5: Investigating Buffers
- Page ID
- 516590
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. Prerequisite Math & Theory
- Henderson-Hasselbalch Equation: You must be able to calculate the mass of sodium acetate needed to achieve a specific target pH:
\[ \text{pH} = \mathrm{p}K_{\mathrm{a}} + \log \left( \frac{[\text{Conjugate Base}]}{[\text{Weak Acid}]} \right) \]
- Rearrangement Skill: Given a target pH and \(\mathrm{p}K_{\mathrm{a}}\), solve for the ratio \(\frac{[\mathrm{C_2H_3O_2^-}]}{[\mathrm{HC_2H_3O_2}]}\).
- Mass Calculation: Calculate the required molarity of conjugate base, then use \(\text{Mass (g)} = \text{Molarity (mol/L)} \times \text{Volume (L)} \times \text{Molar Mass (g/mol)}\) to determine grams of \(\mathrm{NaC_2H_3O_2}\).
- Buffer Capacity: A buffer prepared with \(1.0\text{ M}\) components resists pH changes 10 times more effectively than a buffer prepared with \(0.1\text{ M}\) components, even though both buffers possess the exact same initial pH.
2. Required Technical Skills
- pH Probe Calibration: Calibrating a pH sensor using standard buffer solutions.
- Data Logging (Events with Entry): Recording titrant volume added versus pH during buffer capacity testing.
3. Critical Safety
- Acids and Bases: Concentrated acetic acid, \(0.5\text{ M }\mathrm{NaOH}\), and \(0.5\text{ M }\mathrm{HCl}\) are caustic and corrosive. Wear chemical splash goggles at all times in the laboratory.
- To use the Henderson-Hasselbalch equation to calculate the required mass of sodium acetate to prepare two acidic acetate buffers (Buffer A and Buffer B).
- To experimentally prepare Buffer A (\(0.1\text{ M}\) acetic acid system) and Buffer B (\(1.0\text{ M}\) acetic acid system).
- To determine and compare the buffer capacities of Buffer A and Buffer B when challenged with strong base (\(0.5\text{ M }\mathrm{NaOH}\)) and strong acid (\(0.5\text{ M }\mathrm{HCl}\)).
INTRODUCTION
A buffer solution is an aqueous mixture of a weak acid and its conjugate base (or a weak base and its conjugate acid). The primary function of a buffer is to resist significant changes in pH upon the addition of small amounts of strong acid (\(\mathrm{H^+}\) or \(\mathrm{H_3O^+}\)) or strong base (\(\mathrm{OH^-}\)).
Buffers are vital in biological and industrial systems. For example, human blood plasma is maintained within a strict pH range of 7.35 to 7.45 by a carbonic acid/bicarbonate (\(\mathrm{H_2CO_3}/\mathrm{HCO_3^-}\)) buffer system.
At the molecular level, a buffer is a chemical system at equilibrium. Consider a nitrous acid (\(\mathrm{HNO_2}\)) buffer system. The weak acid establishes the following aqueous ionization equilibrium:
\[ \mathrm{HNO_2(aq)} + \mathrm{H_2O(l)} \rightleftharpoons \mathrm{H_3O^+(aq)} + \mathrm{NO_2^-(aq)} \]
The corresponding acid dissociation equilibrium constant expression is:
\[ K_{\mathrm{a}} = \frac{[\mathrm{H_3O^+}][\mathrm{NO_2^-}]}{[\mathrm{HNO_2}]} \]
To prepare a buffer, a soluble salt containing the conjugate base (such as sodium nitrite, \(\mathrm{NaNO_2}\)) is added to the weak acid solution. Added \(\mathrm{OH^-}\) ions are neutralized by reacting with the weak acid (\(\mathrm{HNO_2}\)), while added \(\mathrm{H_3O^+}\) ions are neutralized by reacting with the conjugate base (\(\mathrm{NO_2^-}\)).
Taking the negative logarithm of the equilibrium expression yields the Henderson-Hasselbalch equation:
\[ \text{pH} = \mathrm{p}K_{\mathrm{a}} + \log \left( \frac{[\text{Conjugate Base}]}{[\text{Weak Acid}]} \right) = \mathrm{p}K_{\mathrm{a}} + \log \left( \frac{[\mathrm{NO_2^-}]}{[\mathrm{HNO_2}]} \right) \]
A buffer is generally considered effective within a working range of \(\text{pH} = \mathrm{p}K_{\mathrm{a}} \pm 1\).
In this experiment, you will calculate the mass of solid sodium acetate (\(\mathrm{NaC_2H_3O_2}\)) required to prepare two acetic acid/acetate buffer solutions (\(\text{pH } 4.0\)). You will prepare both buffers and quantitatively measure their buffer capacities by titrating with \(0.5\text{ M }\mathrm{NaOH}\) and \(0.5\text{ M }\mathrm{HCl}\).
The Henderson-Hasselbalch equation demonstrates that pH depends directly on the logarithm of the conjugate base-to-acid mole ratio:
- Optimal Capacity Ratio: When \([\text{Base}] = [\text{Acid}]\), the ratio is 1. Since \(\log(1) = 0\), \(\text{pH} = \mathrm{p}K_{\mathrm{a}}\). This represents maximum buffer capacity.
- Buffer Range Limits: If the base-to-acid ratio drops below 0.1 or exceeds 10, the logarithmic term shifts pH by more than \(\pm 1\) unit, causing buffer capacity to rapidly diminish.
Henderson-Hasselbalch Equation:
\[ \text{pH} = \mathrm{p}K_{\mathrm{a}} + \log \left( \frac{[\mathrm{A^-}]}{[\mathrm{HA}]} \right) \]
- 5.1: Investigating Buffers - Experiment
- This page covers safety measures and materials for an experiment on buffer solutions using sodium acetate and acetic acid. It details the titration procedure of two buffers with sodium hydroxide and hydrochloric acid to monitor pH changes, highlighting the importance of accurate measurements and data recording. Additionally, it includes instructions for proper disposal and sensor cleaning to ensure safety and accuracy in the experiment.
- 5.2: Investigating Buffers - Pre-lab
- This page covers the preparation of buffer solutions using sodium acetate and acetic acid, focusing on calculations for achieving a specific pH with the Henderson-Hasselbalch equation. Students work with two buffer concentrations (0.1 M and 1.0 M) targeting a pH of 4, and are tasked with selecting an acid/base pair for a buffer at pH 6.10. It emphasizes the impact of concentration on neutralization capacity while maintaining the same pH.
- 5.3: Investigating Buffers - Data and Report
- This page provides a detailed experimental procedure for titrating Buffer A with NaOH and HCl, focusing on data collection related to pH changes and titrant volumes. It explains buffer capacity as the ability to maintain pH when acids or bases are added and includes calculations for buffer capacity (\(\beta\)). The page also discusses how different buffer solutions behave during titration and poses questions to enhance practical understanding of buffer systems.