Acid–Base Titration Calculator
Calculate the unknown concentration of an acid or base from titration data. Enter the concentration and volume of the known solution, the volume of the unknown solution, and the reaction ratio.
Find an Unknown Concentration from Titration Data
Titration Formula
Where:
- \(C_1\) — concentration of the known solution (mol/L)
- \(V_1\) — volume of the known solution at the equivalence point (L)
- \(V_2\) — volume of the unknown solution (L)
- \(n_1\), \(n_2\) — stoichiometric coefficients of the known and unknown reactant in the balanced equation
- \(C_2\) — concentration of the unknown solution (mol/L)
At the equivalence point the number of reaction equivalents supplied by both solutions is equal, which means the moles of each reactant are in the same ratio as their coefficients in the balanced equation.
Titration – Calculation Example
Example: 25.00 mL of 0.1 mol/L sodium hydroxide solution exactly neutralises 20.00 mL of a hydrochloric acid solution of unknown concentration (HCl + NaOH, a 1 : 1 reaction).
\[ n(\text{NaOH}) = C_1 V_1 = 0.1 \ \tfrac{\text{mol}}{\text{L}} \times 0.025\ \text{L} = 0.0025\ \text{mol} = 2.5\ \text{mmol} \]
\[ C_2 = \frac{C_1 V_1}{V_2} = \frac{0.1 \times 0.025}{0.020} = 0.125\ \tfrac{\text{mol}}{\text{L}} \]
Result: the HCl concentration is 0.125 mol/L (125 mmol/L), and the amount of acid that reacted is 2.5 mmol.
How to Use the Titration Calculator
- Enter the Concentration of Known Solution and choose mol/L or mmol/L as the unit.
- Enter the Volume of Known Solution dispensed or measured at the equivalence point, and select mL or L.
- Enter the Volume of Unknown Solution — the acid or base whose concentration you want to find — with its unit.
- Choose the Reaction Equivalents (Known : Unknown) ratio from the balanced chemical equation: 1 : 1 for HCl + NaOH type reactions, 1 : 2 for a diprotic acid such as H₂SO₄, 2 : 1 for a dibasic base such as Ca(OH)₂, and 1 : 3 for a triprotic acid such as H₃PO₄.
- Read the Unknown Concentration in mol/L and mmol/L, together with the Amount of Unknown Reacted in mmol.
What Is Acid–Base Titration?
Titration is a laboratory technique used to find the concentration of an acid or base by reacting it with a standard solution of known concentration. The standard solution is added gradually from a burette until the reaction reaches the equivalence point — the moment at which exactly enough titrant has been added to react with all of the substance being analysed. An indicator or a pH meter signals when this point is reached.
Because the volumes and the concentration of the standard solution are known precisely, the unknown concentration follows directly from the stoichiometry of the reaction. For a simple 1 : 1 neutralisation such as HCl + NaOH, the moles of acid equal the moles of base at the equivalence point. For reactions with different stoichiometry, the coefficient ratio from the balanced equation must be taken into account — this is exactly what the reaction ratio selector in the calculator does.
The result, \(C_2\), tells you how many moles of the unknown acid or base were present in each litre of the original sample. Multiplying \(C_2\) by \(V_2\) gives the total amount that reacted, which the calculator also reports in millimoles. Note that the equivalence point (a stoichiometric concept) may differ slightly from the endpoint you observe experimentally, since indicators change colour over a small pH range.
Assumptions and Practical Tips
- Balanced equation required: the calculator assumes the reaction goes to completion at the equivalence point and that you have chosen the correct molar ratio. If you are unsure of the ratio, first balance the reaction with the Chemical Equation Balancer.
- Units are handled automatically: all inputs are converted internally to mol and L, so you can mix units (e.g. mmol/L with mL) without extra steps.
- Monoprotic vs. polyprotic acids: for a polyprotic acid such as H₂SO₄ or H₃PO₄, the ratio depends on how many protons actually react under your conditions. The preset ratios (1 : 2, 1 : 3) assume complete neutralisation of all acidic protons.
- Accuracy depends on your data: read the burette at the bottom of the meniscus, rinse all glassware, and account for the indicator blank. Averaging several consistent titrations greatly improves reliability.
- Dilution first? This calculator finds an unknown concentration from titration data. If you are simply diluting a solution of known concentration, use the C1V1 = C2V2 dilution calculator instead.
- Once you know the molar amount, you can convert it to particles with the Convert Atoms to Moles calculator; for a related analytical application, see the Estimation of Calcium calculator.
Frequently Asked Questions
How do I calculate the unknown concentration by hand?
Convert volumes to litres, find moles of the known reactant \( n_1 = C_1 V_1 \), use the balanced equation to get moles of the unknown \( n_2 = n_1 \times \frac{n_2}{n_1} \) (coefficient ratio), then divide by the sample volume: \( C_2 = \frac{n_2}{V_2} \). For a 1 : 1 reaction this simplifies to \( C_2 = \frac{C_1 V_1}{V_2} \). Always keep a copy of the balanced equation in front of you to avoid ratio errors.
Does it matter whether the acid and base are strong or weak?
For the stoichiometric calculation, no — the maths is identical for weak and strong acids or bases, because it only relies on the balanced equation. However, the indicator choice differs: weak acid + strong base titrations need phenolphthalein, while strong acid + weak base titrations need methyl orange. Using the wrong indicator can shift your endpoint away from the equivalence point and distort the volume you enter into the calculator.
How do I convert the result from mol/L to g/L or percent concentration?
Multiply the molar concentration by the molar mass of the substance: \( \text{g/L} = C \times M \). For example, 0.125 mol/L HCl is \( 0.125 \times 36.46 \approx 4.56 \) g/L. For a percent concentration, note that 1 % w/v = 10 g/L, so 4.56 g/L ≈ 0.456 % w/v. Solutions can also be converted to ppm: 1 ppm ≈ 1 mg/L for dilute aqueous solutions.
What is the difference between molarity and normality in titration?
Molarity counts moles per litre; normality counts equivalents per litre. For HCl or NaOH they are the same, but for H₂SO₄ a 1 mol/L solution is 2 N because each mole supplies two protons. If your standard solution is labelled in normality, either convert to molarity (divide by the number of protons or hydroxides transferred) or use a 1 : 1 ratio, since normality already accounts for the stoichiometry.
What if I overshot the endpoint — can I still use my data?
If the overshoot is very small, the error is usually minor, but ideally you should repeat the titration. As an estimate, you can subtract the excess titrant: titrate a blank with the same indicator to measure how much titrant the indicator itself consumes, or use the average of your best (most consistent) runs. Never average a badly overshot run with clean ones — discard it, as it systematically overestimates the volume and thus the concentration.
Does this calculator work for back titrations?
Not in a single step. In a back titration you add a known excess of standard reagent to the sample, then titrate the leftover with a second standard. You must first run two separate calculations: use this calculator (or simple \( C \times V \)) to find the moles of excess reagent remaining, then subtract from the moles originally added. The difference equals the moles that reacted with your analyte.
Why is my calculated concentration unrealistic or wildly different between trials?
Check the most common slip-ups: entering mL where litres are expected (a factor-of-1000 error), choosing the wrong reaction ratio, or using the total burette reading instead of the difference between initial and final readings. Also verify that your standard solution has not absorbed CO₂ or evaporated, and that all glassware was rinsed with the solution it will hold. Trial results should agree within about 0.05 mL; if not, repeat the titration.