Topic 4.6: Introduction to Titration

Titration: how much is in there?

This is the inside of an airplane hangar in Southern California, sealed up so tightly that the only light getting in comes through one hole in the wall, a quarter of an inch across. Follow that light across the building, and look at what it’s doing. It’s painting the whole airfield outside onto the far wall, the control tower, the runways and the hills behind them, upside down and a hundred feet wide, which means you’re standing inside a camera.

In July of 2006, six photographers and about four hundred volunteers turned this jet hangar, at the old El Toro Marine base, into the biggest camera anyone had ever built. Across the back they hung one seamless sheet of fabric, painted the day before with eighty liters of light-sensitive chemistry. They let the light pour in for thirty-five minutes, and when they covered the hole again, the fabric looked just as blank as it had before, without a single mark on it.

So they laid it in a tray made from a swimming-pool liner, longer than a basketball court, pumped in six hundred gallons of developer, and the picture came up out of nothing. When they hung it up in the daylight, it was a hundred and seven feet wide, and the next year Guinness certified it as the largest photograph in the world.

Nobody drew that picture and nobody printed it, because chemistry made it. And by the end of this lesson, you’ll be able to point at three of the reactions behind a photograph like this one, and say exactly what kind each one is, whether it moves protons, moves electrons or builds a solid out of ions.

And on the way, you’ll learn how chemists measure exactly how much of a chemical there is, in a bath they can’t see into. Every darkroom bath has a job. So let’s start with the one right after the developer, and find out how much acid it has left.

In a regular darkroom like this one, every print goes through three trays, the developer, the stop bath and the fixer, and the stop bath is just water with a little acetic acid in it, the acid in vinegar. The developer only works while it’s basic, so the stop bath’s acid stops it by using up the base each print carries in, which means every print uses up a little of the acid.

So how much acid is still in there? You can’t count molecules, but you can make them react with something you can measure, a little at a time, until they’re all gone. We take exactly ten milliliters of the stop bath with a pipet, run it into a flask, and add two drops of an indicator, a dye that turns pink once the solution becomes basic.

Then we fill this buret with sodium hydroxide, a base whose concentration we know exactly, zero point two zero zero zero molar, and we call it the titrant. The acid we’re trying to measure is called the analyte, and the buret starts at two point one zero milliliters. Now we open the stopcock. Every time base lands in the flask, you get a flash of pink, right where it hits.

Then it vanishes when we swirl, because there’s still plenty of acid in there, and the acid uses up the base the moment they meet. As we get closer, the pink takes longer and longer to fade, so we slow down to one drop at a time, until this one.

And this time the faintest pink stays, even after we swirl. The buret reads eighteen point five zero milliliters now, so we’ve added sixteen point four zero milliliters of base. Two buret readings, a known concentration and a balanced equation, that’s the setup of one of the AP exam’s classic questions, and in a few minutes you’re going to work a real one.

The moment the base we’ve added has used up all the acid that was in the flask is called the equivalence point. And the color change that tells us we’ve gotten there is called the endpoint. A good indicator makes those two land almost exactly together, so when the pink stays, the acid is all gone.

Now I want you to feel it for yourself. Here’s a fresh sample, so add the base and try to stop on the first pink that stays.

The equivalence point, worked

Let’s go inside the flask and watch what the base is actually doing. These are acetic acid molecules, and each one here stands for a huge number of real ones. Each hydroxide that comes in, with a sodium ion tagging along, takes a hydrogen ion off an acid molecule and turns into water, so halfway there, half of the acid is gone. And at sixteen point four zero milliliters, the last acid molecule is gone, and there’s no extra hydroxide yet, just acetate ions, sodium ions and water.

That’s the equivalence point, and notice the sodium ions are still there, because they were just along for the ride. Keep adding, and now the hydroxide has nothing left to react with, so it piles up and the pink gets darker and darker. That first faint pink showed up right at the equivalence point, because the acetate ions left behind make the solution just a little basic on their own.

Here are four flasks from this same titration, so which one is at the equivalence point? On the board, the titrant is the solution we know, in the buret, and the analyte is what we’re measuring, in the flask.

The equivalence point is when the analyte is all used up, and the endpoint is the change we see. People mix those last two up, so remember, the equivalence point is about amounts and the endpoint is the signal.

Now let’s turn our readings into moles of acid, using this reaction, one acetic acid for every hydroxide. First, the volume we added is the final reading minus the initial one, which is sixteen point four zero milliliters.

I want liters so I can use the molarity, so it’s sixteen point four zero milliliters times one liter over a thousand milliliters, and the milliliters cancel. Then I multiply by zero point two zero zero zero moles of hydroxide per liter, and now the liters cancel too.

The step that links the base to the acid is the mole ratio, one acetic acid for every hydroxide, which gives zero point zero zero three two eight zero moles of acid. For the concentration, we divide by the sample’s volume, zero point zero one zero zero zero liters, and get zero point three two eight zero molar. Look at the measured numbers in that chain. Each one has four significant figures, so the answer keeps four.

Does that make sense? Acetic acid is about sixty grams a mole, so a liter of this bath holds about twenty grams. That’s two grams in every hundred milliliters. Kitchen vinegar has about five, so the stop bath is less than half as strong.

Here’s the same titration as a graph. The acid left drops in a straight line as we add base, and hits zero at sixteen point four zero milliliters. After that, only the extra hydroxide grows, and the equivalence point is where the two lines meet.

When the ratio isn’t 1: 1

So is the equivalence point always where the moles of acid equal the moles of base? It was this time, but only because the equation said one to one. Here’s the AP question I promised you, from the sample questions in the course guide. A chemist titrates the magnesium hydroxide in an antacid tablet with nitric acid.

Here are the buret readings, and the question wants the mass of magnesium hydroxide in the tablet. Here’s the balanced equation, and look at the two in front of the nitric acid, because it takes two nitric acids to use up one magnesium hydroxide. The acid we added is twenty point zero zero milliliters, and the same two steps as before, into liters and then times the molarity, turn that into zero point zero zero two zero zero moles of nitric acid. Next comes the mole ratio, one mole of magnesium hydroxide for every two moles of nitric acid, and this little factor is what the whole question is really testing.

Now you finish it. Using the molar mass, fifty-eight point three grams per mole, how many grams of magnesium hydroxide were in the tablet? So equivalence doesn’t mean equal moles of acid and base. It means the amounts the coefficients call for.

Here’s one that trips people up. Back in our stop-bath titration, if you add twenty milliliters of water to the flask before you start, what happens to the volume of base you’ll need?

Now it’s your turn, so here’s the same stop bath after a long night of prints. This time we titrate a twenty-five milliliter sample with the same base. What’s the concentration of acetic acid in the tired stop bath now? The bath dropped from zero point three two eight zero molar to zero point two one seven zero, so if its volume didn’t change, the prints used up about a third of its acid.