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# pH Curves and Titrations

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Suppose you have an acid and a base. You know the concentration of the acid, but the base is a mystery – it could be any concentration for all you know. In order to find out this unknown concentration, you can do a kind of reaction known as a titration.

• We'll start by defining titration before looking at the titration method.
• After that, we'll discuss what we mean by equivalence point.
• We'll then look at types of pH curves for different combinations of strong and weak acids and bases.
• We'll then practice working out concentrations using pH curve calculations.
• Finally, we'll explore the use of indicators in titrations and learn what makes an indicator suitable. This will involve defining endpoint.

## What are titrations?

A titration is a reaction used to find the unknown concentration of a solution, known as the titrant, by gradually adding it to a solution of known concentration until a perceptible change occurs.

The perceptible change is caused by an indicator.

An indicator is a substance that undergoes a perceptible change when conditions in its solution change. For example, this can be the formation of a precipitate but it is usually a colour change.

In this case, we use titrations to determine the concentration of an unknown acid or base. We use indicators that change colour at a specific pH to help us determine the endpoint of our reaction – we'll come back to this concept in just a moment. However, if we want more precise pH measurements at specific points, we can use a pH probe. This is a digital device that measures pH with great precision. We can use our data to draw a pH curve.

A pH curve, also known as a titration curve, is a graph showing how the pH of a solution changes when an acid or alkali is added to it.

A pH curve. StudySmarter Originals

Don't worry! We'll look at how you interpret and use these graphs in just a minute. But first, let's look at how you carry out a titration in order to collect the data that you need to plot a pH curve.

## Titration method

Suppose we have a 0.100 mol dm-3 solution of hydrochloric acid (HCl). We also have a sodium hydroxide solution (NaOH), the concentration of which we want to determine. To do this, we run a titration. This involves the following steps:

1. Measure out 30 cm3 of your solution of known concentration using a volumetric flask. In this case, we use HCl. Pour the solution into a conical flask.
3. Rinse a burette first with distilled water and then with the solution of the unknown concentration, which is your titrant. In this case, we use NaOH. Use a stand and clamp to set up the burette so that it hangs above the conical flask.
4. Fill the burette with your titrant. Note the volume of this solution, which you can read off from the burette. This is your starting volume.
5. Add the titrant to the conical flask in 1 cm3 intervals, swirling after each addition, until the solution in the conical flask changes colour. Note the value shown on the burette. This is your end volume.
6. To calculate the titre, subtract your end volume from your starting volume. This will give you the volume of titrant added to the flask.
7. Repeat the experiment until you have three titre values within 0.1 cm3 of each other. These are known as concordant results. However, when you reach the end of the titration (i.e. as you approach the point of colour change), add the titrant dropwise. The colour change occurs in a small volume range and so adding the titrant in reduced amounts allows you to be more precise.

Alternatively, you can measure the pH of the solution in the conical flask with a pH probe after each addition of titrant. As you near the point of colour change, add a smaller volume, as explained above.

We've shown the setup for a typical titration below.

The typical setup for a titration experiment. Created using images from commons.wikimedia.org

## Titration curve equivalence point

Suppose you carried out the titration we described above, adding NaOH to HCl. You could then produce a pH (titration) curve that looks a little something like this (note that it is the pH curve that we showed earlier):

A pH curve. StudySmarter Originals

• When you start adding the base, the pH initially rises slowly. Adding a large amount of base has a small effect on the pH value.
• Then the pH increases quickly in a small volume range, creating a steep vertical section. Adding a small amount of base has a large effect on the pH value .
• Then the pH levels off and rises slowly again. Once more, adding a large amount of base has a small effect on the pH value.

You'll notice the steep, almost vertical section of the graph where the pH changes rapidly. In this titration, this happens after we've added about 25 cm3 of our base (NaOH).

Remember that an alkali is an aqueous base. This means that NaOH is both an alkali and a base. All alkalis are bases - 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 just enough 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.

The equivalence point on our pH curve.StudySmarter Originals

Although every pH curve has a similar shape, they are all unique. In this next section, we'll explore various types of pH curves for strong and weak acids and bases.

## Types of titration curves

pH (titration) curves with different combinations of weak and strong acids and bases look slightly different. It may look like a lot of information to remember, but figuring out the shape of a titration curve is actually pretty simple. It is all based on the relative pH values of strong and weak acids and bases:

• Strong acids have very low pH values.
• Weak acids have low pH values.
• Weak bases have high pH values.
• Strong bases have very high pH values.

Remember that strong acids and bases dissociate completely in solution, whereas weak acids and bases dissociate only partially. Check out Weak Acids and Bases for more.

Here's a pH scale, showing you what we mean.

The typical pH values of strong and weak acids and bases. StudySmarter Originals

Let's take some time to look at different examples of pH curves 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. SImply reflect the curve in the y-direction, and you'll end up with the right shape.

### Strong acid and strong base

We've already seen the pH curve for a strong acid and a strong base in the example reaction above. It starts with a very low pH, has a large vertical section, and ends with a very high pH.

The pH curve for the reaction between a strong acid and a strong base.StudySmarter Originals

### Strong acid and weak base

Weak bases have a lower pH than strong bases with the same concentration. Therefore, the graph ends with just a high pH, instead of the very high pH seen in the curve between a strong acid and a strong base. So, the vertical section is shorter.

The pH curve for the reaction between a strong acid and a weak base. StudySmarter Originals

### Weak acid and strong base

Weak acids have a slightly higher pH than strong acids. This graph is the opposite of the one above, with a low starting pH but a very high final pH.

The pH curve for the reaction between a weak acid and a strong base. StudySmarter Originals

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 short vertical section. It starts with a low pH and ends with a high pH. Compare this to the pH curve for the reaction between a strong acid and strong base, which had a very low starting pH and a very high final pH.

The pH curve for the reaction between a weak acid and a weak base.StudySmarter Originals

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.

### Summary of types of titration curves

Here's a table summarising the features of pH (titration) curves between different combinations of strong and weak acids and bases.

 Strong base Weak base Strong acid Very low starting pHLarge vertical sectionVery high final pH Very low starting pHMedium vertical sectionHigh final pH Weak acid Low starting pHMedium vertical sectionVery high final pH Low starting pHShort vertical sectionHigh final pH

## Titration curve calculations

At the beginning of this article, we performed a titration between hydrochloric acid (HCl) and sodium hydroxide (NaOH) to find the concentration of the sodium hydroxide solution. We end up with a set of values that tell us the volume of NaOH we added in each titration before we reached the equivalence point - when we have added just enough NaOH to neutralise all the HCl. Let's learn how to use these results to calculate the concentration of NaOH. We need to take the following steps:

• Identify the concordant results.
• Use the concordant results to calculate the mean titre. Remember that this mean titre is simply the mean volume of NaOH (the unknown solution) added in each titration.
• Use the volume and concentration of HCl (the known solution) to calculate the number of moles of HCl used in each titration.
• Use the balanced chemical equation to find out the number of moles of NaOH that reacts in each titration.
• Use this number of moles, alongside the mean titre you calculated earlier, to work out the concentration of NaOH.

You carry out a titration reaction between HCl and NaOH, using 30 cm3 0.100 mol dm-3 HCl in each titration and a solution of NaOH as the titrant. Use the following results to calculate the concentration of NaOH solution.

 Titre 1 Titre 2 Titre 3 Volume NaOH added (cm3) 24.9 25.2 25.0

First, we need to identify the concordant results. For titration reactions, these are generally defined as results within 0.1 cm3 of each other. You can see that titres 1 and 3 produced concordant results. We highlight these and calculate the mean titre:

 Titre 1 Titre 2 Titre 3 Volume NaOH added (cm3) 24.9 25.2 25.0

(24.9 + 25.0) ÷ 2 = 24.95 cm3

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

Now let's set this mean titre aside for a second and calculate the number of moles of HCl in each titration. We do this using the information given in the question and the equation linking moles, concentration and volume. Our HCl has a concentration of 0.100 mol dm-3 and we used 30 cm3 of it in each titration.

Remember to convert all volumes into dm3. In this case, we convert from cm3 into dm3 by dividing by 1000.

moles = concentration x volume

moles = 0.100 x 0.03 = 0.003 moles

If we write an equation for the reaction between HCl and NaOH, we can see that they react in a 1:1 ratio:

HCl + NaOH → NaCl + H2O

This means we need the same number of moles of NaOH as HCl, in order to neutralise the HCl fully. Therefore, we must have used 0.003 moles of NaOH. We can now use the volume of the average titre (converted into dm3, of course) to calculate the concentration of NaOH:

concentration = moles ÷ volume

concentration = 0.003 ÷ 0.02495 = 0.012 mol dm-3

Pay attention to how many decimal places are given in the question. You must round your answer to this number.

## Titration curves and indicators

When we add an alkali to an acid, or vice versa, the pH changes. For example, the pH increases when we add sodium hydroxide to hydrochloric acid. When the pH reaches a certain level, the indicator changes colour. This is known as the titration's endpoint.

The endpoint is the point at which the indicator changes colour.

We can use endpoints to determine the equivalence points of specific acid-base combinations. Remember that the equivalence point is in the middle of a nearly vertical section of a pH curve. This section spans a wide range of pH values, and adding just a bit more titrant drastically changes the pH. This means that as you reach the reaction's equivalence point, you'll also reach its endpoint. In order to accurately determine the equivalence point of a titration, we need to use indicators whose endpoints fall within the vast pH range of this nearly vertical section.

To be suitable for titration, an indicator must fulfil several criteria.

• The colour change must be distinct.
• The colour change must be abrupt and not occur over a wide range of pH values.
• The endpoint of the indicator must correspond to the equivalence point of the titration.

See an example below.

Use the pH curve given to determine which indicator would be suitable for the following titration. The endpoints of the two possible indicators are represented by a line at the appropriate pH, showing the colour change.

A pH curve for the reaction between a strong acid and a weak base, shown with the end points of two indicators.StudySmarter Originals

Here, phenolphthalein would not be a suitable indicator because its endpoint, at which it changes colour, does not fall within the vertical section of the pH curve. Therefore, its endpoint does not coincide with the titration's equivalence point. However, methyl orange's endpoint does fall within the vertical section of the pH curve, and so methyl orange would be a suitable indicator.

## pH Curves and Titrations – Key takeaways

• A titration is a reaction in which we find the unknown concentration of a solution, known as the titrant, by gradually adding it to a solution of known concentration until a perceptible change occurs. We use indicators to judge when the titration is complete.
• A pH curve is a graph produced from a titration that shows how the pH of a solution changes when we add an acid or alkali to it.
• The equivalence point of a titration is when a sufficient base has been added to neutralise the acid or vice versa.
• The endpoint of a titration is the point at which the indicator changes colour.
• Suitable indicators for titration reactions must produce a distinct colour change over a small range of pH values and have an endpoint equal to the titration's equivalence point.

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

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

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

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.

## Final pH Curves and Titrations Quiz

Question

What is titration?

A titration is a reaction in which we find the unknown concentration of a solution, known as the titrant, by gradually adding it to a solution of known concentration until a perceptible change occurs.

Show question

Question

What is a pH curve?

A graph produced from a titration showing how the pH of a solution changes as an acid or alkali is added to it.

Show question

Question

What is an indicator?

A substance that undergoes an observable change when the conditions of its solution change.

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Question

What is the end point in a titration?

The point where the indicator changes colour.

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Question

Give three properties of a suitable indicator.

• Has a distinct colour change.
• The colour change happens over a short pH range.
• End point is the same as the titration’s equivalence point.

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Question

What is the equivalence point in titration?

The point where sufficient base has been added to neutralise the acid or vice versa.

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Question

Which of the following titre results are concordant?

21.3

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Question

What is a titrant?

The substance added from a burette in a titration reaction.

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