

The pKa can be calculated as follows: pKa = -log(Ka) pKa = -log(\(1.4 \times 10^{-5}\))
02

Calculate the initial pH of the buffer

Using the Henderson-Hasselbalch equation: pH = pKa + log\(\frac{[\text{A}^-]}{[\text{HA}]}\) Since the ratio is given as 4.5, pH = pKa + log(4.50) Calculate the pH.
03

Calculate the amount of propionic acid converted to propionate

Given that 27% of propionic acid is converted to propionate when a strong base is added, let x be the amount of propionic acid (in moles), then 0.27x moles of propionic acid will be converted into propionate.
04

Calculate the new concentrations of propionate and propionic acid

After the reaction, both concentrations change: New concentration of propionic acid [\(\text{HA}\)] = \([4.5 * x - 0.27x]\) New concentration of propionate [\(\text{A}^-\)] = \([x + 0.27x]\)
05

Calculate the new pH of the solution after base addition

Using the Henderson-Hasselbalch equation with the new concentrations: pH = pKa + log\(\frac{[x + 0.27x]}{[4.5 * x - 0.27x]}\) Calculate the new pH.
06

Calculate the new acid/base ratio to increase the pH by 1 unit

To increase the pH by one unit, let the new pH be pH_initial + 1. Use the Henderson-Hasselbalch equation again: pH_initial + 1 = pKa + log\(\frac{[\text{A}_{new}^-]}{[\text{HA}_{new}]}\) Find the appropriate ratio to get the desired pH value.

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Most popular questions from this chapter

Consider the titration of \(\mathrm{HF}\left(K_{\mathrm{a}}=6.7 \times 10^{-4}\right)\) with \(\mathrm{NaOH}\). What is the \(\mathrm{pH}\) when a third of the acid has been neutralized?

WEB To make a buffer with \(\mathrm{pH}=3.0\) from \(\mathrm{HCHO}_{2}\) and \(\mathrm{CHO}_{2}^{-}\), (a) what must the [HCHO \(\left._{2}\right] /\left[\mathrm{CHO}_{2}^{-}\right]\) ratio be? (b) how many moles of \(\mathrm{HCHO}_{2}\) must be added to a liter of \(0.139 \mathrm{M}\) \(\mathrm{NaCHO}_{2}\) to give this \(\mathrm{pH}\) ? (c) how many grams of \(\mathrm{NaCHO}_{2}\) must be added to \(350.0 \mathrm{~mL}\) of \(0.159 \mathrm{MHCHO}_{2}\) to give this \(\mathrm{pH}\) ? (d) What volume of \(0.236 \mathrm{M} \mathrm{HCHO}_{2}\) must be added to \(1.00 \mathrm{~L}\) of a \(0.500 \mathrm{M}\) solution of \(\mathrm{NaCHO}_{2}\) to give this pH? (Assume that volumes are additive.)

At \(25^{\circ} \mathrm{C}\) and \(1.00\) atm pressure, one liter of ammonia is bubbled into \(725 \mathrm{~mL}\) of water. Assume that all the ammonia dissolves and the volume of the solution is the volume of the water. A \(50.0-\mathrm{mL}\) portion of the prepared solution is titrated with \(0.2193 \mathrm{M} \mathrm{HNO}_{3} .\) Calculate the \(\mathrm{pH}\) of the solution (a) before titration. (b) halfway to the equivalence point. (c) at the equivalence point.

Write a net ionic equation for the reaction between aqueous solutions of (a) ammonia and hydrofluoric acid. (b) perchloric acid and rubidium hydroxide. (c) sodium sulfite and hydriodic acid. (d) nitric acid and calcium hydroxide.

Calculate the pH of a solution prepared by mixing \(2.00 \mathrm{~g}\) of butyric acid \(\left(\mathrm{HC}_{4} \mathrm{H}_{7} \mathrm{O}_{2}\right)\) with \(0.50 \mathrm{~g}\) of \(\mathrm{NaOH}\) in water \(\left(K_{\mathrm{a}}\right.\) butyric acid \(\left.=1.5 \times 10^{-5}\right)\)
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