Gay-Lussac's Law, Avogadro's Law and Dalton's Atomic Theory

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Take one volume of hydrogen gas and one volume of chlorine gas. They react, and you get two volumes of hydrogen chloride. One plus one is two. Nothing strange, right? But now think about the particles. Every particle of hydrogen chloride has hydrogen in it. So how does one volume of hydrogen fill two volumes of hydrogen chloride? Wait, did the hydrogen atoms break in half? Even the great Dalton could not explain this. Today, we will. And look, this one idea, that gas volumes behave like moles, comes again and again in JEE gas problems. So, let's begin.

0:44Gay-Lussac's law of gaseous volumes

So, first, Gay-Lussac's law of gaseous volumes. Gases react in volumes that bear a simple whole-number ratio to one another, and also to the volumes of the gaseous products, okay? Not strange numbers like one point three seven. Simple ratios, like one is to one, or two is to one. Now you tell me. In our puzzle, what is the volume ratio? Yes! One volume of hydrogen, one of chlorine, two of hydrogen chloride. So, one is to one is to two. The colons on screen are read as 'is to', okay? That is a simple whole-number ratio, exactly as the law says. Clear? But look, the law has one condition, and examiners love to test it. All the volumes must be measured at the same temperature T and the same pressure P, okay? The law is stated only for that case, so check it first, every time.

1:40Dalton's atomic theory (1808)

Alright, now let's go one level deeper, to atoms. In eighteen oh eight, Dalton gave his atomic theory. Postulate one: matter consists of atoms, and atoms are indivisible. They cannot be broken, okay? Remember this word, indivisible. Our puzzle is going to hit it hard. Postulate two: all atoms of one element are identical, same mass, same properties. So every hydrogen atom is just like every other hydrogen atom. Postulate three: compounds form when atoms of different elements combine in fixed whole-number ratios. One is to one, one is to two, never half an atom. Got it? And postulate four: in a reaction, atoms are only rearranged. They are neither created nor destroyed. Same atoms, just new partners. Really simple.

2:31What Dalton explained, and what he could not

This theory was a big success. Tell me: which postulate explains the law of conservation of mass? Postulate four, exactly! Atoms are neither created nor destroyed, only rearranged. So the total mass does not change. It also explained the law of definite proportions, and the law of multiple proportions. Atoms of fixed mass, joining in whole-number ratios, give simple mass ratios, okay? But Gay-Lussac's law of gaseous volumes? Dalton's theory could not explain it. Our puzzle is exactly this case: one volume of hydrogen making two volumes of hydrogen chloride. With single, indivisible atoms, the counting simply does not work. The fix needed Avogadro's idea of polyatomic molecules: particles made of two or more atoms joined together. So, let's meet Avogadro.

3:26Avogadro's law: volume ratios are mole ratios

Now, Avogadro's law. Take equal volumes of two different gases, both at the same temperature and pressure, okay? Different gases, different molecules. So what can possibly be the same? Think about counting. Yes, the number of molecules! Equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules. The double arrow on screen means 'implies'. Clear? So, for gases, volume ratios are mole ratios. When you compare gas volumes, you are really comparing numbers of molecules. Write this line down. And now, a topper's trick. In a balanced equation, read the coefficients of the gases directly as volumes. Everything a gas, at the same temperature and pressure? Then the coefficients are your volume ratio. No grams needed. Super quick.

4:21JEE trap: Dalton is not fully true today

Now, a classic JEE trap. This one catches many students. Postulate one says atoms are indivisible. Still true today, right? Hmm? No, no, careful! Parts of Dalton's theory are now known to be untrue. Atoms contain electrons, protons and neutrons. So atoms are not indivisible. Next: are all atoms of one element identical in mass? Not always. Isotopes are atoms of the same element with different masses. And isobars are atoms of different elements with the same mass number. Don't mix them up. Isotopes, same element. Isobars, same mass number. Right? Last, nuclear reactions change one element into another. So atoms are not always just rearranged. See, in the exam, if a statement says all of Dalton's postulates are true today, mark it false. Got it?

5:19Example 1: volumes of O2 and CO2 when CO burns

Let's do example one. Two litres of carbon monoxide burns completely, and all the gases are at the same temperature and pressure. What volume of oxygen is used, and what volume of carbon dioxide is formed? Pause the video, and try it first. Done? Okay, let's check. First, the balanced equation: two C O plus O two gives two C O two. The arrow means 'gives', okay? All three are gases at the same temperature and pressure, so use our trick. The coefficients give the volume ratio: two is to one is to two. Oxygen has coefficient one, half of the two for carbon monoxide. So the oxygen used is half of two litres: one litre. Now, carbon dioxide. Two litres of carbon monoxide and one litre of oxygen went in. So three litres of carbon dioxide come out, right? No, no, careful! This is the trap. Gas volumes don't simply add up. They follow the mole ratio. Carbon dioxide to carbon monoxide is two is to two, so two litres of carbon dioxide form. Three litres went in, two came out, and that is perfectly fine. Clear?

6:33Example 2: why hydrogen and chlorine are diatomic

Now, the puzzle from the start. JEE level. One volume of hydrogen combines with one volume of chlorine to give two volumes of hydrogen chloride. Explain why this is impossible if hydrogen and chlorine exist as single atoms. Pause and try. Hint: use Avogadro's law to turn volumes into numbers of molecules. Done? Okay, let's check. By Avogadro's law, equal volumes hold equal numbers of molecules. So, say n molecules of hydrogen and n molecules of chlorine give two n molecules of hydrogen chloride. Here n is just a count, okay? Now, every hydrogen chloride molecule contains hydrogen, right? All two n of them. But only n hydrogen particles went in. So n hydrogen particles have made two n hydrogen-containing molecules. How is that possible? Yes, exactly! Each hydrogen particle must split into at least two atoms. If it were one single indivisible atom, it could sit in only one molecule, couldn't it? So the hydrogen particle is a molecule of at least two atoms: H two. And the same argument works for chlorine, so chlorine is C L two. Puzzle solved! The atoms never broke in half. Each hydrogen molecule had two atoms, and they went into two different hydrogen chloride molecules. This is Avogadro's idea of polyatomic molecules, the idea Dalton was missing.

8:04Quick revision: Gay-Lussac, Avogadro and Dalton

So, quick revision. Gay-Lussac: gases react in simple whole-number ratios by volume. Avogadro: at the same temperature and pressure, volume ratios are mole ratios. Dalton: his theory explains the mass laws, but gas volumes need Avogadro's molecules. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!