## 9.5 Titration Titration is a quantitative chemical analysis method used to determine the concentration of an identified analyte. It involves preparing a standard solution (a solution of known concentration) and reacting it with a solution of unknown concentration until the reaction reaches its endpoint. **Definition:** A method to find the volume of the standard solution required to react completely with a known volume of another solution under analysis. ### Procedure for Acid-Base Titration Acid-base titrations are common laboratory procedures used to determine the concentration of an acid or a base. 1. A solution with a known concentration (for example, an acid) is placed in a **burette**. 2. A precise, known volume of the solution under analysis (for example, a base) is placed into a **conical flask** using a volumetric pipette. 3. A few drops of a suitable acid-base **indicator** are added to the conical flask. 4. The solution from the burette is slowly added to the conical flask while swirling, until the indicator changes color. 5. This color change signifies the **endpoint** of the titration, indicating that the neutralization reaction is complete. For example, in the neutralization of a strong acid with a strong base, *phenolphthalein* is often used as an indicator. It is colorless in acidic solutions and turns pink in basic solutions. The endpoint is reached when the solution in the flask just becomes colorless. > **Do You Know?** > Sherbet sweets contain a mixture of citric acid, baking soda (sodium bicarbonate), and icing sugar. When eaten, the acid dissolves in saliva and reacts with the baking soda. The sherbet fizzes on the tongue as carbon dioxide gas is produced by the neutralization reaction. ### Titration Calculation Formula The molarity of the unknown solution can be determined using the following equation, which relates the molarities, volumes, and mole ratios of the reactants. $$ \frac{M_1 V_1}{n_1} = \frac{M_2 V_2}{n_2} $$ Where: - $M_1$ = Molarity of the base - $V_1$ = Volume of the base taken in the flask - $n_1$ = Number of moles of the base (from the balanced chemical equation) - $M_2$ = Molarity of the acid - $V_2$ = Volume of the acid used from the burette - $n_2$ = Number of moles of the acid (from the balanced chemical equation) Knowing any five of these parameters allows the sixth to be calculated. --- ## Worked Example: Concept Assessment Exercise 9.3 **Problem:** In a titration, it is found that $25 \, \text{cm}^3$ of $0.12 \, \text{M} \, \text{NaOH}$ is neutralized with $30 \, \text{cm}^3$ of HCl of unknown concentration. Calculate the concentration (molarity) and strength of the HCl solution. **Solution:** 1. **Write the balanced chemical equation:** $$ \text{HCl}_{(aq)} + \text{NaOH}_{(aq)} \rightarrow \text{NaCl}_{(aq)} + \text{H}_2\text{O}_{(l)} $$ From the equation, the mole ratio is 1:1, so $n_{\text{HCl}} = 1$ and $n_{\text{NaOH}} = 1$. 2. **Identify the given values:** - **Base (NaOH):** - Molarity ($M_1$) = $0.12 \, \text{M}$ - Volume ($V_1$) = $25 \, \text{cm}^3$ - Moles ($n_1$) = 1 - **Acid (HCl):** - Molarity ($M_2$) = ? - Volume ($V_2$) = $30 \, \text{cm}^3$ - Moles ($n_2$) = 1 3. **Apply the titration formula to find the Molarity of HCl ($M_2$):** $$ \frac{M_1 V_1}{n_1} = \frac{M_2 V_2}{n_2} $$ $$ \frac{0.12 \times 25}{1} = \frac{M_2 \times 30}{1} $$ $$ M_2 = \frac{0.12 \times 25}{30} $$ $$ M_2 = 0.1 \, \text{M} $$ *Thus, the molarity of the HCl solution is 0.1 M.* 4. **Calculate the Strength of the HCl solution:** *Strength* is the concentration in grams per cubic decimeter ($\text{g} \, \text{dm}^{-3}$). $$ \text{Strength} = \text{Molarity} \times \text{Molar Mass} $$ The molar mass of HCl is $1.0 + 35.5 = 36.5 \, \text{g} \, \text{mol}^{-1}$. $$ \text{Strength of HCl} = 0.1 \, \text{mol} \, \text{dm}^{-3} \times 36.5 \, \text{g} \, \text{mol}^{-1} $$ $$ \text{Strength of HCl} = 3.65 \, \text{g} \, \text{dm}^{-3} $$ --- ### 9.5.1 Selection of Indicators Choosing the correct indicator is crucial for an accurate titration. The indicator's pH range for color change must fall within the sharp pH change that occurs at the equivalence point of the reaction. 1. **Strong Acid vs. Strong Base (for example, HCl vs. NaOH):** The pH changes rapidly from about 3 to 11 at the endpoint. **Phenolphthalein** (pH range 8.3-10) is an excellent choice. 2. **Weak Acid vs. Strong Base (for example, Oxalic Acid vs. NaOH):** The pH changes from approximately 6.5 to 10. **Phenolphthalein** is the best choice as its range (8.3-10) fits well. Methyl orange (pH range 3.2-4.4) would not be suitable. 3. **Strong Acid vs. Weak Base (for example, HCl vs. $\text{Na}_2\text{CO}_3$):** The pH changes from about 3.5 to 7.5. **Methyl orange** is the best indicator for this titration. 4. **Weak Acid vs. Weak Base:** There is no sharp change in pH at the endpoint. Therefore, no standard indicator works satisfactorily, and other methods (like using a pH meter) are preferred. **Table 9.1: Indicators and their pH range** | Indicator | Acidic Colour | pH Range of Colour Change | Basic Colour | | :--- | :--- | :--- | :--- | | Phenolphthalein | Colourless | 8.3 - 10.0 | Pink | | Bromothymol Blue | Yellow | 6.0 - 7.6 | Blue | | Phenol Red | Yellow | 6.8 - 8.0 | Red | | Methyl Orange | Red | 3.2 - 4.4 | Yellow |