Lesson video

Hello, my name is Mrs. Collins and I'll be taking you through the learning today.

This lesson forms part of the unit making salts and is called Titrations Calculations of Unknown Concentration.

During this lesson, you'll learn how to calculate the concentration of an acid using results from a neutralisation titration.

Here are the keywords for today's lesson: Titration, titre, concordant, coefficient and mole.

I suggest you pause the video here, read through those explanations and record any information you feel you need to.

Today's lesson is divided into two parts: Analysing titres and determining an unknown concentration.

Some elements of today's lesson may be a little challenging, but I'm going to walk you through them.

So let's start with the first part of the lesson: Analysing titres.

Performing a titration, remember, is a valuable analytical tool for chemists.

And if it's completed with care, it allows 'em to determine a solution's unknown concentration.

The first step is to analyse the collected results.

So having recorded the initial and the final volume of a tirant in the burette, each titre is calculated using the equation: final volume minus the initial volume.

So remember, these are the values that you've taken from the burette during the titration.

So here's an example table.

Now remember, those readings will all be to two decimal places and will end in either a zero or five.

And notice with the trial run, the initial volume was at zero, but they put 0.

00.

So all values in the table are to two decimal places, and that's really important.

And then you've got your titres along the bottom.

That's the difference between the final and the initial volumes.

And remember, we are looking for concordant data, data that is within plus or minus 0.

10 centimetre cubed of each other.

So here are the titres at the bottom of the table.

A minimum of two concordant titres are identified.

Concordant titres are typically within 0.

10 centimetre cubed of each other, remember.

And trial runs can be considered when choosing concordant titres.

So your trial run might have actually been quite accurate.

So here's a set of results here.

And we've got our final volumes, our initial volumes, and our calculated titres.

And we need to work out which are concordant.

So which of these values are within plus or minus 0.

10 centimetre cubed of each other? And we can see that these are the only two values that are that close to each other.

So we exclude all other titres in that table and we find the mean between those two values.

So which of the following sets of results shows concordant titres? So pause the video here, look carefully which of those values are concordant.

Pause the video here, answer the question and I'll see you when you're finished.

Welcome back.

So the answer to that question is A and D.

So those values are within 0.

10 centimetre cubed of each other.

A mean titre is calculated using these concordant titres, as I mentioned earlier.

So the mean titre is the sum of those concordant titres, not all the titres, only the concordant ones divided by the number of concordant titres.

It's quoted to two decimal places.

That is the uncertainty of the burette and it represents the most accurate volume of the titrant used.

So here we've got those values there.

We're gonna find the mean of those two values, which comes to 26.

425, and then we bring it back up to two decimal places.

So our mean titre is 26.

43 centimetre cubed.

So what is the mean titre for the following titres? Okay, so pause the video here, carry out the calculation and I'll see you when you're finished.

Welcome back.

So the answers to that is 14.

47.

We could discount B and D because they're not two decimal places, so we knew it was either A or B.

And then you carry out your calculation.

All of the titres are concordant.

So therefore we can add all three together, divide by three.

That gives us the value of 14.

467, and then we give it to two decimal places, and we need to remember to do that.

So now we're going to do Task A based on the learning so far.

First of all, we're gonna match the following keywords to their description.

So pause the video here and match the terms. I'll see you when you're finished.

Welcome back.

So here are the matched correct matches.

So concordant are titre results within plus or minus 0.

10 centimetre cubed of each other.

Titration is a technique used to determine the exact volume.

Mean is the sum of the concordant results divided by the number of concordant results.

The titre is the volume of titrant used.

And the titrant is the solution that is gradually added via a burette.

So well done if you've got that correct.

So for question two, you're gonna analyse the results of a recent titration.

You're gonna calculate the titres for the titration completed.

Identify which runs are concordant, and calculate the mean titre for this investigation.

So pause the video here, carry out your calculations and I'll see you when you're finished.

Welcome back.

So let's go through those answers then.

So starting with a, calculate the titres.

So these are the values that you should have got that are in the table and you should have got those by carrying out the calculation final volume minus the initial volume.

Which of those runs are concordant? Actually, all of those three values are within 0.

10 centimetre cubed of each other there.

So we can use all them for calculating the mean for part C.

So this is the sum of those concordant titres divided by the number, gives us a value of 25.

633.

But remember, we must give our answer to two decimal places.

So 25.

63 centimetre cubed.

So well done if got that correct.

We're now moving on to question three.

Alex's mean titre doesn't match his partner's.

Identify and correct any errors that you find in that table.

So look really carefully at that calculation and identify any errors in it and correct those errors.

So pause the video here, answer the question, and I'll see you when you're finished.

Welcome back.

So let's have a look at the results then.

He miscalculated the titre for run one.

So this affected his mean titre calculation.

And actually the value should have been 25.

80, which means it was concordant with the rest of the data.

So you should have included it in his mean.

And that gives us a value of 25.

77.

So you can see, calculating your titre incorrectly can have an impact on the overall mean.

Now moving on to the second part of the lesson, determining an unknown concentration.

The stoichiometry or the molar ratio of reactants and products is shown by the coefficients in the balance symbol equation for a reaction.

So you've got a reaction here between sulfuric acid and sodium hydroxide producing sodium sulphate and water.

And we can see there are numbers in front of each of the chemicals in the balanced equation.

And these numbers in front are called coefficients.

And we can see that in this reaction, we've got one mole of sulfuric acid reacting with two moles of sodium hydroxide to form one mole of sodium sulphate and two moles of water.

And remember back from your previous learning, a mole is 6.

02 times 10 to the 23 particles, and that's Avogadro's number, remember.

The stoichiometry of a reaction remains unchanged even if the quantitative amounts change.

So this is the ratio between the chemicals remains the same.

So if we were to double the number of moles of sulfuric acid, this would also double all of the other quantities within that equation.

If we were to divide that by four, then that all of the values will be divided by four in that equation.

So just bear that in mind.

The stoichiometry remains the same.

That ratio between the reactants and the products all remains the same.

So here's a question based on that learning.

Which chemical equation shows similar molar ratio to the reaction shown in that equation? So look really carefully at all of those different answers and think about that stoichiometry.

So what has happened to each of those coefficients and are they similar to the one given in the question? So pause the video here, answer the question and I'll see you when you're finished.

Welcome back.

So B is correct because all of the coefficients have been multiplied by two.

And D is also correct because all of the coefficients have actually been divided by three.

Now do bear in mind that it should be 0.

66666 reoccurring.

Obviously we round that up to 0.

67.

And this is why it says similar to the ratio.

So not precisely the same but similar.

The stoichiometry of a titration can be used to calculate the unknown concentration of the substance in the conical flask.

But it makes the assumption that every single atom has reacted.

So it's gone to completion and there are no excess reactants left in the reaction.

So in order to do this, you're going to need the average titre, the titrant concentration.

So that's the concentration of the substance in the burette.

The analyte volume.

So that's the volume of the substance in the conical flask.

And you're going to need a balanced symbol equation because we need to know the stoichiometry of that chemical reaction.

You'll also obviously need a calculator 'cause it'll make your life a lot easier than trying to do it by hand.

And you need a step-by-step strategy in order to carry this out.

And I'm going to show you what we call the U-turn method, which involves a calculation grid.

A calculation grid helps to organise the information required to complete a multi-step calculation.

They're completed in a U formation, but only work if constructed in the order necessary for the mathematical relationship being used.

So an example is, when using the equation: mass equals relative mass times by moles.

You can see we placing those in this order in the grid here.

So we've got mass at the top, we've got the relative atomic mass or the relative molecular mass.

We've got the moles and we've got the ratio here.

So we go, in this instance, when we go down the column, we will divide, and when we go up the column we are going to multiply.

So this is only works when we are using this equation.

So let's take a look at the equation that we're interested in for these calculations.

So when using concentration equals moles divided by volume, the grid looks like this.

And we're interested in that green box and what it's actually surrounding, which is different to the previous example.

So when we go down this time, we multiply in the known column.

Now I'm gonna explain what known and unknown means a little bit later in the calculation.

So don't worry too much about that at this stage.

I will go through this step-by-step with you.

But in this instance, when we go down the column, we are going to multiply, and when we're going up the unknown column, we're going to divide.

And note that the mathematical processes are reversed to the previous calculation grid.

And when we were doing mass equals relative mass times by moles.

But also notice that the ratio row is not included in the box.

So we're not doing any multiplication or division of the ratio at the moment.

We are just interested in the concentration volume and moles.

So just take care with that.

You may want to pause the video here and just make a note of what's going on on this slide, but I will explain it through later.

So let's have a look at a specific example and how to use that particular grid.

So we've got 25 centimetre cubed of potassium hydroxide, which is an alkaline, reacting with 24.

64 centimetre cubed of 0.

250 moles per decimeter cube sulfuric acid, which is a strong acid.

What was the concentration of potassium hydroxide to three significant figures? So we're going to calculate the concentration of the unknown.

So we know the concentration of the sulfuric acid, but we don't know the concentration of the potassium hydroxide.

So firstly, identify the unknown and the known in your balanced symbol equation.

So we know the concentration of sulfuric acid and we don't know the concentration of the potassium hydroxide.

Potassium hydroxide is unknown and the sulfuric acid is known.

So we're just putting a tick above what we know and a question mark above what we don't know just to identify the difference between the two.

So that means we are not interested in the products of the reaction.

So we just popped a line through those.

So below the known and the unknown substances, we're going to create a calculation grid that includes concentration, volume, moles, which we'll need to calculate, and the ratio.

So we need to write in what we know already from the question and then work out what we don't know.

So first of all, ensure all the volumes are in decimeter cubed.

This might require unit conversions.

So the concentration, if you look at the units for concentration, it's moles per decimeter cubed, but the volumes for the potassium hydroxide and for the sulfuric acid are given in centimetre cubed.

So the first thing we need to do is convert centimetre cubed to decimeter cubed.

And to do this we'll divide by 1000, and then we can write those values into the table.

So we've got 25 centimetre cube divided by 1000 is 0.

025 decimeter cubed.

And 24.

64 divided by 1000 is 0.

02464 decimeter cubed.

We can then put these in the table.

Notice we haven't done any rounding up at this stage.

If you round up too early in titration calculations, it can mean that your results come out incorrect.

So populate the grid with those volumes in decimeter cubed so that that's something that we know.

Step four, we're going to populate the grid with the concentration of the known solution and we're also going to include the stoichiometry from the question.

So that's the ratio between the different substances, those coefficients that we were talking about earlier.

So the concentration of sulfuric acid, remember, is 0.

250 moles per decimeter cubed.

So we can just pop that into the grid.

And then we're going to add the ratios.

So if we look at the equation, we can see we've got two moles of potassium hydroxide reacting with one mole of sulfuric acid there.

So we can put that ratio into the grid.

So now we've got in the grid all of the things that we know from the question.

There's actually a surprising amount of information in the question.

And the next step is, we're gonna fill in the blanks in that table using the information in the table.

So we are going to do this using the U formation that we talked about earlier.

And now you know what the question mark and the tick stands for.

So you've got the known and the unknown.

So we're going to go down the known first and then go up the unknown.

So calculate the number of moles of the known.

So we've got place in the grid there.

So we do that by doing concentration multiplied by the volume.

So we multiply those two numbers together and we get a value of 0.

00616.

So we calculated the number of moles of the known.

So we've completed the known side of the grid now, and we need to go up the unknown.

So the first thing we're going to look at is that ratio, the stoichiometry between the two.

So if we've got 0.

00616 moles of sulfuric acid and there's a ratio of one to two, that means we must have twice as many moles of potassium hydroxide.

So we're going to use the molar ratio to calculate the number of moles of the unknown.

And there's two ways we can do that.

We can just look at the ratio as I just discussed it, or we can carry out a calculation.

So for the calculation, we take the number of moles of the known and we divide it by the ratio of the known.

So in this instance, that's 0.

00616 divided by 1, which obviously equals 0.

00616.

We then multiply that value by 2 and that gives us a value of 0.

0123, that's twice as many moles as the sulfuric acid.

So we've just multiplied it by 2.

We are now going to calculate the concentration of the unknown.

So we're going to go up the step again.

To do this, the concentration is the moles divided by the volume, remember? And that gives us a concentration of 0.

4928 moles per decimeter cubed.

So you might want to pause the video here and just look at that grid in detail and see what we've done to fill it in.

Now we need to ensure the answer is given to the correct number of significant figures and units.

And this is a mistake that's often made on exam paper questions where students forget to do this last step.

So if you look at it, it wants it to three significant figures.

We've got an answer to four significant figures.

So we just need to round it up to 0.

493 moles per decimeter cubed.

Alright, we're gonna go through another example, and then once I've done this, you are going to have a go at doing one yourself.

So we've got the question here.

So 10 centimetre cubed of sodium carbonate reacted with 12.

05 centimetre cubed of 0.

22 moles per decimeter cubed of nitric acid.

What is the concentration of the sodium carbonate? Give your answer to two significant figures.

Now before we start looking through the calculation, I'm just gonna look through that question again and we're gonna spot the pieces of information that we need.

So firstly, we've got two volumes being given to us, but remember, they've been given in centimetre cubed and we are going to need to convert those to decimeter cubed by dividing by 1000.

We've been given the concentration of nitric acid, but we don't know the concentration of sodium carbonate and we need to give our answer to two significant figures.

So firstly, we know that the sodium carbonate is the unknown because we are being asked to find the concentration for that.

So we can label that as the unknown.

And therefore the nitric acid must be the known because we've got the concentration being given there to us.

So we know we're gonna go down the known and up the unknown.

So step one, put the volumes into the table.

And remember, we've divided by 1000 for both of those to make sure they're in decimeter cubed.

Step two, we're gonna put in the concentration and the stoichiometry ratio between the two of them.

Then we're going to calculate the number of moles of the known.

So we're gonna fill in that last part of the question there.

And in order to do that we're gonna multiply concentration by volume and that gives us 0.

00241 moles.

So you may want to pause the video here, and just make sure you are really clear about where those numbers have come from.

So now we're going to use the ratio to help support us.

So we are gonna divide the number of moles by the ratio of two and then we're going to multiply it by the ratio of one to give us the number of moles of sodium carbonate.

So again, you might want to pause the video here for a second and just see where we've got those numbers from.

Notice that we haven't done rounding up at this stage, we're writing the full number down.

Now we need to calculate the concentration of the unknown.

And in order to do that, we do the number of moles divided by the volume, gives us the concentration there of 0.

1205.

So we've carried out all our concentrations.

We now go back to the question and look and see how many significant figures we need to do this to.

And that's to two significant figures.

So our answer will be 0.

12 moles per decimeter cubed of sodium carbonate.

So what I'd like you to do now is following my model is carry out this calculation here.

So pause the video here, answer the question, and I'll see you when you're finished.

Welcome back.

So again, we draw out the grid and we carry out the calculation in the same way.

So what I'd like you to do is just pause the video here, have a look through the answer, check your answer in response to that one there.

And hopefully you've got that correct.

So well done if you have done.

The mathematical relationship between mass and number of moles allows chemists to convert between concentration units, moles per decimeter cubed and grammes per decimeter cubed.

So the concentration, remember, is the moles divided by the volume and the concentration is also the mass divided by the volume.

So it depends what information you're given in the question basically.

So we can convert between moles and mass because mass is the relative atomic mass or relative molecular mass multiplied by the number of moles that are present.

So a periodic table is needed for this conversion because we need to find the relative atomic masses and then calculate any relative formula masses of any molecules.

So what is 0.

48 moles per decimeter cube of sodium carbonate in grammes per decimeter cube.

So we're going to carry out this calculation together and then I'm going to ask you to do one yourself following this model.

So here we've got the number of particles of sodium carbonate dissolved in one decimeter cubed of water.

So that is the number of moles that we need for the equation.

And then the second part of the equation we need is this relative mass.

And this is where the periodic table comes in.

In order to find the relative mass of sodium carbonate, we need to add together the relative atomic masses of all of the atoms in the formula.

So here's the equation for that.

So the relative atomic mass of sodium is 28, and we can see there are two of them in the formula.

The relative atomic mass of carbon is 12 and there's one of them.

And the relative atomic mass of oxygen is 16 and there are three of those.

And if we add all those together, we come up with a relative formula mass.

So putting those numbers into that equation, we've got 106, which is the relative formula mass there, multiplied by 0.

48, which is the number of moles.

And that gives us a mass of 50.

88.

And then we can round this up to two significant figures because that's how many significant figures we've got in the question.

So that gives us 51 grammes per decimeter cubed of sodium carbonate.

So what I'd like you to do is follow that model and complete this question.

So pause the video here, answer the question, and I'll see you when you're finished.

Welcome back.

So the answer to that question is here.

And remember, you will have needed a periodic table to answer that question.

Pause the video here, check your answer next to that one, and I'll see you when you're finished.

Welcome back.

So now we're going to move on to Task B, which is pulling together all of that information that we've covered so far.

So question one is about a titration calculation carried out by Sam.

And we've got a variety of information there.

And question A is, you've got to calculate the concentration of citric acid in moles per decimeter cube.

So citric acid is the unknown, so you'll need to draw your grid there to carry out that calculation.

And then B, citric acid has the formula C6H8O7.

What is the concentration of citric acid Sam used in the titration in grammes per decimeter cubed.

And this time you're going to give your answer to three significant figures.

So that's quite challenging as a task, so you need to pause the video here, carry out those calculations, and I'll see you when you're finished.

Welcome back.

So here we have got the answers to that question then.

So the firstly, what is the concentration of citric acid in moles per decimeter cubed? Give your answer to three significant figures.

Now here's the information that we're interested in, highlighted here.

So we know we need to give our answer to three significant figures, that's really important.

And then we've got 42.

65 centimetre cubed of 0.

035 moles per decimeter cubed of sodium hydroxide.

And we've only got the volume of the citric acid.

So we know that is the unknown.

We know that those two values for the volume need to be given in decimeter cube.

So we know there's some conversion that needs to happen there.

So here's our table of data.

So what I'd like you to do is, pause the video here, check that alongside your answer, and make any corrections that you need to.

For part B, the concentration in grammes per decimeter cube this time.

So what we need to do is use the formula for the relative mass, that's important.

So you'd need your periodic table there to do that.

So we've got 6 multiplied by 12 for the carbon, 8 multiplied by 1 for the hydrogen, and 7 multiplied by 16 for the oxygen.

So that gives us a relative formula mass of 192.

If we go back to the question, we know we've got 0.

0199 moles.

So we can multiply together the relative formula mass and the number of moles to give us our mass.

And that gives us a value of 3.

82 grammes per decimeter cube.

So well done if you've got that correct.

Make sure you've done it to three significant figures.

3.

821 is three decimal places and we need it to three significant figures.

So pause the video here, check your answer next to that one, and I'll see you when you're finished.

Now we're back to question two.

So Izzy, Sam's lab partner, used the same values to calculate the concentration of citric acid; however, her answer was different from Sam's.

Review the calculations.

Identify and correct any errors that you find.

So you need to work through this really carefully using that step-by-step approach.

So pause the video here, answer the question, and I'll see you when you're finished.

Welcome back.

So hopefully you have identified that she completed her calculation grid using the opposite mathematical processes that were required.

She divided when she should have multiplied and vice versa, and that means her final value is incorrect.

So her answer shows only two significant figures and not three significant figures.

So correcting Izzy's errors, her new calculations and answers should look like this.

So pause the video here and just check through.

Make sure your answer matches the one on the screen.

Here is the summary of today's lesson.

Data collected during a titration allows chemists to determine a solution's unknown concentration.

Concordant titres should be used when calculating mean volume used to neutralise a solution.

The coefficients in a balanced symbol equation indicate the stoichiometry or the molar ratio between substances in a reaction.

The concentration of an unknown solution can be determined using the relationship: concentration equals moles divided by volume in decimeter cubed and the stoichiometry of the titration reaction.

Thank you very much for joining me for today's lesson.