If you have an acid and you don't know the concentration of the base, you can use a titration to find out. A titration is when you gradually add a solution of known concentration to the unknown solution until you see a change. We add an indicator to the known solution, which makes it easier to see the change. An indicator is a substance that changes color when the conditions in its solution change. We use titrations to find the concentration of an unknown acid or base. We use indicators that change color at a specific pH to help us determine the endpoint of our reaction. If we want more precise measurements, we can use a pH probe. This is a digital device that measures pH very accurately. We can use our data to draw a pH curve – a graph that shows how the pH of a solution changes when we add an acid or a base.

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This article is about pH curves and titrations in chemistry. We'll start by describing how you do titrations before defining some key terms. We'll then look at examples of pH curves. We'll then practice calculating concentrations using pH curves. Finally, we'll explore the properties of a suitable indicator in titrations.

How do you carry out titrations?

Let's say we have hydrochloric acid and we want to find out the concentration of sodium hydroxide. We can do this by running a titration. Here's how it works:

First, we measure out a known amount of our hydrochloric acid solution, in this case, we'll use 25 ml. We pour it into a conical flask and add a few drops of an indicator. Then, we rinse a burette with distilled water and then with our sodium hydroxide solution, which is the titrant we'll use. We fill the burette with our titrant and note the starting value. We add the titrant to the flask in 1 ml intervals, swirling after each addition, until the solution changes color. We note the final value on the burette and calculate the titre by subtracting the final value from the starting value. This gives us the volume of titrant added to the flask. We repeat the experiment until we have three titre values within 0.1 ml of each other. When we reach the point of color change, we add the titrant drop by drop to be more precise. Alternatively, we can measure the pH of the solution in the flask with a pH probe, adding more titrant each time. As we get closer to the point of color change, we add the titrant in smaller quantities.

We've included a picture below to show you how the setup for a typical titration looks like.

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Analysing titrations

Suppose you carried out the titration we described above, adding  to . You could then produce a titration curve that looks a little something like this:

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What can you say about this graph? Well, the pH increase isn't linear. When you start adding the base, the pH rises slowly at first. Then the pH increases quickly in a small volume range. Then the pH levels off and slowly rises again. Adding more base has a negligible effect on the pH value. You'll notice a steep, almost vertical section of the graph where the pH changes rapidly. In this titration, this happens when of our base, , has been added.

Remember that alkali is an aqueous base. This means that is both an alkali and a base - but not all bases are alkalis.

The vertical section contains the equivalence point, found in the middle of the vertical section. The equivalence point is where a sufficient base has been added to neutralise the acid in a titration reaction or vice versa.

In this reaction, the equivalence point is at a pH of about 7, but that isn't always the case – you'll see in just a moment.

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pH curves with different combinations of weak and strong acids and bases look slightly different. Let's take some time to examine them now. In all of our examples, we add an alkali to an acid. However, it is perfectly possible to add an acid to an alkali – it just means that the graph starts with a higher pH and ends with a lower pH.

Strong acid and strong base

We've looked at the pH curve for a strong acid and a strong base above. It starts with a very high pH, has a large vertical section, and ends with a very low pH.

Strong acid and weak base

Weak bases have a lower pH than strong bases with the same concentration. The graph thus ends with a slightly lower pH than the pH curve between a strong acid and a strong base. So, the vertical section is shorter. Ammonia is an example of a weak base.

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Weak acid and strong base

Weak acids have a slightly higher pH than strong acids. Ethanoic acid is an example of a weak acid. This graph is the opposite of the one above, with a somewhat higher starting pH than a strong acid but a very high final pH.

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 You may have noticed that the pH rises sharply at first when we add some of the alkali. The increase is due to the weak acid reacting with the alkali to form a buffer solution. You'll find out more about these in Buffer Solutions.

Weak acid and weak base

The pH curve for a weak acid and a weak base has a tiny vertical section. Compared to the strong acid and strong base curve, it has a relatively high starting pH and a relatively low final pH.

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All of these examples have used monoprotic acids. These are acids that donate one proton per acid molecule. However, you can also do titrations with diprotic acids or even polyprotic acids. Diprotic acids give pH curves with two distinct, steeply-sloping sections. In the first section, each acid molecule loses its first proton. In the second section, each molecule loses its second proton.

Calculations with titrations

At the beginning of this article, we performed a titration between hydrochloric acid, , and sodium hydroxide, , to find the concentration of the . Let's say that we got the following titres:

These titres tell us when we reach the equivalence point – when there is just enough  to neutralise all the . It would be best to keep repeating the titration until you get two concordant results. For titration, these are generally defined as results within  of each other. You can see that titres 1 and 3 produced concordant results. We highlight these and calculate the mean titre:

Concordant generally means 'agreeing'. You can think of these results as 'agreeing' on the volume of titrant needed to neutralise your solution.

Now that we know the mean titre, we can calculate the concentration of  used.

How do we go about this? Well, first we use the values we know to calculate the number of moles of  in solution. Our  has a concentration of  and we used  of it.

Remember to convert all volumes into  by dividing by .

moles = concentration x volume

moles  moles

If we write an equation for the reaction between and , we can see that they react in a ratio.

This means we need precisely as many moles of  as to neutralise it fully. Therefore, we must have  moles of . We can now use the volume of the average titre to calculate the concentration of :

concentration = moles / volume

concentration

Pay attention to how many decimal places are given in the question. You must round your answer to this number.Note: If your acid is a diprotic acid, for example, you'll need twice as many moles of NaOH to neutralise it accurately. This is because each mole of a diprotic acid dissociates into two moles of hydrogen ions. Read Acids and Bases for more information.

Explaining titration reaction

When performing a titration, it is crucial to choose the appropriate indicator to obtain accurate results. The indicator's endpoint should coincide with the equivalence point of the titration, which is the point where the amount of acid and base is stoichiometrically equivalent.

To be a suitable indicator for a titration, the indicator should have a distinct colour change that occurs abruptly and not over a wide range of pH values. Additionally, the endpoint of the indicator should fall within the vertical section of the pH curve, which spans a wide range of pH values and indicates the equivalence point of the titration.

Choosing the wrong indicator can result in inaccurate results, as the endpoint will not coincide with the equivalence point. Therefore, it is important to carefully select the appropriate indicator based on the acid and base being used in the titration.

For example, phenolphthalein would not be a suitable indicator for a titration where its endpoint does not coincide with the equivalence point. However, methyl orange may be a suitable indicator for the same titration because its endpoint falls within the vertical section of the pH curve.

In summary, selecting the appropriate indicator is crucial for obtaining accurate results in a titration. The indicator should have a distinct colour change that occurs abruptly, and its endpoint should coincide with the equivalence point of the titration.

Additionally, pH curves provide valuable information about the strength and concentration of the acid and base being titrated. The pH curve shows how the pH of the solution changes as the titrant is added, and the shape of the curve can indicate whether the acid or base being titrated is strong or weak.

In summary, titrations and pH curves are essential tools in chemistry used to determine the concentration of unknown solutions and provide valuable information about the acid and base being titrated. Careful selection of indicators is necessary to obtain accurate results, and repetition of the titration is essential to ensure concordant results.

pH Curves and Titrations

How do you find the pH of a titration curve? 

To find the pH in a titration, you can use a pH probe. pH probe accurately measures the pH of a solution. 

What is pH titration curve? 

A pH curve is a graph showing how the pH of a solution changes when we add an acid or alkali to it.

What are titration curves used for? 

We use titration curves to find the pH in titration experiments. These are reactions between an acid and an alkali.

How do pH indicators work in titrations? 

Titrations have an equivalence point. This is when just enough acid has been added to sufficiently neutralise the alkali, or vice versa. The equivalence point occurs in a part of the titration curve with a sharp change in pH. Indicators are substances that change when the conditions of their solution change. Typically, they change colour at a certain pH. When carrying out titrations, we choose an indicator with an endpoint similar to the reaction's equivalence point, ensuring that the endpoint falls within the sharply-sloping section of the graph. The solution will thus change colour when we reach the equivalence point and tell us that the reaction is complete.

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