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Chapter 2: Problem 21

When a \(0.1 \mathrm{M}\) solution of a weak acid was titrated with base, the following results were obtained: $$\begin{array}{cc}\begin{array}{c}\text { Equivalents of } \\\\\text { base added }\end{array} & \text { pH observed } \\\\\hline 0.05 & 3.4 \\\0.15 & 3.9 \\\0.25 & 4.2 \\\0.40 & 4.5 \\\0.60 & 4.9 \\\0.75 & 5.2 \\\0.85 & 5.4 \\\0.95 & 6.0\end{array}$$ Plot the results of this titration and determine the \(\mathrm{p} K_{\mathrm{a}}\) of the weak acid from your graph.

Short Answer

Expert verified
Following the steps outlined, the pKa of the weak acid can be derived from the given titration data by locating the pH at the half-equivalence point on the plot of pH versus amount of base added.

Step by step solution

01

Plot the data

Plot the observed pH against the equivalents of base added. Make sure to plot pH on the y-axis and equivalents of base added on the x-axis. From the data given, the plot should resemble a sigmoid curve, characteristic of titrations.
02

Identify the half-equivalence point

The half-equivalence point is reached when half the moles of the weak acid have been neutralized by the base, which in this case would be equivalent to 0.05 base equivalents (half of 0.1 M). On the plotted graph, find the pH value corresponding to this value of base equivalents. This pH value marks the half-equivalence point.
03

Determine the pKa

The pKa is the pH at the half-equivalence point. Thus, simply read off the pKa from the pH value at the half-equivalence point identified in Step 2. This is your pKa value for the weak acid.

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Most popular questions from this chapter

a. Draw the titration curve for Bicine, assuming the \(\mathrm{p} K_{\mathrm{a}}\) for its free COOH group is 2.3 and the \(\mathrm{p} K_{\mathrm{a}}\) for its tertiary amino group is 8.3 b. Draw the structure of the fully deprotonated form (completely dissociated form) of bicine. c. You have available a \(0.1 ~ M\) solution of Bicine at its isoelectric point \(\left(\mathrm{pH}_{\mathrm{I}}\right), 0.1 \mathrm{M}\) solutions of \(\mathrm{HCl}\) and \(\mathrm{NaOH}\), and ample distilled \(\mathrm{H}_{2} \mathrm{O}\) Describe the preparation of 1 L of 0.04 M Bicine buffer, pH 7.5 d. What is the concentration of fully protonated form of Bicine in your final buffer solution?

Given a solution of \(0.1 \mathrm{M}\) HEPES in its fully protonated form, and ready access to \(0.1 \mathrm{M} \mathrm{HCl}, 0.1 \mathrm{M} \mathrm{NaOH}\) and distilled water, describe the preparation of 1 L of 0.025 M HEPES buffer solution, \(\mathrm{pH} 7.8\)

Citric acid, a tricarboxylic acid important in intermediary metabolism, can be symbolized as \(\mathrm{H}_{3} \mathrm{A}\). Its dissociation reactions are \\[\begin{array}{ll}\mathrm{H}_{3} \mathrm{A} \rightleftharpoons \mathrm{H}^{+}+\mathrm{H}_{2} \mathrm{A}^{-} & \mathrm{p} K_{1}=3.13 \\\\\mathrm{H}_{2} \mathrm{A}^{-} \rightleftharpoons \mathrm{H}^{+}+\mathrm{HA}^{2-} & \mathrm{p} K_{2}=4.76 \\\\\mathrm{HA}^{2-} \rightleftharpoons \mathrm{H}^{+}+\mathrm{A}^{3-} & \mathrm{p} K_{3}=6.40 \end{array}\\] If the total concentration of the acid and its anion forms is \(0.02 \mathrm{M}\) what are the individual concentrations of \(\mathrm{H}_{3} \mathrm{A}, \mathrm{H}_{2} \mathrm{A}^{-}, \mathrm{HA}^{2-},\) and \(\mathrm{A}^{3-}\) at pH \(5.2 ?\)

Bicine is a compound containing a tertiary amino group whose relevant \(\mathrm{p} K_{\mathrm{a}}\) is 8.3 (Figure 2.17 ). Given \(1 \mathrm{L}\) of \(0.05 \mathrm{M}\) Bicine with its tertiary amino group in the unprotonated form, how much \(0.1 N \mathrm{HCl}\) must be added to have a Bicine buffer solution of \(\mathrm{pH} 7.5 ?\) What is the molarity of Bicine in the final buffer? What is the concentration of the protonated form of Bicine in this final buffer?

Tris-hydroxymethyl aminomethane (TRIS) is widely used for the preparation of buffers in biochemical research. Shown here is the structure of TRIS in its protonated form: Its acid dissociation constant, \(K_{\mathrm{a}},\) is \(8.32 \times 10^{-9} M .\) You have available at your lab bench a \(0.1 \mathrm{M}\) solution of TRIS in its protonated form, 0.1 \(M\) solutions of \(\mathrm{HCl}\) and \(\mathrm{NaOH}\), and ample distilled water. Describe the preparation of a 1 L solution of 0.02 M TRIS buffer, pH 7.8.
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