Double Titration

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. I give you a flask with sodium hydroxide and sodium carbonate mixed together. Both are bases, and both use up hydrochloric acid. With one burette of acid, can you find how much of each is inside? Hmm, one titration gives one reading, right? And here we have two unknowns! The secret is two indicators, so the same flask gives two end points. This is double titration, and believe me, JEE loves it. So, let's begin.

0:36Two indicators, two end points

So, look at this graph. It shows the p H of sodium carbonate solution as we add hydrochloric acid from the burette. Up the side is the p H, and along the bottom, VHC l, the volume of acid added, okay? The p H falls in two big drops, right? Our first indicator, phenolphthalein, changes colour near p H eight to nine. That is the orange band, and the orange dot is the first end point. The second indicator, methyl orange, changes colour near p H three to four. That is the blue band, and the blue dot is the second end point. So, one flask, two readings. Clear? Now the names. The acid used up to the phenolphthalein end point is the first titre, small a, the mark below the orange dot. The extra acid after that, up to methyl orange, is the further titre, small b. We count both in millimoles of acid, okay? And look, the blue dot sits at a plus b, the total, not at b alone. Remember this for Example two.

1:40What the acid does in each stage

Alright, now the real chemistry. Suppose the flask has hydroxide ions and carbonate ions. At the first end point, has all the carbonate become carbon dioxide? Not yet! Up to the phenolphthalein end point, two things happen. First, all the hydroxide, O H minus, is neutralised, okay? Second, the carbonate ion, C O three two minus, goes only half way. It picks up one hydrogen ion and becomes bicarbonate, HCO three minus. The arrow means, turns into. And it stops there. Got it? Then we continue to methyl orange. Now all the bicarbonate goes to carbon dioxide. And notice the word all: the bicarbonate formed in the first stage, and also any bicarbonate that was in the flask from the start. Both are counted in small b. Quick check. Pure sodium carbonate, nothing else. Is small b bigger than small a, smaller, or equal? Equal, yes! Each carbonate ion takes one hydrogen ion in the first stage, and the same bicarbonate takes one more in the second. So for pure sodium carbonate, b equals a. Perfectly balanced.

2:53Mixture 1: NaOH + Na2CO3

Let's take the first mixture: sodium hydroxide with sodium carbonate. Up to phenolphthalein, every hydroxide is neutralised and every carbonate goes to bicarbonate, one hydrogen ion each. So the first titre is sodium hydroxide plus sodium carbonate, in millimoles, okay? Now, there was no bicarbonate in this flask at the start. So where does the bicarbonate for the second stage come from? Yes, only from the carbonate! Sodium hydroxide is already finished. So small b counts just the sodium carbonate. So now, just subtract. Sodium carbonate is b, and sodium hydroxide is a minus b. Write this down. Clear?

3:33Mixture 2: Na2CO3 + NaHCO3

Now the second mixture: sodium carbonate with sodium bicarbonate. No hydroxide now. Up to phenolphthalein, only the carbonate reacts, going to bicarbonate. The bicarbonate already present just waits. So here, the first titre is the sodium carbonate alone. In the second stage, all the bicarbonate goes: the part formed from carbonate, plus the part present from the start. So small b is sodium carbonate plus sodium bicarbonate. So, sodium carbonate is a, and sodium bicarbonate is b minus a. See, the two pairs look like mirror images, right? This is exactly where students mix them up.

4:13Topper's trick: compare a and b first

Now a trick that toppers use. Before any formula, compare the two titres. Sodium hydroxide is a minus b, and an amount can never be negative. So if a is bigger than b, use the hydroxide pair, okay? And sodium bicarbonate is b minus a. So if b is bigger than a, use the bicarbonate pair. One look at the readings, and you know the formulas. Really simple. And one more JEE trap. Sometimes the question gives the further volume, and sometimes the total volume from the very start. Our small b is always the further titre. If you get the total, subtract the first titre. Remember the blue dot at a plus b.

4:56Example 1: molarity of NaOH and Na2CO3 in a mixture

Now, Example one, and this is our flask from the start! Fifty millilitres of a solution of sodium hydroxide and sodium carbonate needs thirty millilitres of zero point one molar hydrochloric acid with phenolphthalein, and then a further ten millilitres with methyl orange. Find the molarity of each. Pause the video and try it first. Done? Okay, let's check. Millilitres times molarity gives millimoles. So small a is thirty times zero point one, three point zero millimoles. Small b is ten times zero point one, one point zero millimoles. The word further tells us this ten is already our b, nothing to subtract. The mixture has sodium hydroxide. So tell me, which titre gives the sodium carbonate directly? The further titre, exactly! So sodium carbonate is one point zero millimoles, and sodium hydroxide is three minus one, two point zero millimoles. And a is bigger than b, just as our trick said. Both sit in fifty millilitres, and millimoles per millilitre is molarity. Sodium hydroxide: two point zero by fifty, zero point zero four molar. Sodium carbonate: one point zero by fifty, zero point zero two molar. Two unknowns, two readings, puzzle solved!

6:18Example 2: percent Na2CO3, NaHCO3 and inert matter

Now a harder one, JEE level. One point zero zero gram of a sample has sodium carbonate, sodium bicarbonate, and some inert matter. It is dissolved in water. It needs five point zero millilitres of one molar hydrochloric acid to the phenolphthalein end point, and fifteen point zero millilitres in all to the methyl orange end point. Find the composition. Pause the video and try it. Done? Okay, let's check. Small a is five point zero times one, five point zero millimoles. And small b is fifteen point zero millimoles, right? No, no, careful! This is the JEE trap. Read again: fifteen millilitres in all. That is the total, a plus b. So small b is fifteen minus five, ten point zero millimoles, okay? Now b is bigger than a, so the bicarbonate pair applies, and that matches the sample. Sodium carbonate equals a, five point zero millimoles. Its molar mass is one hundred and six, so five times one hundred and six, five hundred and thirty milligrams. Zero point five three gram. Sodium bicarbonate is b minus a, again five point zero millimoles. Its molar mass is eighty four, so four hundred and twenty milligrams, zero point four two gram. The rest is inert: one point zero zero, minus zero point five three, minus zero point four two. Zero point zero five gram. The sample is exactly one gram, so grams turn into percentages directly. Fifty three percent sodium carbonate, forty two percent sodium bicarbonate, and five percent inert. And if you had taken b as fifteen? Bicarbonate would be ten millimoles, zero point eight four gram, and with the carbonate, one point three seven gram. More than the whole sample! Impossible, right? So always check: further, or in all?

8:20Quick revision: what titres a and b give in each mixture

So, quick revision. Up to phenolphthalein, the first titre: all the hydroxide is neutralised, and carbonate goes only to bicarbonate. From there to methyl orange, the further titre: every bicarbonate goes to carbon dioxide. Hydroxide with carbonate: carbonate is b, hydroxide is a minus b. Carbonate with bicarbonate: carbonate is a, bicarbonate is b minus a. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!