21.23: Buffers
- Page ID
- 53953
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Diabetes mellitus is a disorder of glucose metabolism in which insulin production by the pancreas is impaired. Since insulin helps glucose enter the cells, a decrease of this hormone means that glucose cannot be used in its normal fashion. When this happens, the body begins to break down fats, producing a decrease in blood pH. Chemical systems in the body can balance this pH shift for a while, but excessive acid production can create serious problems if not corrected by administering insulin to restore normal glucose use.
Buffers
If only \(1.0 \: \text{mL}\) of \(0.10 \: \text{M}\) hydrochloric acid is added to \(1.0 \: \text{L}\) of pure water, the pH drops drastically from 7.0 to 4.0. This is a 1000-fold increase in the acidity of the solution. For many purposes, it is desirable to have a solution which is capable of resisting such large changes in pH when relatively small amounts of acid or base are added to it. Such a solution is called a buffer. A buffer is a solution of a weak acid or a base and its salt. Both components must be present for the system to act as a buffer to resist changes in pH. Commercial buffer solutions, which have a wide variety of pH values, can be obtained.
Some common buffer systems are listed in the table below.
| Buffer System | Buffer Components | pH of buffer (equal molarities of both components) |
|---|---|---|
| Acetic acid/acetate ion | \(\ce{CH_3COOH}\)/\(\ce{CH_3COO^-}\) | 4.74 |
| Carbonic acid/hydrogen carbonate ion | \(\ce{H_2CO_3}\)/\(\ce{HCO_3^-}\) | 6.38 |
| Dihydrogen phosphate ion/hydrogen phosphate ion | \(\ce{H_2PO_4^-}\)/\(\ce{HPO_4^{2-}}\) | 7.21 |
| Ammonia/ammonium ion | \(\ce{NH_3}\)/\(\ce{NH_4^+}\) | 9.25 |
One example of a buffer is a solution made of acetic acid (the weak acid) and sodium acetate (the salt). The pH of a buffer consisting of \(0.50 \: \text{M} \: \ce{CH_3COOH}\) and \(0.50 \: \text{M} \: \ce{CH_3COONa}\) is 4.74. If \(10.0 \: \text{mL}\) of \(1.0 \: \text{M} \: \ce{HCl}\) is added to \(1.0 \: \text{L}\) of the buffer, the pH only decreases to 4.73. This ability to "soak up" the additional hydrogen ions from the \(\ce{HCl}\) that was added is due to the reaction below.
\[\ce{CH_3COO^-} \left( aq \right) + \ce{H^+} \left( aq \right) \rightarrow \ce{CH_3COOH} \left( aq \right)\nonumber \]
Since both the acetate ion and the acetic acid were already present in the buffer, the only thing that changes is the ratio of one to the other. Small changes in that ratio have only very minor effects on the pH.
If \(10.0 \: \text{mL}\) of \(1.0 \: \text{M} \: \ce{NaOH}\) were added to another \(1.0 \: \text{L}\) of the same buffer, the pH would only increase to 4.76. In this case the buffer takes up the additional hydroxide ions.
\[\ce{CH_3COOH} \left( aq \right) + \ce{OH^-} \left( aq \right) \rightarrow \ce{CH_3COO^-} \left( aq \right) + \ce{H_2O} \left( l \right)\nonumber \]
Again the ratio of acetate ion to acetic acid changes slightly, this time causing a very small increase in the pH.
It is possible to add so much acid or base to a buffer that its ability to resist a significant change in pH is overwhelmed. The buffer capacity is the amount of acid or base that can be added to a buffer solution before a large change in pH occurs. The buffer capacity is exceeded when the number of moles of \(\ce{H^+}\) or \(\ce{OH^-}\) that are added to the buffer exceeds the number of moles of the buffer components.
Summary
- A buffer is a solution of a weak acid or a base and its salt.
- The buffer capacity is the amount of acid or base that can be added to a buffer solution before a large change in pH occurs.
- Reactions showing how buffers regulate pH are described.