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Chapter 16: Problem 5

Determine the \(\mathrm{pH}\) of (a) a \(0.40 \mathrm{MCH}_{3} \mathrm{COOH}\) solution, (b) a solution that is \(0.40 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) and \(0.20 \mathrm{M} \mathrm{CH}_{3} \mathrm{COONa} .\)

Short Answer

Expert verified
By carrying out the calculations described above, the pH of the 0.40 M \(CH_{3}COOH\) solution will be found, as well as the pH of the buffer solution composed of 0.40 M \(CH_{3}COOH\) and 0.20 M \(CH_{3}COONa\). The final answers will depend on the results of the calculations.

Step by step solution

01

Understanding the dissociation of \(CH_{3}COOH\)

The first step involves understanding that \(CH_{3}COOH\) (acetic acid) is a weak acid, and as such it partially dissociates in water according to the reaction: \(CH_{3}COOH ⇌ CH_{3}COO^- + H^+\). This reaction can be described by the equilibrium constant, Ka, given by the expression: \(Ka = [CH_{3}COO^-][H^+]/[CH_{3}COOH]\). For acetic acid, \(Ka = 1.8 × 10^{-5}\).
02

Calculating the pH of \(0.40 \mathrm{M CH_{3}COOH}\)

To calculate the pH, we'll use the equilibrium expression for acetic acid and the Ka value given above. Assuming that the initial concentration of acetic acid equals the initial molarity (0.40 M) and that the change in concentration with equilibrium equals -x, the equilibrium concentrations for \(CH_{3}COOH\), \(CH_{3}COO^-\), and \(H^+\) are \(0.40 - x\), \(x\), and \(x\) M, respectively. By substituting these values into the Ka expression, we'll get the quadratic equation: \(1.8 × 10^{-5} = x^2/(0.40 - x)\). Solve this equation to find x, the concentration of \(H^+\), then use this to find the pH using the formula \(pH = -log[H^+]\).
03

Understanding the action of the buffer

A buffer solution contains a weak acid and its conjugate base. In this case, the buffer is composed of \(CH_{3}COOH\) (acetic acid) and \(CH_{3}COONa\) (sodium acetate). In solution, the sodium acetate completely dissociates to yield the acetate ion: \(CH_{3}COONa → CH_{3}COO^- + Na^+\). The presence of both the weak acid and its conjugate base allows the buffer to resist changes in pH.
04

Calculating the pH of the buffer solution

To find the pH of the buffer solution, we'll use the Henderson-Hasselbalch equation, which is \(pH = pKa + log([A^-]/[HA])\), where [A^-] is the molar concentration of the acetate ion and [HA] is the molar concentration of acetic acid. Given the concentrations of the acetic acid and acetate ion (0.40 M and 0.20 M, respectively) and the pKa of acetic acid (-log(1.8 × 10^-5)), we can substitute these values into the equation to find the pH of the buffer solution.

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Most popular questions from this chapter

(a) Assuming complete dissociation and no ionpair formation, calculate the freezing point of a \(0.50 \mathrm{~m}\) NaI solution. (b) What is the freezing point after the addition of sufficient \(\mathrm{HgI}_{2},\) an insoluble compound, to the solution to react with all the free \(\mathrm{I}^{-}\) ions in solution? Assume volume to remain constant.

The molar solubility of \(\mathrm{Pb}\left(\mathrm{IO}_{3}\right)_{2}\) in a \(0.10 \mathrm{M} \mathrm{NaIO}_{3}\) solution is \(2.4 \times 10^{-11} \mathrm{~mol} / \mathrm{L} .\) What is \(K_{\mathrm{sp}}\) for \(\mathrm{Pb}\left(\mathrm{IO}_{3}\right)_{2} ?\)

Amino acids are building blocks of proteins. These compounds contain at least one amino group \(\left(-\mathrm{NH}_{2}\right)\) and one carboxyl group \((-\mathrm{COOH})\) Consider glycine \(\left(\mathrm{NH}_{2} \mathrm{CH}_{2} \mathrm{COOH}\right) .\) Depending on the pH of the solution, glycine can exist in one of three possible forms: $$ \begin{array}{l} \text { Fully protonated: } \mathrm{NH}_{3}-\mathrm{CH}_{2}-\mathrm{COOH} \\ \text { Dipolar ion: } \mathrm{NH}_{3}-\mathrm{CH}_{2}-\mathrm{COO}^{-} \\ \text {Fully ionized: } \mathrm{NH}_{2}-\mathrm{CH}_{2}-\mathrm{COO}^{-} \end{array} $$ Predict the predominant form of glycine at \(\mathrm{pH} 1.0\), 7.0, and 12.0. The \(\mathrm{p} K_{\mathrm{a}}\) of the carboxyl group is 2.3 and that of the ammonium group \(\left(-\mathrm{NH}_{3}^{+}\right)\) is 9.6

Find the approximate \(\mathrm{pH}\) range suitable for separating \(\mathrm{Mg}^{2+}\) and \(\mathrm{Zn}^{2+}\) by the precipitation of \(\mathrm{Zn}(\mathrm{OH})_{2}\) from a solution that is initially \(0.010 M\) in \(\mathrm{Mg}^{2+}\) and \(\mathrm{Zn}^{2+}\)

Sketch titration curves for the following acid-base titrations: (a) \(\mathrm{HCl}\) versus \(\mathrm{NaOH},\) (b) \(\mathrm{HCl}\) versus \(\mathrm{CH}_{3} \mathrm{NH}_{2},\) (c) \(\mathrm{CH}_{3} \mathrm{COOH}\) versus \(\mathrm{NaOH}\). In each case, the base is added to the acid in an Erlenmeyer flask. Your graphs should show \(\mathrm{pH}\) on the \(y\) axis and volume of base added on the \(x\) axis.
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