Learning Materials
Features
Discover
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.
Millions of flashcards designed to help you ace your studies
Sign up for free
Achieve better grades quicker with Premium
Geld-zurück-Garantie, wenn du durch die Prüfung fällst
Did you know that StudySmarter supports you beyond learning?
Review generated flashcards
Start learning or create your own AI flashcards
Team pH Curves and Titrations Teachers
Thanks for your interest in learning preferences!
Which learning mode do you prefer? (e.g. “Audio,” “Video” “Text” “No preference”) (optional)
Send FeedbackA 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.
Fig. 1 - A pH curve
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.
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:
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.
Fig. 2 - A typical titration setup
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):
Fig. 3 - A pH curve
What can you say about this graph? Well, the pH increase isn't linear.
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.
Fig. 4 - The equivalence point on our pH curve
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.
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:
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.
Fig. 5 - The typical pH values of strong and weak acids and bases
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.
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.
Fig. 6 - The pH curve for the reaction between a strong acid and a strong 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.
Fig. 7 - The pH curve for the reaction between a strong acid and a weak 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.
Fig. 8 - The pH curve for the reaction between a weak acid and a strong base
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.
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.
Fig. 9 - The pH curve for a reaction between a weak acid and a weak base
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.
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 |
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:
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.
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.
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.
Fig. 10 - A pH curve for the reaction between a strong acid and a weak base, shown with the end points of two indicators
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.
Sign up for free to gain access to all our flashcards.
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.
At StudySmarter, we have created a learning platform that serves millions of students. Meet the people who work hard to deliver fact based content as well as making sure it is verified.
Lily Hulatt is a Digital Content Specialist with over three years of experience in content strategy and curriculum design. She gained her PhD in English Literature from Durham University in 2022, taught in Durham University’s English Studies Department, and has contributed to a number of publications. Lily specialises in English Literature, English Language, History, and Philosophy.
Get to know Lily
Gabriel Freitas is an AI Engineer with a solid experience in software development, machine learning algorithms, and generative AI, including large language models’ (LLMs) applications. Graduated in Electrical Engineering at the University of São Paulo, he is currently pursuing an MSc in Computer Engineering at the University of Campinas, specializing in machine learning topics. Gabriel has a strong background in software engineering and has worked on projects involving computer vision, embedded AI, and LLM applications.
Get to know Gabriel
StudySmarter is a globally recognized educational technology company, offering a holistic learning platform designed for students of all ages and educational levels. Our platform provides learning support for a wide range of subjects, including STEM, Social Sciences, and Languages and also helps students to successfully master various tests and exams worldwide, such as GCSE, A Level, SAT, ACT, Abitur, and more. We offer an extensive library of learning materials, including interactive flashcards, comprehensive textbook solutions, and detailed explanations. The cutting-edge technology and tools we provide help students create their own learning materials. StudySmarter’s content is not only expert-verified but also regularly updated to ensure accuracy and relevance.
Learn moreSave explanations to your personalised space and access them anytime, anywhere!
Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of StudySmarter.
Already have an account? Log in
Sign up to highlight and take notes. It’s 100% free.
The first learning app that truly has everything you need to ace your exams in one place
Already have an account? Log in
The first learning platform with all the tools and study materials you need.
Explanations 
Flashcards 
StudySmarter AI 
Notes 
Study Plans 
Study Sets 
Exams 
Find a job 
Student Deals 
Magazine 
Mobile App 
