10.3 Acid-base Titrations and Buffers

Acid-base Titrations and Buffers

Acid-base titrations let chemists figure out the concentration of an unknown acid or base by reacting it with a solution of known concentration. Buffers, on the other hand, are solutions that resist pH changes when small amounts of acid or base are added. Together, these two topics connect equilibrium, stoichiometry, and pH in ways that show up constantly in both lab work and the real world.

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Understanding Acid-Base Titrations

What is an Acid-Base Titration?

In a titration, you slowly add a solution of known concentration (the titrant) to a solution of unknown concentration (the analyte) until the reaction between them is complete. The goal is to find the exact volume of titrant needed to fully neutralize the analyte, then use stoichiometry to calculate the unknown concentration.

The point where moles of acid exactly equal moles of base is called the equivalence point. That's the target of every titration.

How do Indicators Work?

Indicators are substances that change color over a specific pH range. You choose an indicator whose color change occurs as close to the equivalence point as possible. For example, phenolphthalein is colorless in acidic solution and turns pink around pH 8.2–10, making it a good choice for strong acid–strong base titrations.

One thing to keep straight: the endpoint (where the indicator changes color) and the equivalence point (where moles of acid equal moles of base) are close but not always identical. A well-chosen indicator minimizes that gap.

Types of Titrations

The shape of a titration curve and the pH at equivalence depend on the strengths of the acid and base involved:

• Strong Acid–Strong Base: The equivalence point is at pH 7. The curve shows a sharp, dramatic pH jump near equivalence.
• Weak Acid–Strong Base: The equivalence point is above pH 7 because the weak acid's conjugate base is present at equivalence, making the solution slightly basic.
• Strong Acid–Weak Base: The equivalence point is below pH 7 because the weak base's conjugate acid is present at equivalence, making the solution slightly acidic.
• Weak Acid–Weak Base: The pH change near equivalence is very gradual, making it hard to detect with a simple indicator. A pH meter is usually needed.

Detecting Equivalence Points

There are two main ways to detect the equivalence point:

• pH meters give continuous, precise numerical readings throughout the titration. Plotting pH vs. volume of titrant added produces a titration curve, and the equivalence point sits at the steepest part of the curve.
• Colorimetric indicators provide a visual signal but are less precise. Each indicator only works well within a narrow pH range, so you need to pick the right one for your specific titration type.

Calculations Involving Titration Curves

Interpreting Titration Curves

A titration curve plots pH (y-axis) against volume of titrant added (x-axis). Two points on the curve matter most:

• Equivalence point: Where moles of $H^+$ equal moles of $OH^-$. On the curve, this is the center of the steepest vertical section.
• Half-equivalence point: Where exactly half the analyte has been neutralized. At this point, $[HA] = [A^-]$, which means $\text{pH} = \text{p}K_a$. This is the easiest way to determine the $K_a$ of an unknown weak acid from a titration curve.

Calculating Unknown Concentrations

For a monoprotic acid–base titration (one $H^+$ per acid molecule, one $OH^-$ per base molecule), the moles of acid equal the moles of base at equivalence:

$M_1V_1 = M_2V_2$

where $M$ is molarity and $V$ is volume for the acid (1) and base (2).

Practice: Molarity & Volume Calculations

Suppose you titrate 25 mL of HCl with 0.1 M NaOH, and it takes 30 mL of NaOH to reach the equivalence point.

1. Write the relationship at equivalence: $M_{\text{HCl}} \times V_{\text{HCl}} = M_{\text{NaOH}} \times V_{\text{NaOH}}$
2. Plug in known values: $M_{\text{HCl}} \times 25\ \text{mL} = 0.1\ \text{M} \times 30\ \text{mL}$
3. Solve for the unknown:

$M_{\text{HCl}} = \frac{(0.1)(30)}{25} = 0.12\ \text{M}$

Note: volumes don't need to be converted to liters here because the units cancel, but both volumes must be in the same unit.

Buffer Solutions

A buffer is a solution that resists changes in pH when small amounts of strong acid or strong base are added. Buffers consist of a weak acid and its conjugate base (or a weak base and its conjugate acid) in appreciable concentrations.

Composition & Function

A classic example is a buffer made from acetic acid ($CH_3COOH$, the weak acid) and sodium acetate ($CH_3COONa$, which provides the conjugate base $CH_3COO^-$).

Here's how it resists pH change:

• If you add a strong acid (extra $H^+$): The conjugate base $CH_3COO^-$ reacts with the added $H^+$ to form more $CH_3COOH$. The $H^+$ gets consumed, so pH barely drops.
• If you add a strong base (extra $OH^-$): The weak acid $CH_3COOH$ reacts with the added $OH^-$ to form more $CH_3COO^-$ and water. The $OH^-$ gets consumed, so pH barely rises.

The Henderson-Hasselbalch Equation

This equation calculates the pH of a buffer solution:

$\text{pH} = \text{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right)$

where $[A^-]$ is the concentration of the conjugate base and $[HA]$ is the concentration of the weak acid.

Henderson-Hasselbalch Practice

Consider a buffer with acetic acid ($CH_3COOH$, $\text{p}K_a = 4.76$) and its conjugate base ($CH_3COO^-$). If $[CH_3COO^-] = 0.1\ \text{M}$ and $[CH_3COOH] = 0.05\ \text{M}$, find the pH:

1. Write the equation: $\text{pH} = \text{p}K_a + \log\left(\frac{[A^-]}{[HA]}\right)$
2. Substitute values: $\text{pH} = 4.76 + \log\left(\frac{0.1}{0.05}\right)$
3. Simplify the ratio: $\text{pH} = 4.76 + \log(2)$
4. Evaluate: $\text{pH} = 4.76 + 0.30 = 5.06$

The pH of 5.06 makes sense: there's more conjugate base than acid, so the pH is slightly higher than the $\text{p}K_a$.

Buffer Capacity & Factors Affecting It

Buffer capacity is the amount of strong acid or base a buffer can absorb before its pH changes significantly. Three factors control it:

• Total concentration: A buffer made with 1.0 M components can neutralize far more added acid or base than one made with 0.01 M components.
• Ratio of components: Buffers work best when $[A^-]$ and $[HA]$ are roughly equal. When one component is used up, the buffer fails.
• Effective range: A buffer is most effective within $\pm 1$ pH unit of its $\text{p}K_a$. Outside that range, one component is too depleted to absorb further additions.

Real-World Applications

Titrations

• In medicine, titrations help determine the concentration of active ingredients in pharmaceutical solutions, ensuring correct dosages.
• In the food and beverage industry, titrations measure acidity in products like wine and fruit juice to maintain consistent flavor and quality.

Buffers

• Human blood is buffered by the carbonic acid–bicarbonate system ($H_2CO_3 / HCO_3^-$), which keeps blood pH tightly regulated between 7.35 and 7.45. Even small deviations outside this range can be life-threatening.
• In brewing and fermentation, buffers maintain the pH conditions that enzymes need to function properly, directly affecting the final product's taste and quality.