# Titration Calculator

Created by Jack Bowater
Reviewed by Bogna Szyk and Steven Wooding
Last updated: Dec 30, 2022

Our titration calculator will help you never have to ask "how do I calculate titrations?" again. Acid-base titration calculations help you identify a solution's properties (such as pH) during an experiment or what an unknown solution is when doing fieldwork.

By using a solution with a known molarity and a color indicator, we measure how much of the solution is required to neutralize the unknown solution, indicated by a change in the indicator, which we can use to work out information about the unknown solution.

## How to calculate titrations?

As you may know, when an acid or a base dissolves in water, their $\small\text{H}^+$ and $\small\text{OH}^-$ ions respectively dissociate, shifting the natural self-ionization equilibrium of water ($\small2\text{H}_2\text{O}\rightleftharpoons\text{H}_3\text{O}^+ + \text{OH}^-$), making the solution more acidic or more basic. At pH 7, the concentration of $\small\text{H}_3\text{O}^+$ ions to $\small\text{OH}^-$ ions is a ratio of $\small1:1$ (the equivalence point).

🙋 The pH is, in fact, a way to calculate concentration: learn about it at our pH calculator.

When doing a titration, we usually have a solution with a known volume but unknown molarity (the analyte), to which a color indicator (e.g., phenolphthalein) is added. The indicator will change colour when this $1:1$ ratio (governed by its titration curve) is achieved. By adding either an acid or a base with a known molarity (the titrant) and measuring how much is needed to cause this change, we can work out the molarity of the unknown using the equation below:

$n_{\text{H}^+}\cdot M_{\text{a}}\cdot V_{\text{a}} = n_{{\rm OH^-}}\cdot M_{\text{b}}\cdot V_{\text{b}},$

where:

• $n_{\text{H}^+}$ — Number of H+ ions contributed per molecule of acid;
• $M_{\text{a}}$ — Molarity of the acid;
• $V_{\text{a}}$ — Volume of the acid;
• $n_{\rm OH^-}$ — Number of OH- ions contributed per molecule of base;
• $M_{\text{b}}$ — Molarity of base; and
• $V_{\text{b}}$ — Volume of the base.

## Acid-base titration method

Here is the method for an acid-base titration:

1. Fill a burette with the solution of the titrant. Make sure not to pour the solution above your head and to remove the funnel after you have finished pouring. Place the burette on a burette stand. Note the start point of the solution on the burette. You may need to remove some of the solution to reach where the measurements start.

2. Measure out an amount of the analyte (it should be less than the amount in your burette) and add it to an Erlenmeyer flask. Add the indicator to the flask. Place on a white tile under the burette to better observe the color.

3. Start adding the titrant slowly, swirling the Erlenmeyer flask constantly. When the color change becomes slow, start adding the titrant dropwise. Once the color change is permanent, stop adding the solution.

4. Note the endpoint on the burette. The difference between this and the starting point gives you the volume, and from this, you can calculate the molarity of the analyte using the equation above.

5. Dispose of all chemicals safely.

Did you know molecules can have a pH at which they are free of a negative charge, and that is what our isoelectric point calculator determines?

## Titration curves

A titration curve is a plot of the concentration of the analyte at a given point in the experiment (usually pH in an acid-base titration) vs. the volume of the titrant added. This curve tells us whether we are dealing with a weak or strong acid/base for an acid-base titration.

The curve around the equivalence point will be relatively steep and smooth when working with a strong acid and a strong base. This curve means that a small increase in the amount of titrant will cause a significant change in pH, allowing a variety of indicators to be used (such as phenolphthalein or bromothymol blue).

Here's the titration curve of $\small\text{NaOH}$ neutralising $\small\text{HCl}$. The blue line is the curve, while the red line is its derivative.

When dealing with a strong acid and a weak base, or vice versa, the titration curve becomes more irregular. Weak acids and bases are molecules that do not fully dissociate when in solution; that is, they are not salts. An example of a weak acid is acetic acid (ethanoic acid), and an example of a weak base is ammonia. Because these molecules do not fully dissociate, the pH shifts less near the equivalence point.

The equivalence point will occur at a pH within the pH range of the stronger solution, i.e., for a strong acid and a weak base, the pH will be <7. For this reason, you must select the correct indicator for the right combination of solutions, as the range of color changes needs to have the equivalence point in it. For example, when using a strong acid and a weak base, an indicator that changes at a low pH is needed, such as methyl orange (3.1-4.4).

As titration curves using a weak acid and a weak base are highly irregular, indicators cannot be used accurately. Instead, a pH meter is often used.

💡 For more tools about acids and bases, have a look at our neutralization calculator or learn how to calculate pH of buffer solution as well!

## History and uses

The word titration comes from the French word tiltre, originally meaning the "proportion of gold or silver in coins," later meaning the "concentration of a substance in a given sample." It is then easy to see why French chemist Joesph Louis Gay-Lussac first used the term when performing early experiments into the atomic composition of materials (he would later go on to improve the burette and invent the pipette).

It was not until Mohr developed the modern burette in 1855 that the technique would become recognizable to us today and has since become a popular method of performing analytical chemistry.

Titrations have many applications in the modern world, although a lot of the original uses have been made redundant by more modern techniques:

• To help determine an unknown solution, e.g., one collected from the field. Although exact determination is impossible, titration is a valuable tool for finding the molarity. The titration curve can also determine whether the solution is a strong or weak acid/base.

• If waste vegetable oil is being used to produce biodiesel, it is necessary to neutralize the batch before processing it. To do this, a small sample is titrated to find its acidity, which tells us how much base we need to neutralize the batch successfully. The addition of a base removes the free fatty acids present, which can then be used to produce soap.

• Titrations are commonly used to determine the concentration of acid rain that falls. These experiments are helpful in monitoring the amount of pollution in the upper atmosphere.

## Table of common acids and bases and their strengths

#### Acids

Formula

Name

Strength

$\text{HCl}$

Hydrochloric acid

Strong

$\text{HNO}_3$

Nitric acid

Strong

$\text{H}_2\text{SO}_4$

Sulfuric acid

Strong

$\text{HBr}$

Hydrobromic acid

Strong

$\text{HI}$

Hydroiodic acid

Strong

$\text{HClO}_3$

Perchloric acid

Strong

$\text{HClO}_3$

Chloric acid

Strong

$\text{HCOOH}$

Formic acid

Weak

$\text{CH}_3\text{COOH}$

Acetic acid

Weak

$\text{C}_6\text{H}_5\text{COOH}$

Benzoic acid

Weak

$\text{HF}$

Hydrofluoric acid

Weak

$\text{HNO}_2$

Nitrous acid

Weak

$\text{H}_3\text{PO}_4$

Phosphoric acid

Weak

#### Bases

Formula

Name

Strength

$\text{NaOH}$

Sodium hydroxide

Strong

$\text{KOH}$

Potassium hydroxide

Strong

$\text{Ca(OH)}_2$

Calcium hydroxide

Strong

$\text{Ba(OH)}_2$

Barium hydroxide

Strong

$\text{NH}_3$

Ammonia

Weak

$\text{CH}_3\text{NH}_2$

Methylamine

Weak

$\text{C}_5\text{H}_5\text{N}$

Pyridine

Weak

## FAQ

### What is a titration?

Titration is a method to determine the unknown concentration of a specific substance (analyte) dissolved in a sample of known concentration.

When the reaction between the analyte and titrant is complete, you can observe a change in the color of the solution or pH changes. From the volume of titrant used, the composition of the analyte can be calculated knowing the stoichiometry of the chemical reaction.

### What is the equivalence point in the titration?

Equivalence point means the point during titration at which the titrant added has completely neutralized the analyte solution. At the equivalence point, the number of moles of titrant added equals the number of moles of an analyte according to the reaction stoichiometry. You may notice on the titration curve that the pH will rise sharply around the equivalence point.

### What is the concentration of 0.15 mL HCl if 20.7 mL of 0.5 M NaOH is required to neutralize it?

To work out an unknown concentration of 0.15 mL HCl:

1. Use the 1:1 ratio formula because one mole of HCl reacts with one mole of NaOH – HCl + NaOH → NaCl + H2O.

2. Multiply the molarity of the strong base NaOH by the volume of the NaOH (MB × VB = 0.500 M × 20.70 mL).

3. Divide this answer (10.35 M × mL) by the volume of the acid HCl (0.15 mL) MA = (MB × VB)/VA = (0.500 M × 20.70 mL)/0.15 mL = 0.690 M. The concentration is expressed as a number of moles per liter of solute.

### What is the pH of 49 mL of 0.1 M HCl and 50 mL of 0.1M HCl solution?

pH is 3.00. The number of moles of H+ ions from HCl is equal to:

50.00 × 10-3 L × 0.100 M HCl = 5.00 × 10-3 moles.

You have added 49.00 × 10-3 L × 0.100 M NaOH = 4.90 × 10-3 moles of OH- ions.

Then it remains 5.00 × 10-3 - (4.90 × 10-3) = 1.0 × 10-4 moles H+.

The H+ concentration is 1.0 × 10-4/(0.049 L + 0.050 L) = 1.0 × 10-4/(0.099 L) = 1.00 × 10-3 M. As pH = -log[H+], pH will be 3.

Jack Bowater
Is the solution neutralized?
Yes
Note that some fields (mol, advanced pH calculations, etc.) are hidden by default. To see them, click the 'Advanced mode' button at the bottom of the calculator.
Acid
Strength
Strong
Concentration
M
Volume
ml
H+ donated
Base
Strength
Strong
Concentration
M
Volume
ml
OH- donated
Resultant solution
Yes
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