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Ch.17 - Additional Aspects of Aqueous Equilibria
Brown - Chemistry: The Central Science 14th Edition
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook
All textbooksBrown 14th EditionCh.17 - Additional Aspects of Aqueous EquilibriaProblem 31b
Chapter 17, Problem 31b

You have to prepare a pH = 3.50 buffer, and you have the following 0.10 M solutions available: HCOOH, CH3COOH, H3PO4, HCOONa, CH3COONa, and NaH2PO4. How many milliliters of each solution would you use to make approximately 1 L of the buffer?

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Identify the acid-base pairs available: HCOOH/HCOONa, CH3COOH/CH3COONa, and H3PO4/NaH2PO4. These pairs can form buffers.
Determine the pKa values for each acid: HCOOH (pKa ≈ 3.75), CH3COOH (pKa ≈ 4.76), and H3PO4 (pKa ≈ 2.15 for the first dissociation). Choose the acid-base pair with a pKa closest to the desired pH of 3.50, which is HCOOH/HCOONa.
Use the Henderson-Hasselbalch equation to find the ratio of the concentrations of the acid and its conjugate base: \( \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \). Substitute pH = 3.50 and pKa = 3.75 to solve for the ratio \( \frac{[\text{HCOONa}]}{[\text{HCOOH}]} \).
Calculate the volumes of HCOOH and HCOONa needed to achieve the desired concentration ratio. Assume the total volume of the buffer is approximately 1 L, and use the concentration of 0.10 M for both solutions. Let \( V_1 \) be the volume of HCOOH and \( V_2 \) be the volume of HCOONa, then \( V_1 + V_2 \approx 1000 \text{ mL} \).
Solve the system of equations derived from the Henderson-Hasselbalch equation and the total volume constraint to find the specific volumes of HCOOH and HCOONa needed to prepare the buffer.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Buffer Solutions

A buffer solution is a system that resists changes in pH upon the addition of small amounts of acid or base. It typically consists of a weak acid and its conjugate base or a weak base and its conjugate acid. In this case, the pH of 3.50 indicates the use of a weak acid and its salt to maintain the desired acidity.
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Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of its acid and conjugate base. It is expressed as pH = pKa + log([A-]/[HA]), where pKa is the acid dissociation constant. This equation is essential for calculating the required amounts of the acid and its salt to achieve the target pH.
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Concentration and Dilution

Concentration refers to the amount of solute present in a given volume of solution, typically expressed in molarity (M). When preparing a buffer, it is crucial to understand how to calculate the volumes of concentrated solutions needed to achieve the desired final concentrations in the buffer. This involves using dilution principles to ensure the correct proportions of the components.
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Related Practice
Textbook Question

(b) What is the ratio of HCO3- to H2CO3 in an exhausted marathon runner whose blood pH is 7.1?

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Textbook Question

The accompanying graph shows the titration curves for two monoprotic acids. (d) Estimate the pKa of the weak acid.

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Textbook Question

You have to prepare a pH = 5.00 buffer, and you have the following 0.10 M solutions available: HCOOH, HCOONa, CH3COOH, CH3COONa, HCN, and NaCN. How many milliliters of each solution would you use to make approximately 1 L of the buffer?

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Textbook Question

(a) What is the ratio of HCO3- to H2CO3 in blood of pH 7.4?

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