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Chapter 14: Problem 52

Which of the following mixtures would result in a buffered solution when 1.0 L of each of the two solutions are mixed? a. \(0.2 M\) HNO and \(0.4 M \mathrm{NaNO}_{3}\) b. \(0.2 M \mathrm{HNO}_{3}\) and \(0.4 \mathrm{M} \mathrm{HF}\) c. \(0.2 \mathrm{M} \mathrm{HNO}_{3}\) and \(0.4 \mathrm{M} \mathrm{NaF}\) d. \(0.2 M\) HNO \(_{3}\) and \(0.4 M\) NaOH

Short Answer

Expert verified
Option \(c\) will result in a buffered solution when 1.0 L of each of the two solutions are mixed.

Step by step solution

01

Identify weak acid/base and conjugate pairs

Start by identifying the strong acids or bases in each of the given mixtures. Strong acids are HNO鈧� and H鈧係O鈧�, and strong bases include NaOH. Once we identify the strong and weak acids/bases, then we can find their conjugate acid or base pairs. a. HNO (typo, supposed to be HNO鈧�) is a strong acid. The conjugate base is NO鈧冣伝. The conjugate pair is HNO鈧�/NO鈧冣伝. b. HNO鈧� is a strong acid. HF is a weak acid. The conjugate base is F鈦�. The conjugate pairs are HNO鈧�/H鈧侽, HF/F鈦�. c. HNO鈧� is a strong acid, and its conjugate base is NO鈧冣伝. NaF is a salt of a strong base and a weak acid (HF). Its conjugate pair is HF/F鈦�. d. HNO鈧� is a strong acid, and its conjugate pair is HNO鈧�/H鈧侽. NaOH is a strong base.
02

Determine the initial concentration of the acid and its conjugate base

Option a has a strong acid and its conjugate base, but it would not be a buffered solution because HNO鈧�/NO鈧冣伝 is not a weak acid/conjugate base pair. Same goes for option d. So, we are left with options b and c. Option b: \(0.2 \mathrm{M}\) HNO鈧� and \(0.4 \mathrm{M}\) HF Since HNO鈧� is a strong acid, it will completely dissociate in the solution. In this case, the conjugate base, F鈦�, will also be present at the concentration of \(0.4 \mathrm{M}\). However, HNO鈧� and HF are not a weak acid/conjugate base pair, so option b is not a buffered solution. Option c: \(0.2 \mathrm{M} \mathrm{HNO}_{3}\) and \(0.4 \mathrm{M} \mathrm{NaF}\) NaF will dissociate completely in the solution, resulting in a concentration of F鈦� at \(0.4 \mathrm{M}\). The conjugate acid is HF. Since HNO鈧� is a strong acid, all F鈦� ions will react with HNO鈧� to form HF. The reaction: \[HNO_{3} + F鈦� \rightarrow HF + NO鈧冣伝\] Since HNO鈧� and F鈦� have the same concentration, they will react completely, forming \(0.2 \mathrm{M}\) HF and leaving \(0.2 \mathrm{M}\) F鈦� unreacted. Therefore, option c will result in a buffered solution with HF/F鈦� conjugate pair.
03

Check if the ratio between the acid and conjugate base concentrations is in a buffering range

For a buffering solution, the ratio should be close to 1:1. In option c, we have \(0.2 \mathrm{M}\) HF and \(0.2 \mathrm{M}\) F鈦�, which is a 1:1 ratio. Hence, the solution in option c will be a buffered solution. #Answer#: Option \(c\) will result in a buffered solution when 1.0 L of each of the two solutions are mixed.

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Key Concepts

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

Acid-Base Conjugate Pairs
Understanding the concept of acid-base conjugate pairs is vital in chemistry, especially when dealing with buffered solutions. Conjugate acid-base pairs are two substances that transform into each other by the gain or loss of a proton (H+). In simple terms, when an acid donates a proton, it becomes its conjugate base. Conversely, when a base accepts a proton, it becomes its conjugate acid.

For instance, in the reaction between hydrofluoric acid (HF) and water (H2O), HF donates a proton to become fluoride ion (F-), the conjugate base, while water accepts a proton to become the hydronium ion (H3O+), the conjugate acid. The ability to identify these pairs is crucial for predicting the behavior of acids and bases in solution, which leads to a better understanding of buffer solutions and acid-base equilibria.
Strong and Weak Acids
Acids can be classified into two categories: strong and weak. Strong acids, such as hydrochloric acid (HCl) and nitric acid (HNO3), dissociate completely in solution, releasing all their protons into the solution. This characteristic confers upon them the ability to significantly alter the pH of a solution.

In contrast, weak acids, like hydrofluoric acid (HF) and acetic acid (CH3COOH), only partially dissociate in solution. This incomplete dissociation is due to the reversible nature of their reaction with water, leading to an equilibrium between the undissociated acid and the ions. Understanding the distinction between strong and weak acids is essential for predicting the outcome when creating a buffered solution, as only a mixture involving a weak acid or base and its conjugate can constitute a proper buffer.
Buffer Capacity
The buffer capacity is a measure of a buffer solution's ability to resist changes in pH when strong acids or bases are added. It is determined by both the concentration of the acid-base conjugate pairs and the closeness of their concentration ratio to 1:1.

A buffer's effectiveness is maximized when the concentrations of the weak acid and its conjugate base are high and nearly equal. This optimal condition allows the buffer to neutralize added acids or bases by the reaction of the buffer components. For instance, if an acid is added to the solution, the conjugate base present in the buffer will neutralize the acid. Similarly, any added base will be neutralized by the weak acid in the buffer. In exercises such as the one provided, determining whether the given mixtures can form buffers with sufficient capacity involves checking their concentration ratios and the strength of the acid or base.
Acid-Base Equilibria
Acid-base equilibria refer to the balance that exists in a solution between a weak acid or base and its conjugate. This equilibrium is described by the acid dissociation constant (Ka) for weak acids or the base dissociation constant (Kb) for weak bases.

The concept is exemplified in the reaction of a weak acid, HA, in water:
HA <==> H+ + A-.
The equilibrium constant for this reaction is given by Ka = [H+][A-]/[HA]. For weak bases, the reaction and constant would be analogous but with OH- in place of H+. This constant helps in predicting the direction of the reaction and the concentrations of the species in solution at equilibrium. It is also key in buffer calculations and understanding the extent of ionization for a given acid or base in a buffer solution.

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Most popular questions from this chapter

Derive an equation analogous to the Henderson-Hasselbalch equation but relating \(\mathrm{pOH}\) and \(\mathrm{p} K_{\mathrm{b}}\) of a buffered solution composed of a weak base and its conjugate acid, such as \(\mathrm{NH}_{3}\) and \(\mathrm{NH}_{4}^{+}\).

Tris(hydroxymethyl)aminomethane, commonly called TRIS or Trizma, is often used as a buffer in biochemical studies. Its buffering range is \(\mathrm{pH} 7\) to \(9,\) and \(K_{\mathrm{b}}\) is \(1.19 \times 10^{-6}\) for the aqueous reaction $$\left(\mathrm{HOCH}_{2}\right)_{3} \mathrm{CNH}_{2}+\mathrm{H}_{2}\mathrm{O}\rightleftharpoons\left(\mathrm{HOCH}_{2}\right)_{3} \mathrm{CNH}_{3}^{+}+\mathrm{OH}^{-}$$ a. What is the optimal pH for TRIS buffers? b. Calculate the ratio [TRIS]/[TTRISH \(\left.^{+}\right]\) at \(\mathrm{pH}=7.00\) and at \(\mathrm{pH}=9.00\) c. A buffer is prepared by diluting \(50.0 \mathrm{g}\) TRIS base and \(65.0 \mathrm{g}\) TRIS hydrochloride (written as TRISHCl) to a total volume of 2.0 L. What is the pH of this buffer? What is the \(\mathrm{pH}\) after \(0.50 \mathrm{mL}\) of \(12 \mathrm{M}\) HCl is added to a 200.0-mL portion of the buffer?

Sketch a pH curve for the titration of a weak acid (HA) with a strong base (NaOH). List the major species, and explain how you would go about calculating the pH of the solution at various points, including the halfway point and the equivalence point.

Consider the titration of \(100.0 \mathrm{mL}\) of \(0.200 M\) acetic acid \(\left(K_{\mathrm{a}}=1.8 \times 10^{-5}\right)\) by \(0.100 M\) KOH. Calculate the \(\mathrm{pH}\) of the resulting solution after the following volumes of KOH have been added. a. \(0.0 \mathrm{mL}\) b. \(50.0 \mathrm{mL}\) c. \(100.0 \mathrm{mL}\) d. \(40.0 \mathrm{mL}\) e. \(50.0 \mathrm{mL}\) f. \(100.0 \mathrm{mL}\)

A buffer is prepared by dissolving \(\mathrm{HONH}_{2}\) and \(\mathrm{HONH}_{3} \mathrm{NO}_{3}\) in some water. Write equations to show how this buffer neutralizes added \(\mathrm{H}^{+}\) and \(\mathrm{OH}^{-}\).
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