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Chapter 2: Problem 11

a. If \(50 \mathrm{mL}\) of \(0.01 \mathrm{MHCl}\) is added to \(100 \mathrm{mL}\) of \(0.05 \mathrm{M}\) phosphate buffer at \(\mathrm{pH} 7.2,\) what is the resultant \(\mathrm{pH}\) ? What are the concentrations of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\) in the final solution? b. If \(50 \mathrm{mL}\) of \(0.01 \mathrm{MNaOH}\) is added to \(100 \mathrm{mL}\) of \(0.05 \mathrm{M}\) phosphate buffer at \(\mathrm{pH} 7.2,\) what is the resultant \(\mathrm{pH}\) ? What are the concentrations of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\) in this final solution?

Short Answer

Expert verified
The step by step method described above leads to the calculation of the final pH and concentrations of \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) and \( \mathrm{HPO}_{4}^{2-}\) after the addition of an acid or a base to a phosphate buffer. The buffers resist changes in pH upon addition of acid or base due to their ability to consume or produce \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\) ions, thus maintaining a relatively constant pH.

Step by step solution

01

Calculation of final concentrations upon addition of \(0.01 \mathrm{MHCl}\)

Start by finding the mmols of \(\mathrm{HCl}\), \( \mathrm{HPO}_{4}^{2-}\), and \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\). From there calculate the mmols of \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) and \( \mathrm{HPO}_{4}^{2-}\) after reactions, and divide by the total volume to get their new concentrations. Use the Henderson-Hasselbalch equation to get the new pH of the solution. Considering the reactions: \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-} + \mathrm{OH}^{-} -> \mathrm{H}_{2}\mathrm{O} + \mathrm{HPO}_{4}^{2-} \) and \( \mathrm{H}_{2}\mathrm{PO}_{4}^{-} + \mathrm{H}^{+} -> \mathrm{H}_{3}\mathrm{O}^{+} + \mathrm{H}_{2}\mathrm{PO}_{4}^{-} \)
02

Calculation of final concentrations upon addition of \(0.01 \mathrm{MNaOH}\)

Repeat the process of Step 1, but consider the mmols of \(\mathrm{NaOH}\) instead of \(\mathrm{HCl}\). Use the reactions: \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-} + \mathrm{OH}^{-} -> \mathrm{H}_{2}\mathrm{O} + \mathrm{HPO}_{4}^{2-} \) and \( \mathrm{HPO}_{4}^{2-} + \mathrm{H}^{+} -> \mathrm{H}_{2}\mathrm{O} + \mathrm{H}_{2}\mathrm{PO}_{4}^{-} \) to calculate the new mmols of \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) and \( \mathrm{HPO}_{4}^{2-}\). Divide by total volume to get the new concentrations.
03

Calculation of new pH

Now that the final concentrations of \(\mathrm{H}_{2}\mathrm{PO}_{4}^{-}\) and \( \mathrm{HPO}_{4}^{2-}\) are known after the addition of \(\mathrm{NaOH}\), use the Henderson-Hasselbalch equation to calculate the new pH of the solution.

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Most popular questions from this chapter

The \(K_{\mathrm{a}}\) for formic acid is \(1.78 \times 10^{-4} M.\) a. What is the pH of a \(0.1 \mathrm{M}\) solution of formic acid? b. \(150 \mathrm{mL}\) of \(0.1 \mathrm{MNaOH}\) is added to \(200 \mathrm{mL}\) of \(0.1 \mathrm{M}\) formic acid, and water is added to give a final volume of 1 L. What is the pH of the final solution?

Calculate the \(\mathrm{pH}\) of the following. a. \(5 \times 10^{-4} \mathrm{MHCl}\) d. \(3 \times 10^{-2}\) M KOH b. \(7 \times 10^{-5} M\) NaOH e. \(0.04 \mathrm{m} M \mathrm{HCl}\) c. \(2 \mu M\) HCl f. \(6 \times 10^{-9}\) M HCl

The pH of a \(0.02 \mathrm{M}\) solution of an acid was measured at 4.6. a. What is the \(\left[\mathrm{H}^{+}\right]\) in this solution? b. Calculate the acid dissociation constant \(K_{\mathrm{a}}\) and \(\mathrm{p} K_{\mathrm{a}}\) for this acid.

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 \(5.2 ?\)

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, \(\mathrm{pH} 7.8\)
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