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Chapter 17: Problem 32

You have to prepare a pH \(5.00\) buffer, and you have the following \(0.10 \mathrm{M}\) solutions available: HCOOH, HCOONa, \(\mathrm{CH}_{3} \mathrm{COOH}, \mathrm{CH}_{3} \mathrm{COONa}, \mathrm{HCN}\), and NaCN. Which solutions would you use? How many milliliters of each solution would you use to make approximately \(1 \mathrm{~L}\) of the buffer?

Short Answer

Expert verified
To make approximately 1 L of the pH 5.00 buffer, mix 355 mL of 0.10 M CH3COOH (Acetic acid) solution with 645 mL of 0.10 M CH3COONa (Sodium acetate) solution.

Step by step solution

01

Identify pKa values for the given solutions

Since we have HCOOH, HCOONa, CH3COOH, CH3COONa, HCN, and NaCN, first we need to find the pKa values of the corresponding weak acids, HCOOH (Formic acid), CH3COOH (Acetic acid), and HCN (Hydrocyanic acid): HCOOH: pKa = 3.75 CH3COOH: pKa = 4.74 HCN: pKa = 9.31
02

Choose the appropriate buffer pair

We want a buffer with a pH of 5.00. The weak acid with the pKa value closest to 5.00 is CH3COOH (Acetic acid), with a pKa value of 4.74. Therefore, we will use the CH3COOH/CH3COONa (Acetic acid/Sodium acetate) buffer pair. The Henderson-Hasselbalch equation is: pH = pKa + log10([A-]/[HA]) For our buffer, pH = 5.00 pKa = 4.74
03

Find the concentration ratio of conjugate base to weak acid in the buffer

Plug in the pH and pKa values into the Henderson-Hasselbalch equation: 5.00 = 4.74 + log10([CH3COONa]/[CH3COOH]) Now solve for the concentration ratio: 0.26 = log10([CH3COONa]/[CH3COOH]) 10^0.26 = [CH3COONa]/[CH3COOH] 1.82 鈮� [CH3COONa]/[CH3COOH]
04

Calculate the amount of each solution to mix together

Since we want to make approximately 1 L of the buffer solution, let [CH3COOH] = x and [CH3COONa] = 1.82x. At a concentration of 0.10 M for both solutions, using the relationship: mol = M 脳 L we find the volume (in L) of both solutions, x = (0.10 M)(Volume of CH3COOH solution) 1.82x = (0.10 M)(Volume of CH3COONa solution) Let V1 be the volume of CH3COOH and V2 be the volume of CH3COONa. The total volume is approximately 1 L, so: V1 + V2 鈮� 1 L Now solve the equations together: V1 = 10x V2 = 10(1.82x) V1 + V2 鈮� 1 L 10x + 10(1.82x) 鈮� 1 10x(1 + 1.82) 鈮� 1 2.82x 鈮� 0.1 x 鈮� 0.0355 Now we can find the volumes of each solution: Volume of CH3COOH = 10x 鈮� 0.355 L 鈮� 355 mL Volume of CH3COONa = 10(1.82x) 鈮� 0.645 L 鈮� 645 mL Therefore, to make approximately 1 L of the pH 5.00 buffer, mix 355 mL of 0.10 M CH3COOH (Acetic acid) solution with 645 mL of 0.10 M CH3COONa (Sodium acetate) solution.

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Key Concepts

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

Henderson-Hasselbalch equation
In the world of chemistry, the Henderson-Hasselbalch equation is a vital tool. It helps us understand how the pH of a buffer solution connects to the concentration of the acid and its conjugate base. This equation is expressed as:\[pH = pK_a + \log_{10}\left(\frac{[A^-]}{[HA]}\right)\]Here, \([A^-]\) stands for the concentration of the conjugate base, and \([HA]\) is the concentration of the weak acid. The equation showcases how a buffer's pH adjusts based on the ratio of these concentrations.
In practice, if the concentration of the conjugate base is higher than that of the acid, the pH will be greater than the pKa, making the solution more basic. Conversely, if the acid's concentration exceeds that of the base, the pH will be lower than the pKa, creating a more acidic environment.
  • This equation is extremely useful in predicting and creating buffer solutions with specific pH values.
  • It allows chemists to calculate how much of each component to add to a solution to achieve a desired pH.
pKa values
In buffer solutions, pKa values play a significant role. The pKa serves as the key identifier of an acid's strength, essentially telling us how easily an acid can donate its proton to the surrounding solution. The pKa is derived from the acid dissociation constant, Ka, using the expression:\[pK_a = -\log_{10}(K_a)\]A lower pKa signalizes a stronger acid, as it more readily releases protons into the solution. Conversely, a higher pKa indicates a weaker acid.
  • Choosing a buffer system involves selecting an acid whose pKa is close to the desired pH of the buffer.
  • This ensures that the buffer can effectively neutralize added acids or bases, thus maintaining a stable pH.
For example, in the exercise, we used Acetic acid (CH鈧僀OOH), which has a pKa of 4.74, because it is closest to the target pH of 5.00 for the buffer. This makes acetic acid the best candidate for maintaining stability at this pH point.
Acid-base pairs
In buffer solutions, the concept of acid-base pairs is crucial. An acid-base pair consists of a weak acid and its conjugate base, or vice versa. They work together to resist significant pH changes when small amounts of acid or base are added.
  • A weak acid like CH鈧僀OOH (acetic acid) partially dissociates in water, producing its conjugate base, CH鈧僀OO鈦� (acetate ion).
  • These pairs are at the heart of buffer systems, as they enable the absorption of added H鈦� ions (making the solution less acidic) or OH鈦� ions (making the solution less basic).
An effective buffer requires careful balancing. The concentration of the weak acid must be enough to neutralize added bases. Similarly, the conjugate base should counteract added acids. This balancing act is exactly why in our exercise, we calculate the precise volumes of each component to ensure an optimal ratio of acid to conjugate base. Buffer solutions help maintain the pH of various environments in scientific studies and practical applications, ensuring reaction conditions remain consistent.

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Most popular questions from this chapter

Assume that \(30.0 \mathrm{~mL}\) of a \(0.10 \mathrm{M}\) solution of a weak base B that accepts one proton is titrated with a \(0.10 \mathrm{M}\) solution of the monoprotic strong acid HA. (a) How many moles of HA have been added at the equivalence point? (b) What is the predominant form of B at the equivalence point? (c) Is the pH 7, less than 7, or more than 7 at the equivalence point? (d) Which indicator, phenolphthalein or methyl red, is likely to be the better choice for this titration?

You are asked to prepare a pH \(=4.00\) buffer starting from \(1.50 \mathrm{~L}\) of \(0.0200 \mathrm{M}\) solution of benzoic acid \(\left(\mathrm{C}_{4} \mathrm{H}_{4} \mathrm{COOH}\right)\) and any amount you need of sodium benzoate \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COONa}\right)\). (a) What is the \(\mathrm{pH}\) of the benzoic acid solution prior to adding sodium benzoate? (b) How many grams of sodium benzoate should be added to prepare the buffer? Neglect the small volume change that occurs when the sodium benzoate is added.

Which of these statements about the common-ion effect is most correct? (a) The solubility of a salt MA is decreased in a solution that already contains either \(\mathrm{M}^{+}\)or \(A^{-}\). (b) Common ions alter the equilibrium constant for the reaction of an ionic

A 1.00- \(\mathrm{L}\) solution saturated at \(25^{\circ} \mathrm{C}\) with calcium oxalate \(\left(\mathrm{CaC}_{2} \mathrm{O}_{4}\right)\) contains \(0.0061 \mathrm{~g}\) of \(\mathrm{CaC}_{2} \mathrm{O}_{4}\). Calculate the solubility-product constant for this salt at \(25^{\circ} \mathrm{C}\).

(a) Calculate the percent ionization of \(0.0075 \mathrm{M}\) butanoic acid \(\left(K_{a}=1.5 \times 10^{-5}\right)\). (b) Calculate the percent ionization of \(0.0075 \mathrm{M}\) butanoic acid in a solution containing \(0.085 \mathrm{M}\) sodium butanoate.
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