Grade 11

Advanced

10 min

Lesson 10 of 12

Titration Techniques and Analysis

Not Started

Using volumetric analysis to determine the unknown concentration of an acid or base.

How do food scientists ensure that every bottle of vinegar has exactly 5% acidity without tasting every single batch? They use the power of titration to count molecules using nothing but volume and color.

Learning Objectives

1.Calculate the concentration of an unknown analyte using stoichiometric ratios and volumetric data.
2.Differentiate between the theoretical equivalence point and the experimental end point.
3.Select the ideal chemical indicator by matching its $pK_{a}$ to the expected pH at the equivalence point.

The Fundamentals of Volumetric Analysis

Titration is a quantitative analytical technique used to determine the concentration of an unknown solution, called the analyte. This is achieved by reacting it with a solution of known concentration, known as the titrant or standard solution. The process relies on the precise measurement of volumes. In an acid-base titration, we add the titrant from a burette into the analyte in an Erlenmeyer flask until the reaction is neutralized. The goal is to reach the equivalence point, where the number of moles of titrant added is chemically equivalent to the number of moles of analyte originally present, according to the balanced chemical equation.

Quick Check

What is the name of the solution with the known concentration that is placed in the burette?

It is the solution used to 'test' the other.

Answer

The titrant (or standard solution).

A $25.0\text{ mL}$ sample of $HCl$ (analyte) is titrated with $0.100\text{ M } NaOH$ (titrant). The titration requires $32.5\text{ mL}$ of $NaOH$ to reach the equivalence point. Calculate the concentration of $HCl$ .

1. Write the balanced equation: $HCl + NaOH \rightarrow NaCl + H_2O$ . The ratio is $1:1$ . 2. Calculate moles of $NaOH$ : $n = C \times V = 0.100\text{ mol/L} \times 0.0325\text{ L} = 0.00325\text{ moles}$ . 3. Since the ratio is $1:1$ , moles of $HCl = 0.00325\text{ moles}$ . 4. Calculate concentration of $HCl$ : $C = \frac{n}{V} = \frac{0.00325\text{ mol}}{0.0250\text{ L}} = 0.130\text{ M}$ .

Equivalence Point vs. End Point

While often used interchangeably, these two terms are distinct. The equivalence point is the theoretical point where the stoichiometric amounts of reactants have combined. At this point, the $pH$ is determined by the salt formed. For a strong acid-strong base titration, the $pH = 7$ . However, we cannot 'see' the equivalence point. Instead, we observe the end point, which is the physical point where a chemical indicator changes color. To minimize titration error, we must choose an indicator whose color change occurs as close to the equivalence point as possible.

Quick Check

If a titration ends when the color changes, but the moles aren't perfectly equal yet, what is the difference between these two points called?

Answer

Titration error.

Strategic Indicator Selection

Choosing the right indicator is critical because the $pH$ at the equivalence point isn't always $7$ . This occurs due to salt hydrolysis. - Strong Acid + Strong Base: $pH = 7$ (e.g., Bromothymol Blue). - Weak Acid + Strong Base: $pH > 7$ because the conjugate base of the weak acid makes the solution basic (e.g., Phenolphthalein). - Strong Acid + Weak Base: $pH < 7$ because the conjugate acid of the weak base makes the solution acidic (e.g., Methyl Orange). An indicator is most effective when its $pK_{In}$ value is within $\pm 1$ unit of the equivalence point $pH$ .

You are titrating $0.1\text{ M } CH_3COOH$ (acetic acid) with $0.1\text{ M } NaOH$ .

1. Identify the salt formed: $NaCH_3COO$ . 2. Determine the $pH$ nature: The $CH_3COO^-$ ion reacts with water: $CH_3COO^- + H_2O \rightleftharpoons CH_3COOH + OH^-$ . 3. This produces $OH^-$ ions, making the equivalence point $pH \approx 8.8$ . 4. Select indicator: Phenolphthalein (range $8.2-10$ ) is appropriate; Methyl Red (range $4.4-6.2$ ) would change color far too early.

Calculate the volume of $0.250\text{ M } KOH$ needed to fully neutralize $15.0\text{ mL}$ of $0.500\text{ M } H_2SO_4$ .

1. Balanced Equation: $H_2SO_4 + 2KOH \rightarrow K_2SO_4 + 2H_2O$ . 2. Note the stoichiometry: $1$ mole of acid requires $2$ moles of base. 3. Moles of $H_2SO_4 = 0.0150\text{ L} \times 0.500\text{ mol/L} = 0.0075\text{ moles}$ . 4. Moles of $KOH$ needed $= 0.0075 \times 2 = 0.0150\text{ moles}$ . 5. Volume of $KOH = \frac{n}{C} = \frac{0.0150\text{ mol}}{0.250\text{ mol/L}} = 0.0600\text{ L} = 60.0\text{ mL}$ .

Key Takeaways

1The equivalence point occurs when $n_{acid} \times ext{protons} = n_{base} \times ext{hydroxides}$ .
2The end point is the visual signal (color change) provided by an indicator.
3Salt hydrolysis determines the $pH$ at the equivalence point, which dictates indicator choice.
4Use the formula $\frac{C_a V_a}{n_a} = \frac{C_b V_b}{n_b}$ where $n$ represents the stoichiometric coefficients.

Quick Check

Multiple Choice

Which indicator is best for a titration between $HCl$ (strong acid) and $NH_3$ (weak base)?

Multiple Choice

If $20\text{ mL}$ of $0.5\text{ M } NaOH$ neutralizes $10\text{ mL}$ of $H_2SO_4$ , what is the concentration of the acid?

True/False

The equivalence point and the end point are always at the exact same pH.

What's Next?

Review Tomorrow

In 24 hours, try to sketch the titration curves for a strong acid/strong base vs. a weak acid/strong base. Where does the equivalence point sit on each?

Practice Activity

Find a nutrition label for vinegar or lemon juice and try to calculate how many mL of $1.0\text{ M } NaOH$ would be needed to neutralize one serving.

Browse

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Titration Techniques and Analysis

Learning Objectives

The Fundamentals of Volumetric Analysis

Equivalence Point vs. End Point

Strategic Indicator Selection

Key Takeaways

Quick Check

What's Next?

Titration Techniques and Analysis

Learning Objectives

The Fundamentals of Volumetric Analysis

Equivalence Point vs. End Point

Strategic Indicator Selection

Key Takeaways

Quick Check

What's Next?