Dalton's Law of Partial Pressures

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. I take a vessel, and I put four grams of hydrogen and thirty two grams of oxygen inside it. The total pressure is three atmospheres. Now tell me, which gas is responsible for more of that pressure? Oxygen, obviously, right? Thirty two grams against just four grams, eight times the mass! Hmm. Are you sure? Today we will find out, and the answer may surprise you. The idea is called Dalton's law of partial pressures. And look, in JEE this law shows up everywhere: gas mixtures, gases collected over water, even the air we breathe. So, let's begin.

0:44Dalton's law: each gas acts as if it were alone

So, imagine a vessel with a mixture of gases. One condition first: the gases must not react with each other, okay? They simply share the same vessel. Clear? Now think. Inside this vessel, how much space does each gas get? Only a part of the vessel, or the whole vessel? The whole vessel, yes! Every gas spreads through the full volume. And that is Dalton's idea. Each gas exerts the pressure it would have if it were alone in the whole volume, as if the other gases were not there at all. We call this the partial pressure of that gas, and we write it with a small p, okay? So what is the total pressure of the mixture? Simple: just add them up! Capital P equals p one, plus p two, plus p three, and so on. The big sigma on screen, sigma of p sub i, is only a short way of writing: add all the partial pressures, p sub i for every gas i. As simple as that.

1:45Each gas's share: the mole fraction

Alright, now the real question. The total pressure is shared between the gases. But in what proportion? Let's see. First, the mole fraction. x sub i equals n sub i, the moles of that gas, divided by the total moles of all the gases in the vessel. So it tells you what share of all the moles belongs to that one gas. And the partial pressure is simply the mole fraction times the total pressure. p sub i equals x sub i times capital P, okay? Its share of the moles is its share of the pressure. Right? Now, a JEE trap. Suppose the question gives you the masses in grams. Many students directly share the pressure in the ratio of the masses. Is that okay? No, no, careful! Look at the formula again. It has n, the number of moles, not the mass. So always convert grams to moles first. Share by moles, never by mass. One mole of a light gas and one mole of a heavy gas get exactly the same share. Got it? And here is a small trick that toppers use. Once you have all the partial pressures, add them. They must give back the total pressure, because all the mole fractions together make exactly one. Five seconds, and you catch a silly mistake. Perfect!

3:09Gas collected over water

Next, one more situation that JEE loves. Very often a gas is collected over water. But such a gas is never pure. It is saturated with water vapour, okay? So what we actually collect is a mixture: our gas, plus water vapour. Now, the question gives you the total pressure. Is that the pressure of our gas? Hmm. Remember Dalton's law. Who else is sitting in that vessel? Yes, the water vapour! So by Dalton's law, the total pressure equals p gas plus p water. Two gases, two partial pressures, that's it. So the pressure of our gas is the total pressure, minus the pressure of the water vapour. Always do this subtraction first, and only then use this pressure for the gas, okay? And this pressure of the water vapour has a special name: the aqueous tension. The question will give you its value. So whenever you see the words aqueous tension, your brain should say: subtract it! With me?

4:12Example 1: partial pressures of H2 and O2

So, remember our puzzle from the start? Let's finish it. Four grams of hydrogen and thirty two grams of oxygen are in a vessel, at a total pressure of three atmospheres. Find the partial pressures. Pause the video, and try it first. Done? Okay, let's check. Oxygen has eight times the mass, so oxygen gets most of the pressure, right? No, no! That is exactly the trap we just saw. Share by moles, not by mass. So, moles first. Hydrogen, H two, has molar mass two, so four grams is four by two: two moles. Oxygen, O two, has molar mass thirty two, so thirty two grams is just one mole. Total moles: two plus one, three. So the mole fraction of hydrogen is two by three, and of oxygen, one by three. See? Less mass, but more moles! Now p equals x times capital P, okay? For hydrogen: two by three, times three atmospheres. That is two atmospheres. And for oxygen: one by three, times three. One atmosphere. Topper's check: two plus one is three, the total pressure. Absolutely correct! So, mystery solved. Just four grams of hydrogen gives twice the pressure of thirty two grams of oxygen, because the pressure is shared by moles, right?

5:35Example 2: moles of H2 collected over water

Now a slightly harder one, JEE level. Read it with me. Two hundred fifty millilitres of hydrogen is collected over water at three hundred kelvin, and a total pressure of seven hundred sixty millimetres of mercury. The aqueous tension is twenty seven millimetres of mercury. Find the moles of hydrogen. Pause and try. Hint: who else is in that gas? You know, so many students put seven hundred sixty millimetres straight into p V equals n R T, and they are done. Correct? No, no, careful! The words collected over water are a signal. This hydrogen is saturated with water vapour. So the pressure of hydrogen alone is seven hundred sixty minus twenty seven: seven hundred thirty three millimetres of mercury. Our value of R is in litre atmosphere, so we need the pressure in atmospheres. Seven hundred sixty millimetres of mercury is one atmosphere, so divide by seven hundred sixty. Zero point nine six four atmosphere. And the volume. Careful here too! If you put millilitres with R in litre atmosphere, your answer is a factor of one thousand out. So, two hundred fifty millilitres is zero point two five zero litres, okay? Now Dalton's law says hydrogen behaves as if it were alone in the whole volume, at its own partial pressure. So n equals p V over R T, with R, the gas constant, zero point zero eight two one, and T, the temperature, three hundred kelvin. Zero point nine six four times zero point two five zero, divided by zero point zero eight two one times three hundred. That comes to about nine point eight times ten to the power minus three moles. See? One subtraction at the start, and the whole question falls into place. That's it!

7:28Quick revision: p = xP and aqueous tension

So, quick revision. The total pressure is the sum of the partial pressures. Each gas gets its share: p sub i equals x sub i times capital P, by moles, never by mass. And for a gas collected over water, subtract the aqueous tension first. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!