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Chapter 17: Problem 21

\(\begin{array}{lll}\text { Given } & 1.00 & \mathrm{L}\end{array}\) of a solution that is \(0.100 \mathrm{M}\) \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COOH}\) and \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COO}\) (a) Over what pH range will this solution be an effective buffer? (b) What is the buffer capacity of the solution? That is, how many millimoles of strong acid or strong base can be added to the solution before any significant change in pH occurs?

Short Answer

Expert verified
The effective pH range of the buffer solution would be between 3.82 and 5.82. The buffer capacity of the solution is 1 mol/L.

Step by step solution

01

Determine the pH range

First, it is important to know that a buffer is most effective when pH is within 1 unit of the pKa of the buffering system. The acid mentioned, CH3CH2COOH ethanol, is a weak acid. Its pKa value is 4.82. So, the effective buffer range of the solution would be the pKa 卤1, giving a pH range of 3.82 to 5.82.
02

Calculate the buffer capacity

Buffer capacity refers to the amount of acid or base a buffer can neutralize before the pH begins to change to an appreciable degree. Using the buffer capacity formula, we know \(Buffer Capacity = 0.5 * Volume * (10^(pH-pKa) + 10^(pKa-pH))\). The pKa of ethanol is 4.82, the volume is 1.00 L, and we want to determine the buffer capacity at pH 4.82 (the pKa value). So, \(Buffer Capacity = 0.5 * 1 * (1 + 1) = 1 \). So, the buffer can neutralize up to 1 mol of strong acid or 1 mol of strong base. Therefore, the buffer capacity of the solution is 1 mol/L.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

pH Range
Understanding the pH range is crucial to grasping how buffer solutions work effectively. A buffer solution begins to change its ability to resist pH changes when it's outside of its effective range. This range is typically within one pH unit above and below the pKa value of the weak acid involved.
For example, if a weak acid has a pKa value of 4.82, then the effective pH range for the buffer would be from 3.82 to 5.82.
  • Within this range, the buffer can successfully neutralize small amounts of added acids or bases without a substantial shift in pH.
  • Beyond this range, the buffer's capacity to maintain its pH stabilizes.
This concept helps in designing effective buffers for various chemical reactions.
Buffer Capacity
Buffer capacity is the measure of a buffer's ability to resist changes in pH when an acid or base is added. It is a crucial property of buffer solutions.
The formula used to calculate buffer capacity is: \( \text{Buffer Capacity} = 0.5 \times \text{Volume} \times \left( 10^{\text{pH} - \text{pKa}} + 10^{\text{pKa} - \text{pH}} \right) \).
  • In the case of ethanol, the pKa is 4.82, and typically, we assess buffer capacity at this exact pH for simplicity.
  • If you apply this at a pH of 4.82 with a volume of 1 liter, the buffer capacity is determined to be 1 mol/L.
This means the buffer solution can effectively neutralize up to 1 mole of a strong acid or strong base. A higher buffer capacity indicates a stronger buffer that can handle more significant quantities of acid or base without drastic pH changes.
pKa Value
The pKa value is a key factor in understanding how weak acids behave in buffer solutions. It reflects the acid's strength, indicating how readily the acid donates protons in solution.
A low pKa value suggests a strong acid, while a higher pKa indicates a weaker acid. For acetic acid, or ethanol in this instance, the pKa is an intermediate 4.82, classifying it as a weak acid.
  • The pKa value directly informs the buffer range, as effective buffering occurs within 1 pH unit of this value.
  • Knowing the pKa helps predict how the acid will behave in different pH environments.
The strategic selection of a weak acid for buffer solutions aids in applications where a stable pH is critical.
Weak Acids
Weak acids, such as acetic acid (ethanol in this case), only partially ionize in solution. This partial ionization is what enables them to effectively participate in buffer systems.
Understanding the behavior of weak acids is essential because they are key components in maintaining the desired pH in a buffer system.
  • In solution, they exist in equilibrium between their ionized and non-ionized forms.
  • This balance allows them to neutralize added acids by absorbing excess hydrogen ions and neutralize bases by providing hydrogen ions.
Weak acids, with their characteristic pKa values, are chosen according to the required pH range of the buffer system. Their ability to maintain equilibrium makes them indispensable in creating effective buffer solutions.

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Most popular questions from this chapter

The neutralization of \(\mathrm{NaOH}\) by \(\mathrm{HCl}\) is represented in equation (1), and the neutralization of \(\mathrm{NH}_{3}\) by HCl in equation (2). 1. \(\mathrm{OH}^{-}+\mathrm{H}_{3} \mathrm{O}^{+} \rightleftharpoons 2 \mathrm{H}_{2} \mathrm{O} \quad K=?\) 2\. \(\mathrm{NH}_{3}+\mathrm{H}_{3} \mathrm{O}^{+} \rightleftharpoons \mathrm{NH}_{4}^{+}+\mathrm{H}_{2} \mathrm{O} \quad K=?\) (a) Determine the equilibrium constant \(K\) for each reaction. (b) Explain why each neutralization reaction can be considered to go to completion.

A very common buffer agent used in the study of biochemical processes is the weak base TRIS, \(\left(\mathrm{HOCH}_{2}\right)_{3} \mathrm{CNH}_{2},\) which has a \(\mathrm{pK}_{\mathrm{b}}\) of 5.91 at \(25^{\circ} \mathrm{C} . \mathrm{A}\) student is given a sample of the hydrochloride of TRIS together with standard solutions of \(10 \mathrm{M}\) NaOH and HCl. (a) Using TRIS, how might the student prepare 1 L of a buffer of \(\mathrm{pH}=7.79 ?\) (b) In one experiment, 30 mmol of protons are released into \(500 \mathrm{mL}\) of the buffer prepared in part (a). Is the capacity of the buffer sufficient? What is the resulting pH? (c) Another student accidentally adds \(20 \mathrm{mL}\) of \(10 \mathrm{M}\) HCl to 500 mL of the buffer solution prepared in part (a). Is the buffer ruined? If so, how could the buffer be regenerated?

Piperazine is a diprotic weak base used as a corrosion inhibitor and an insecticide. Its ionization is described by the following equations. \(\mathrm{HN}\left(\mathrm{C}_{4} \mathrm{H}_{8}\right) \mathrm{NH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\) \(\left[\mathrm{HN}\left(\mathrm{C}_{4} \mathrm{H}_{8}\right) \mathrm{NH}_{2}\right]^{+}+\mathrm{OH}^{-} \quad \mathrm{p} K_{\mathrm{b}_{1}}=4.22\) \(\left[\mathrm{HN}\left(\mathrm{C}_{4} \mathrm{H}_{8}\right) \mathrm{NH}_{2}\right]^{+}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons\) \(\left[\mathrm{H}_{2} \mathrm{N}\left(\mathrm{C}_{4} \mathrm{H}_{8}\right) \mathrm{NH}_{2}\right]^{2+}+\mathrm{OH}^{-} \quad \mathrm{p} K_{\mathrm{b}_{2}}=8.67\) . The piperazine used commercially is a hexahydrate, \(\mathrm{C}_{4} \mathrm{H}_{10} \mathrm{N}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O} .\) A \(1.00-\mathrm{g}\) sample of this hexahydrate is dissolved in \(100.0 \mathrm{mL}\) of water and titrated with 0.500 M HCl. Sketch a titration curve for this titration, indicating (a) the initial \(\mathrm{pH} ;\) (b) the pH at the halfneutralization point of the first neutralization; (c) the volume of \(\mathrm{HCl}(\text { aq })\) required to reach the first equivalence point; (d) the pH at the first equivalence point; (e) the \(\mathrm{pH}\) at the point at which the second step of the neutralization is half-completed; (f) the volume of \(0.500 \mathrm{M} \mathrm{HCl}(\) aq) required to reach the second equivalence point of the titration; (g) the pH at the second equivalence point.

Explain whether the equivalence point of each of the following titrations should be below, above, or at pH 7: (a) \(\mathrm{NaHCO}_{3}(\text { aq) titrated with } \mathrm{NaOH}(\mathrm{aq}) ; \text { (b) } \mathrm{HCl}(\mathrm{aq})\) titrated with \(\mathrm{NH}_{3}(\mathrm{aq}) ;\) (c) KOH(aq) titrated with HI(aq).

You are asked to prepare a buffer solution with a pH of 3.50. The following solutions, all \(0.100 \mathrm{M},\) are available to you: HCOOH, CH \(_{3} \mathrm{COOH}, \mathrm{H}_{3} \mathrm{PO}_{4}, \mathrm{NaCHOO}\) \(\mathrm{NaCH}_{3} \mathrm{COO},\) and \(\mathrm{NaH}_{2} \mathrm{PO}_{4} . \quad\) Describe how you would prepare this buffer solution. [Hint: What volumes of which solutions would you use?
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