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Chapter 2: Problem 32

Which of the following pairs of ions would make the best buffer with a pH between 6 and 7? \(K_{\mathrm{a}}\) for \(\mathrm{HC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}=1.75 \times 10^{-5}\) \(K_{\mathrm{a}}\) for \(\mathrm{HPO}_{4}^{2-}=4.8 \times 10^{-13}\) (A) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and \(\mathrm{H}_{2} \mathrm{PO}_{4}\) (B) \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{Na}_{3} \mathrm{PO}_{4}\) (C) \(\mathrm{HC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}\) and \(\mathrm{NaC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}\) (D) \(\mathrm{NaOH}\) and \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\)

Short Answer

Expert verified
The most suitable buffer with a pH between 6 and 7 is created using \(\mathrm{HC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}\) and \(\mathrm{NaC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}\). Therefore, the answer is C.

Step by step solution

01

Examine all options

Look at each option and identify the conjugate acid-base pairs. For option A, the pairs are \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and \(\mathrm{H}_{2} \mathrm{PO}_{4}\), which are not conjugate pairs. For option B, the pairs are \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{Na}_{3} \mathrm{PO}_{4}\), where \(\mathrm{PO}_{4}^{3-}\) is the base. Option C has pairs \(\mathrm{HC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}\) and $\mathrm{NaC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}$, where \(\mathrm{C}_{3} \mathrm{H}_{2} \mathrm{O}_{2}^{-}\) is the base. Finally, option D pairs \(\mathrm{NaOH}\) and \(\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}\), but \(\mathrm{NaOH}\) is a strong base and therefore doesn't make good buffers.
02

Check the pH range

Using Henderson-Hasselbalch equation, \(\mathrm{pH} = \mathrm{pKa} + \log_{10}\left(\frac{[\mathrm{Base}]}{[\mathrm{Acid}]}\right)\), the best buffer will have a pKa close to the desired pH, which is between 6 and 7 in this case. From the given acid dissociation constants, calculate pKa by taking the negative logarithm of Ka. For \(\mathrm{HC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}\), pKa = -log(1.75 x 10^-5) = 4.76. For \(\mathrm{HPO}_{4}^{2-}\), pKa = -log(4.8 x 10^-13) = 12.32. It's clear that \(\mathrm{HC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}\)'s pKa is closer to the desired pH range.
03

Choose the correct answer

Based on the discussion above, option C, \(\mathrm{HC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}\) and $\mathrm{NaC}_{3} \mathrm{H}_{2} \mathrm{O}_{2}$, makes the most suitable buffer with a pH between 6 and 7. The other options either do not form conjugate acid-base pairs or their pKa values are not within the vicinity of the desired pH range.

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Most popular questions from this chapter

A stock solution of 0.100 \(\mathrm{M}\) cobalt (II) chloride is used to create several solutions, indicated in the data table below: \(\begin{array}{|c|c|c|}\hline \text { Sample } & {\text { Volume } \mathrm{CoCl}_{2}} & {\text { Volume }} \\ \hline & {(\mathrm{mL})} & {\mathrm{H}_{2} \mathrm{O}(\mathrm{mL})} \\ \hline 1 & {20.00} & {0} \\\ \hline 2 & {15.00} & {5.00} \\ \hline 3 & {10.00} & {10.00} \\ \hline 4 & {5.00} & {15.00} \\ \hline\end{array}\) (a) In order to achieve the degree of accuracy shown in the table above, select which of the following pieces of laboratory equipment could be used when measuring out the CoCl_{2} : \(150-\mathrm{mL}\) beaker \(\quad 400-\mathrm{mL}\) beaker \(\quad 250-\mathrm{mL}\) Erlenmeyer flask \(\begin{array}{ll}{\text { 50-mL buret }} & {\text { 50-mL graduated }} \\ {} & {\text { cylinder }}\end{array} \quad 100\) -mL graduated cylinder (b) Calculate the concentration of the CoCl, in each sample. The solutions are then placed in cuvettes before being inserted into a spectrophotometer calibrated to 560 \(\mathrm{nm}\) and their values are measured, yielding the data below: \(\begin{array}{|c|c|}\hline \text { Sample } & {\text { Absorbance }} \\\ \hline 1 & {0.485} \\ \hline 2 & {0.364} \\ \hline 3 & {0.243} \\ \hline 4 & {0.121} \\ \hline\end{array}\) (c) If gloves are not worn when handling the cuvettes, how might this affect the absorbance values gathered? (d) If the path length of the cuvette is \(1.00 \mathrm{cm},\) what is the molar absorptivity value for \(\mathrm{CoCl}_{2}\) at 560 \(\mathrm{nm}\) ? (e) On the axes on the next page, plot a graph of absorbance vs. concentrrion. The \(y\) -axes scale is set, and be sure to scale the \(x\) -axes appropriately (f) What would the absorbance values be for \(\mathrm{CoCl}_{2}\) , solutions at the following concentrations? (i) 0.067 (ii) 0.180 \(\mathrm{M}\)

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