$$\newcommand{\xrightleftharpoons}[2]{\overset{#1}{\underset{#2}{\rightleftharpoons}}}$$ $$\newcommand{\conc}[1]{\left[\mathrm{#1}\right]}$$ $$\newcommand{\chem}[1]{\mathrm{#1}}$$

# Chapter 15 Acid-Base Equilibria

Shaun Williams, PhD

### Common Ion Effect

• Shift in equilibrium position that occurs because of the addition of an ion already involved in the equilibrium reaction.
• An application of Le Châtelier’s principle.
• $$\chem{HCN(aq)+H_2O(l) \rightleftharpoons H_3O^+(aq)+CN^-(aq)}$$
• Addition of $$\chem{NaCN}$$ will shift the equilibrium to the left because of the addition of $$\chem{CN^-}$$, which is already involved in the equilibrium reaction.
• A solution of $$\chem{HCN}$$ and $$\chem{NaCN}$$ is less acidic than a solution of $$\chem{HCN}$$ alone.

### Key Points about Buffered Solutions

• Buffered Solution – resists a change in pH.
• They are weak acids or bases containing a common ion.
• After addition of strong acid or base, deal with stoichiometry first, then the equilibrium.

### Henderson-Hasselbalch Equation

$$\mathrm{pH} = \mathrm{p}K_a + \log \frac{\conc{A^-}}{\conc{HA}}$$

• For a particular buffering system (conjugate acid–base pair), all solutions that have the same ratio $$\frac{\conc{A^-}}{\conc{HA}}$$ will have the same $$\mathrm{pH}$$.

### Exercise

What is the $$\mathrm{pH}$$ of a buffer solution that is $$0.45\,\mathrm{M}$$ acetic acid ($$\chem{HC_2H_3O_2}$$) and $$0.85\,\mathrm{M}$$ sodium acetate ($$\chem{NaC_2H_3O_2}$$)? The $$K_a$$ for acetic acid is $$1.8 \times 10^{–5}$$.

$$\mathrm{pH} = 5.02$$

### Buffered Solution Characteristics

• Buffers contain relatively large concentrations of a weak acid and corresponding conjugate base.
• Added $$\chem{H^+}$$ reacts to completion with the weak base.
• Added $$\chem{OH^-}$$ reacts to completion with the weak acid.
• The $$\mathrm{pH}$$ in the buffered solution is determined by the ratio of the concentrations of the weak acid and weak base. As long as this ratio remains virtually constant, the $$\mathrm{pH}$$ will remain virtually constant. This will be the case as long as the concentrations of the buffering materials ($$\chem{HA}$$ and $$\chem{A^–}$$ or $$\chem{B}$$ and $$\chem{BH^+}$$) are large compared with amounts of $$\chem{H^+}$$ or $$\chem{OH^–}$$ added.

### Buffering Capacity

• The amount of protons or hydroxide ions the buffer can absorb without a significant change in pH.
• Determined by the magnitudes of $$\conc{HA}$$ and $$\conc{A^-}$$.
• A buffer with large capacity contains large concentrations of the buffering components.
• Optimal buffering occurs when $$\conc{HA}$$ is equal to $$\conc{A^-}$$.
• It is for this condition that the ratio $$\frac{\conc{A^-}}{\conc{HA}}$$ is most resistant to change when $$\chem{H^+}$$ or $$\chem{OH^–}$$ is added to the buffered solution.

### Choosing a Buffer

• $$\mathrm{p}K_a$$ of the weak acid to be used in the buffer should be as close as possible to the desired $$\mathrm{pH}$$.

### Titration Curve

• Plotting the $$\mathrm{pH}$$ of the solution being analyzed as a function of the amount of titrant added.
• Equivalence (Stoichiometric) Point – point in the titration when enough titrant has been added to react exactly with the substance in solution being titrated.
• When a strong acid and strong base are used, the equivalence point will be at a $$\mathrm{pH}$$ of 7.

### Weak Acid-Strong Base Titration

1. A stoichiometry problem (reaction is assumed to run to completion) then determine concentration of acid remaining and conjugate base formed.
2. An equilibrium problem (determine position of weak acid equilibrium and calculate $$\mathrm{pH}$$.

### Concept Check

Calculate the $$\mathrm{pH}$$ of a solution made by mixing $$0.20\,\mathrm{mol}\,\chem{HC_2H_3O_2}$$ ($$K_a=1.8 \times 10^{--5}$$) with $$0.030\,\mathrm{mol}\,\chem{NaOH}$$ in $$1.0\,\mathrm{L}$$ of aqueous solution.

$$\mathrm{pH}=3.99$$

### Exercise

Calculate the $$\mathrm{pH}$$ of a $$100.0\,\mathrm{mL}$$ solution of $$0.100\,\mathrm{mol}\,\chem{HC_2H_3O_2}$$, with $$K_a=1.8 \times 10^{--5}$$.

$$\mathrm{pH}=2.87$$

### Acid-Base Indicators

• Marks the end point of a titration by changing color.
• The equivalence point is not necessarily the same as the end point (but they are ideally as close as possible).

/