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pH Curves and Titrations

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Chemistry

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. You can do a kind of reaction known as titration to find it out.

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 add an indicator to the known solution, which causes the perceptible change.

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 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 is a graph showing how the pH of a solution changes when an acid or alkali is added to it.

pH Curves and Titrations pH curve StudySmarter

A pH curve. Anna Brewer, StudySmarter Originals
  • 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?

Suppose we have a solution of hydrochloric acid, . We also have a sodium hydroxide solution, , the concentration of which we want to determine. To do this, we can run a titration. To do this, we perform the following steps:

  1. Measure out of your solution of known concentration using a volumetric flask. In this case, we will use . Pour the solution into a conical flask.
  2. Add 2-3 drops of your indicator and swirl the 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 . Using a stand and clamp, set up the burette to hang over the conical flask.
  4. Fill the burette with your titrant. Note the value of this solution displayed on the burette. This is your starting value.
  5. Add the titrant to the conical flask in 1 cm3 interval, swirling after each addition, until the solution in the conical flask changes colour. Note the value shown on the burette. This is your end value.
  6. To calculate the titre, subtract your final value from your starting value. This will give you the volume of titrant added to the flask.
  7. Repeat the experiment until you have three titre values within of each other. However, when you reach the end of the titration, i.e. 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, each time adding more titrant. As you near the point of colour change, add the titrant in smaller quantities as explained above.

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

pH curves and titrations titration apparatus set up StudySmarter

The typical setup for a titration experiment. Anna Brewer, StudySmarter Originals, made from image sourced from commons.wikimedia.org

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:

pH curves and titrations pH curve StudySmarter

A pH curve. Anna Brewer, StudySmarter Originals

The graph shows a pH curve for a strong acid and a strong base reaction.

Remember that strong acids and bases dissociate completely in solution, whereas weak acids and bases dissociate only partially.

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.

pH curves and titrations pH curve equivalence point StudySmarterThe pH curve for the reaction between a strong acid and a strong base, with the equivalence point marked in blue. Anna Brewer, StudySmarter Originals

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.

pH curves and titrations pH curve weak base StudySmarter

The pH curve between a strong acid and a weak base. Anna Brewer, StudySmarter Originals

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.

pH curves and titrations pH curve weak acid StudySmarter

The pH curve for the reaction between a weak acid and a strong base. Anna Brewer, 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 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.

pH curves and titrations pH curve weak acid weak baseStudySmarter

The pH curve between a weak acid and a weak base. Anna Brewer, 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.

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:

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

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:

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

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 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. The increase is due to the indicator changing colour at a certain pH. This is known as the 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. We want to use indicators whose endpoints fall within the vast pH range of this nearly vertical section. This means that as you reach the equivalence point, you'll also reach the endpoint.

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 some examples below.

pH curves and titrations pH curve indicatorStudySmarter

Which indicator would be suitable for the titration shown? Anna Brewer, 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. It does not coincide with the titration's equivalence point. However, methyl orange's endpoint does, so methyl orange would be a suitable indicator.

pH curves and titrations pH curve indicator StudySmarter

Which indicator would be suitable for the titration shown? Anna Brewer, StudySmarter Originals

Here, the phenolphthalein's endpoint falls within the vertical section of the pH curve and would therefore be a suitable indicator. However, methyl orange would not.

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.
  • Titrations use conical flasks and burettes. It would be best if you repeated the titration until you got two concordant results within of each other.
  • You can use titrations to calculate the concentrations of unknown solutions.
  • 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 in a small range and have an endpoint equal to the titration's equivalence point.

pH Curves and Titrations

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?

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Answer

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?

Show answer

Answer

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?


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Answer

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?


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Answer

The point where the indicator changes colour.

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Question

Give three properties of a suitable indicator.


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Answer

  • 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.

Show question

Question

What is the equivalence point in titration?


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Answer

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?


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Answer

21.3

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Question

What is a titrant?


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Answer

The substance added from a burette in a titration reaction.

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