Titration is a lab technique for finding the concentration of an unknown solution by adding a measured volume of a titrant (a solution of known molarity) until the reaction is complete. Unlike molarity vs molality, which often confuses beginners, titration focuses only on molarity.
In an acid–base titration, for example, we slowly add a strong base (in a burette) to an unknown acid in a flask (or vice versa) until neutralization. We often include an indicator (like phenolphthalein) that changes color at the endpoint (which closely marks the equivalence point where moles H⁺ = moles OH⁻. This allows us to read the volume of titrant used and calculate the unknown molarity.
The Titration Process
A typical titration setup. The titrant is in a burette (a tall, graduated tube with a stopcock) over a flask containing the analyte and indicator. The burette’s scale lets us measure exactly how much solution is added.
In a strong acid-strong base titration, the acid (H⁺) and base (OH⁻) fully neutralize each other to form water, and the equivalence point occurs at pH ~7. We carefully add titrant dropwise and stir the flask until the indicator first shows a permanent color change. This marks the endpoint. At that moment, the amount of titrant added is exactly what is needed to neutralize the analyte. A controlled addition (usually with stirring) ensures accuracy.
The key is that at the equivalent point, the moles of acid equal the moles of base. In other words:
- Moles of titrant added = Moles of analyte reacted.
For a 1:1 neutralization (one H+ per OH⁻), this becomes the simple formula:
Here M1 and V1 are the molarity and volume of solution 1 (e.g. the acid), and M2 and V2 are for solution 2 (e.g. the base). Volume can be in liters or mL (but use the same units on both sides). This equation arises because
$$ \text{moles of acid} = \text{moles of base} \quad \Rightarrow \quad M_1 V_1 = M_2 V_2 $$- M1 (Molarity 1) = Molarity/Concentration of the first solution.
- V1 (Volume 1) = Volume of the first solution (liters or mL).
- M2 (Molarity 2) =Molarity Concentration of the second solution.
- V2 (Volume 2) = Volume of the first solution (liters or mL).
If one of the molarities is unknown, we rearrange the formula. For example, to find M2:
This only works directly when the acid and base react 1:1. In some cases, instead of molarity, chemists use normality calculations when dealing with titrations involving equivalents.
(For polyprotic acids like H₂SO₄, you’d include stoichiometric factors.) The essential idea is that the moles are conserved.
Since this relies on the mole concept, reviewing what a mole in chemistry means can help beginners understand titration better.
Example Calculations
Let’s apply M1V1 = M2V2 in concrete examples. We’ll use a friendly, step-by-step approach. If you start with a substance in grams, using a grams to moles converter makes the calculation easier before plugging values into the titration formula.
Example 1: Finding an Unknown Acid Concentration. Suppose we titrate 15.00 mL of an unknown HCl with 20.70 mL of 0.500 M NaOH. The reaction is:
HCl + NaOH → NaCl + H2O. At the end point:
$$ M_{\text{acid}} \times V_{\text{acid}} = M_{\text{base}} \times V_{\text{base}} $$Plug in known values:
$$ M_{\text{acid}} \times 15.00\ \text{mL} = 0.500\ \text{M} \times 20.70\ \text{mL} $$Solve for M acid
Answer: The HCl concentration is 0.690 M.
Example 2: Finding an Unknown Acid (Another Case). A student titrates 21.20 mL of an unknown monoprotic acid with 18.25 mL of 0.1255 M NaOH. Using the formula:
- Moles of NaOH added = mol.
- Since the acid is monoprotic (1 H⁺ per mole), moles of acid = moles of NaOH = mol.
- Convert 21.20 mL to L (0.02120 L). Then
Answer: The unknown acid is 0.1080 M.
These steps highlight the process: write the balanced reaction, equate moles (or use M1V1 = M2V2), plug in volumes and known molarity, and solve for the unknown molarity.
Indicators and the Endpoint
An indicator is a dye that changes color at a certain pH range. For strong acid-strong base titrations, phenolphthalein is a common choice. It is colorless in acid and turns pink as the solution becomes basic (around pH 8.3-10).
The chosen indicator should have its color change near the expected equivalence point. When the indicator just changes color, that marks the endpoint (the point we stop adding titrant). Ideally the endpoint closely matches the equivalence point (when moles H⁺ = moles OH⁻).
Practical Applications
Acid-Base titrations are used in many fields:
- Medicine/Pharmaceuticals: Titration is a workhorse for analyzing drug purity and dosage. In pharma labs, titrations “analyze the purity” and content of medicines by verifying how much acid or base they contain for example, titration can check that an HCl solution in a medication has the correct concentration or that an active ingredient is as labeled.
- Environmental Testing: Water quality is often monitored with titration. Scientists routinely measure the pH or alkalinity of water bodies (rivers, lakes, tap water) to detect pollution or treatment levels. For instance, acid-base titration can determine how much acid rain has lowered the pH of lake water. Municipal water treatment plants also use titration to keep effluent pH within safe limits
- Food and Beverage Industry: The acidity of foods and drinks is crucial for safety and flavor. Titration is used to measure titratable acidity in juices, milk, vinegar, etc. For example, elevated lactic acid in milk (found by titration) can indicate bacterial spoilage, and measuring acids like tartaric or malic in fruit juices helps confirm their content. Food laws often require acidity testing (via titration or pH meter) to ensure products won’t spoil or cause illness.
Tips to Avoid Common Errors
Getting precise titration results depends on good technique. Here are some practical tips:
- Read the burette carefully. Always eye-level the meniscus on the burette. Read the initial and final volume using the same eye position to avoid parallax error. Record volumes to the nearest 0.01 mL. Never assume starting at 0.00 mL (since 0.00 is least accurate). Instead, note the actual starting reading and subtract it from the final reading.
- Use consistent units. If you measure volumes in mL, use mL throughout (or convert all volumes to L consistently) before plugging into M1V1=M2V2. Molarity should be in mol/L.
- Place white paper under the flask. A white sheet or paper background helps you see the indicator color change more clearly.
- Add indicator and titrant properly. Be sure to add a few drops of the chosen indicator before titration begins. (Forgetting the indicator will ruin the titration). Add titrant dropwise, especially near the endpoint. Swirl the flask gently as you titrate so the solution mixes evenly and all titrant reacts.
- Rinse the burette tip. When filling the burette, rinse it with a little titrant first. Make sure no air bubbles remain in the tip. Any titrant clinging to the outside of the burette can also drip down and waste solution.
- Perform multiple trials. Good practice is to do at least three titrations and take the average of consistent results. Titration is a skill that improves with practice.
By following these tips and the M1V1=M2V2 calculation carefully, you can avoid common mistakes and get accurate results. Many students also double-check their work with an online molarity calculator to save time and reduce errors.
