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Chapter 16: Problem 18

Equal volumes of two buffers are prepared with equal concentrations of acid and conjugate base, but they use different weak acids with different p \(K_{\mathrm{a}}\) values. Do the two buffers have the same buffer capacity?

Short Answer

Expert verified
Answer: No, the buffer capacities of the two buffers will not be the same due to their different pKa values. In general, a buffer will have a higher buffer capacity when its pH is close to its pKa value. So, even though the two buffers have equal concentrations, their different pKa values will lead to different buffer capacities.

Step by step solution

01

Understanding Buffer Capacity

Buffer capacity refers to the ability of a buffer solution to resist changes in pH when an acid or base is added. In other words, it is an indication of how effectively a buffer can maintain its pH. Mathematically, the buffer capacity (尾) can be defined as the amount of strong acid or base that must be added to change the pH of 1 L of the buffer solution by 1 unit.
02

Knowing the Buffer Capacity Formula

The buffer capacity (尾) can be calculated using the following formula: \[ \beta = \frac{2.303 \times (C_\mathrm{A} + C_\mathrm{B})}{1+\frac{10^{\mathrm{pH}-\mathrm{pKa}}}{1+10^{\mathrm{pH}-\mathrm{pKa}}}} \] Here, 尾 is the buffer capacity, C鈧� is the acid concentration, C_b is the conjugate base concentration, pH is the pH of the buffer solution, and pKa is the acid dissociation constant.
03

Considering the Given Situation

In the exercise, we are given two buffers with equal volumes and equal concentrations of acid and conjugate base. Therefore, the values of C鈧� and C_b are the same for both buffers. However, the pKa values are different. We need to find out if the buffer capacities of the two buffers are the same.
04

Analyzing the Buffer Capacity Formula

From the buffer capacity formula, we can see that the buffer capacity depends on the concentrations of acid and conjugate base (C鈧� and C_b), as well as the pH and pKa values. Since C鈧� and C_b are the same for both buffers, the only factors that can affect the buffer capacity are the pH and pKa values.
05

Conclusion

Based on the analysis of the buffer capacity formula, we can conclude that the buffer capacities of the two buffers will not be the same due to their different pKa values. In general, a buffer will have a higher buffer capacity when its pH is close to its pKa value. So, even though the two buffers have equal concentrations, their different pKa values will lead to different buffer capacities.

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Key Concepts

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

Buffer Solution
A buffer solution is a special kind of solution that helps maintain a stable pH, even when small amounts of acid or base are added. This is because it contains a weak acid and its conjugate base or a weak base and its conjugate acid. Together, they work to neutralize any added acid or base. Buffer solutions are very useful in various scientific applications and are used in everything from biological systems to industrial processes. Understanding how buffer solutions work is all about balance. The weak acid in the buffer will react with any added bases, while the conjugate base will react with any added acids. This balance is crucial for keeping the pH steady. For example, in a laboratory setting, a buffer solution may be used to create an environment with a specific pH that won't change easily, allowing experiments to be conducted consistently. Thus,
  • Buffer solutions stabilize pH changes.
  • They are made from a weak acid or base and its conjugate counterpart.
  • They are essential for many scientific experiments and biological processes.
pKa value
The pKa value is a key concept to understand when discussing buffers. It is the negative logarithm of the acid dissociation constant (Ka) of a solution. In simpler terms, it tells us how strong or weak an acid is. The lower the pKa value, the stronger the acid; the higher the pKa value, the weaker the acid. In the context of buffer solutions, knowing the pKa value of the acid involved is essential because a buffer is most effective when the pH is close to the pKa. At this point, equal concentrations of the acid and its conjugate base exist, maximizing the buffer's ability to neutralize added acids or bases. Here are some critical points about pKa values:
  • pKa provides insight into acid strength.
  • It dictates the effectiveness of a buffer solution.
  • Buffers work best when the pH is at or near the pKa of the acid.
Acid and Conjugate Base
In buffer solutions, understanding the relationship between an acid and its conjugate base is essential. The acid is the substance that donates protons (H鈦� ions), while the conjugate base is what remains after the acid has donated a proton. When acids and bases work together in a buffer, they manage to stabilize the pH by neutralizing added acids or bases. Consider a weak acid, such as acetic acid, and its conjugate base, acetate. When a little bit of a strong acid like hydrochloric acid (HCl) is added to the buffer, the acetate ion (conjugate base) reacts with the added H鈦� ions to form acetic acid, hence preventing a significant change in pH. The relationship between acids and their conjugate bases is vital for a few reasons:
  • They maintain the buffer's ability to resist pH changes.
  • The balance between the two in a solution is what makes a buffer effective.
  • They are crucial for the practical use of buffers in various chemical and biological systems.

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Most popular questions from this chapter

Why is \(\mathrm{BF}_{3}\) a Lewis acid but not a Bronsted-Lowry acid?

A \(25.0 \mathrm{mL}\) sample of \(0.100 M\) acetic acid is titrated with \(0.125 \mathrm{M} \mathrm{NaOH}\) at \(25^{\circ} \mathrm{C} .\) What is the \(\mathrm{pH}\) of the solution after \(10.0,20.0,\) and \(30.0 \mathrm{mL}\) of the base have been added?

Draw Lewis structures that show how electron pairs move and bonds form and break in the following reaction, and identify the Lewis acid and Lewis base. $$\mathrm{B}(\mathrm{OH})_{3}(a q)+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightleftharpoons \mathrm{B}(\mathrm{OH})_{4}^{-}(a q)+\mathrm{H}_{3} \mathrm{O}^{+}(a q)$$

(a) What is the concentration of ammonia in a popular window cleaner if \(25.34 \mathrm{mL}\) of \(1.162 \mathrm{M} \mathrm{HCl}\) is needed to titrate a \(10.00 \mathrm{mL}\) sample of the cleaner? (b) Suppose that the sample was diluted to about \(50 \mathrm{mL}\) with deionized water prior to the titration to make it easier to mount a pH electrode in it. What effect did this dilution have on the volume of titrant needed?

What masses of acetic acid and sodium acetate are needed to prepare \(125 \mathrm{mL}\) of \(\mathrm{pH}=5.00\) buffer if the total concentration of the two components is \(0.500 M ?\)
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