AP Chemistry 8.5: Acid-Base Titrations

Monoprotic acid

An acid molecule that can donate one ionizable proton per molecule. Examples include HCl, HNO$_3$, HCN, and acetic acid; in acetic acid, only the carboxyl-group hydrogen is acidic.

Titration curve

A graph of a solution property, usually pH for acid-base titrations, versus the volume or amount of titrant added. Its shape shows how composition changes and helps locate the equivalence point.

Why must total volume be used when calculating concentrations during a titration?

The titrant increases the solution volume, so concentration is based on total volume: $V_{\text{total}}=V_{\text{sample}}+V_{\text{titrant}}$. Ignoring dilution gives an incorrect pH.

Equivalence point in an acid-base titration

The point at which stoichiometrically equivalent amounts of acid and base have reacted. For a monoprotic acid and strong base, $n(OH^-)=n(HA)$ at equivalence.

Equivalence point vs. endpoint

The equivalence point is the stoichiometric point where chemically equivalent amounts have reacted. The endpoint is the experimentally observed signal, such as an indicator color change, used to estimate the equivalence point.

What are the four major regions of a strong acid-strong base titration curve?

They are the initial solution, the pre-equivalence region with excess acid, the equivalence point, and the post-equivalence region with excess strong base.

How is the pH calculated before the equivalence point in a strong acid-strong base titration?

Use stoichiometry to find the moles of excess $H_3O^+$, divide by the total volume, and calculate $pH=-\log[H_3O^+]$. The strong acid is assumed to ionize completely.

A 25.00 mL sample of 0.100 M HCl is titrated with 0.100 M NaOH. What is the pH after 12.50 mL of NaOH is added?

Initial moles of $H^+$ are $0.002500$ mol, and added $OH^-$ is $0.001250$ mol. The excess $H^+$ concentration is $0.001250/0.03750=0.0333$ M, so $pH=1.48$.

What is the pH at the equivalence point of a strong acid titrated with a strong base?

Approximately 7.00 at $25\ ^\circ\mathrm{C}$, because the dissolved salt contains ions that do not appreciably hydrolyze and water autoionization controls the small concentrations of $H_3O^+$ and $OH^-$.

How is the pH calculated after the equivalence point in a strong acid-strong base titration?

Find the moles of excess $OH^-$ after neutralization, divide by the total solution volume, and use $pOH=-\log[OH^-]$ followed by $pH=14.00-pOH$ at $25\ ^\circ\mathrm{C}$.

A 25.00 mL sample of 0.100 M HCl is titrated with 0.100 M NaOH. What is the pH after 37.50 mL of NaOH is added?

Excess $OH^-$ is $0.003750-0.002500=0.001250$ mol. Thus, $[OH^-]=0.001250/0.06250=0.0200$ M, giving $pOH=1.70$ and $pH=12.30$.

How do strong-acid and weak-acid titration curves compare before equivalence?

At equal initial concentrations, the weak acid begins at a higher pH. During the pre-equivalence region, the weak-acid titration has a buffer region and its pH changes more gradually than that of the strong-acid titration.

How do strong-acid and weak-acid titration curves compare after the equivalence point?

They become very similar because the pH is dominated by the same excess strong base titrant. The identity of the original acid has little effect in this region.

How is the initial pH of a weak monoprotic acid commonly approximated?

For a sufficiently weak acid, use $[H_3O^+]\approx\sqrt{K_a[HA]_0}$, then calculate $pH=-\log[H_3O^+]$. This approximation assumes the acid's ionization is small compared with its initial concentration.

Why is the initial pH of a weak acid higher than that of an equally concentrated strong acid?

A weak acid ionizes only partially, producing a smaller $[H_3O^+]$ than a strong acid of the same formal concentration. Consequently, its initial pH is higher.

What species are present before the equivalence point when a weak acid is titrated with a strong base?

The solution contains unreacted weak acid, $HA$, and its conjugate base, $A^-$. Together they form a buffer, so the Henderson-Hasselbalch equation can often be used.

Henderson-Hasselbalch equation for a weak acid buffer

$pH=pK_a+\log\left(\frac{[A^-]}{[HA]}\right)$. In titration calculations, mole ratios may replace concentration ratios when both species are in the same total volume.

What is special about the half-equivalence point in a weak acid-strong base titration?

Half of the original weak acid has been converted to conjugate base, so $[A^-]=[HA]$. Therefore, $pH=pK_a$ because $\log(1)=0$.

How is the equivalence-point pH calculated for a weak acid titrated with a strong base?

First determine the concentration of the conjugate base $A^-$ after dilution. Then use $K_b=K_w/K_a$ and, when appropriate, $[OH^-]\approx\sqrt{K_b[A^-]}$ before converting pOH to pH.

How does a weak acid-strong base titration differ from a strong acid-strong base titration at equivalence?

The conjugate base of the weak acid remains in solution and reacts with water to produce $OH^-$. Therefore, the equivalence-point pH is greater than 7.

Why is the pH after equivalence primarily controlled by excess strong base in a weak acid titration?

Once strong base is present in stoichiometric excess, its $OH^-$ concentration is much larger than the $OH^-$ produced by conjugate-base hydrolysis. Calculate pH from the excess $OH^-$.

Acid-base indicator

A weak organic acid or base whose conjugate forms have different colors. Its color changes over a characteristic pH interval and can signal the endpoint of a titration.

Indicator equilibrium for a weak-acid indicator

A weak-acid indicator can be represented as $HIn+H_2O\rightleftharpoons H_3O^++In^-$. The colors of $HIn$ and $In^-$ differ, so pH changes alter the observed color.

How does adding acid or base change the color of a weak-acid indicator?

Adding acid increases $[H_3O^+]$ and shifts the equilibrium toward $HIn$, the conjugate-acid color. Adding base removes $H_3O^+$ and shifts equilibrium toward $In^-$, the conjugate-base color.

How is an indicator's color related to its $pK_a$?

For $pH>pK_a$, the conjugate-base form predominates; for $pH<pK_a$, the conjugate-acid form predominates. When $pH\approx pK_a$, both forms are present and an intermediate color is observed.

Indicator color-change interval

The range of pH over which an indicator visibly changes color. It is typically approximated as $pK_a\pm1$.

How should an indicator be selected for an acid-base titration?

Choose an indicator whose color-change interval lies within the steep portion of the titration curve and brackets the equivalence-point pH. This makes the indicator endpoint close to the stoichiometric equivalence point.

Which indicator is generally suitable for titrating a weak acid with a strong base, and why?

Phenolphthalein is suitable because its transition interval occurs near the basic equivalence point and within the sharp pH rise. An indicator that changes at lower pH would signal an endpoint too early.

Why can several indicators work for a strong acid-strong base titration?

The pH changes very sharply through a broad range near the equivalence point, so multiple indicator transition intervals fall within that steep region. Their endpoints therefore approximate the equivalence volume.

Polyprotic acid

An acid capable of donating more than one proton. Its ionization occurs stepwise, producing species with progressively greater negative charge.

Diprotic acid

An acid that can donate two protons through two successive ionization reactions. Examples include $H_2SO_4$ and $H_2CO_3$.

Triprotic acid

An acid that can donate three protons in successive ionization steps. Phosphoric acid, $H_3PO_4$, is a common example.

Why does each successive ionization of a polyprotic acid occur less extensively?

After each proton is removed, the remaining species becomes more negatively charged, making further proton loss less favorable. Thus, $K_{a1}>K_{a2}>K_{a3}$ in general.

What is the general relationship among successive acid ionization constants?

For a polyprotic acid, $K_{a1}>K_{a2}>K_{a3}$, so $pK_{a1}<pK_{a2}<pK_{a3}$. Successive constants often differ by several orders of magnitude.

Why can the ionization steps of a weak polyprotic acid often be treated separately?

If $K_{a1}$ is at least about 20 times larger than $K_{a2}$, the first step produces nearly all of the initial $H_3O^+$ and intermediate anion. Later ionizations cause much smaller concentration changes and can be calculated afterward.

How does a polyprotic acid affect the number of possible equivalence points in a titration?

Each ionizable proton can potentially produce a separate equivalence point. Distinct equivalence points are most apparent when successive $pK_a$ values are sufficiently separated.

What features appear in a titration curve for a polyprotic acid?

A polyprotic acid may show multiple buffer regions and multiple steep rises, one for each distinguishable proton-neutralization step. Each half-equivalence point corresponds approximately to a successive $pK_a$, and each separated equivalence point represents neutralization of another proton.

When are multiple equivalence points of a polyprotic acid most clearly visible?

They are most clearly separated when the successive $pK_a$ values differ substantially. If the values are too close, the buffer regions and pH jumps overlap, making separate equivalence points difficult to distinguish.

What is the relationship between the acid and conjugate-base equilibrium constants?

For a conjugate acid-base pair, $K_aK_b=K_w$. Therefore, $K_b=K_w/K_a$ and, at $25\ ^\circ\mathrm{C}$, $pK_a+pK_b=14.00$.