Volume Relations in Reactions

Transcript

0:00Introduction

Hello everyone! Now, one small experiment before we start. I take twenty millilitres of hydrogen and twenty millilitres of oxygen in a tube. Forty millilitres of gas in total, okay? Now I pass a spark. Bang! I cool the tube back to room temperature, and measure the gas again. It is much less than forty millilitres! Hmm, where did the gas go? Gas cannot just vanish, right? And here is a second puzzle. Pass a mixture of gases over red hot charcoal, and its volume grows, from thirty to forty millilitres. Today we will learn to read volumes straight from a balanced equation, and solve both puzzles. And look, in JEE, these gas volume questions are quick marks, if you know the traps. So, let's begin.

0:51Gay-Lussac in practice: coefficients are volumes

So, a balanced equation tells you how many moles react, right? But in the lab, we measure a gas in millilitres, not in moles. So tell me, can the same equation tell us volumes directly? Yes, it can! But only under one condition. At constant temperature T and constant pressure P, the coefficients of the gaseous species give their volume ratios. This is Gay-Lussac's law, in practice. Why does it work? Because at the same temperature and pressure, the volume of a gas goes with its moles, straight from the ideal gas equation, P V equals n R T, okay? Same temperature, same pressure: that condition is everything. Clear? Take our hydrogen and oxygen. Two H two plus O two gives two H two O, the equation on screen. And the little l in brackets means the water forms as a liquid, okay? So, read the coefficients as volumes. Two volumes of hydrogen react with one volume of oxygen. Two millilitres with one millilitre, two litres with one litre: the ratio is always two to one. Really simple.

2:03JEE trap: liquids and solids have no volume

Alright, now think back to that equation, and its right side. Two H two O, the water, written in the badge on screen, okay? So after the reaction, we have two volumes of water to count, right? No, no, careful! This is the JEE trap. Only gases count. Liquids and solids contribute no volume to the gas, okay? In these questions, the gases are cooled back to room temperature, right? Then the water condenses into a liquid. That is the little l in the equation. So, after cooling, water counts zero. Write zero, not two. Got it? And the same rule for solids. Charcoal is solid carbon, so it also counts zero. Keep this in mind; example two depends on it.

2:50A change in volume tells you what reacted

Now the third idea, and the most useful one. At the same temperature and pressure, a change in the total volume is a change in the total moles of gas. So you see, when the volume changes, the gas is telling you exactly how much has reacted. Take an ozoniser, a device where oxygen turns into ozone. Three O two give two O three, okay? Now tell me: will the total volume go up, or down? Count the gas volumes on each side. Down, exactly! Three volumes become two volumes. So every two millilitres of ozone formed reduces the volume by one millilitre. Measure the fall in volume, and you know how much ozone was formed. Simple as that. And now the opposite case. When ammonia decomposes, two N H three give one N two plus three H two. Two volumes become one plus three, that is four. So here, the volume rises. Up or down, the change always tells the story. With me?

3:51Topper's trick: let the volume change do the work

Now a trick that toppers use for every volume change question. Step one: write the balanced equation, and count only the gas volumes. Liquids and solids, zero. Step two: find how much the volume changes per millilitre of the gas you are looking for. For ozone, the volume falls by one millilitre for every two millilitres formed, right? That is half a millilitre per millilitre of ozone. Step three: divide the measured change by this change per millilitre. That's all. It gives the volume of that gas directly. Say the volume in an ozoniser falls by ten millilitres. Ten divided by half: twenty millilitres of ozone. No long algebra. Three lines, and done.

4:39Example 1: H2 and O2 exploded, which gas remains

So, remember our experiment from the start? Let's finish it. Twenty millilitres of hydrogen and twenty millilitres of oxygen are exploded, and cooled to room temperature. What gas remains, and what is its volume? Pause the video, and try it first. Done? Okay, let's check. Equation first. Hydrogen and oxygen react two to one by volume, and the water is a liquid. So, which gas runs out first? Hydrogen, exactly! Equal volumes were taken, but we need twice as much hydrogen as oxygen. Twenty millilitres of hydrogen needs half of that: ten millilitres of oxygen. So all the hydrogen is used up. Now the trap. Ten millilitres of oxygen left over, plus twenty millilitres of water from the equation. Thirty millilitres, right? No, no! The tube was cooled to room temperature. What happens to the water? It condenses, and liquids count zero. So the only gas left is the extra oxygen: twenty minus ten, ten millilitres. Answer: ten millilitres of oxygen. And there you go, mystery solved! Forty millilitres went in, and ten came out. The missing thirty millilitres, twenty of hydrogen and ten of oxygen, became liquid water. Nothing vanished. Clear?

6:07Example 2: CO and CO2 over red-hot charcoal

Now a harder one, JEE level. And this is our second puzzle, the volume that grows. Read it with me. Thirty millilitres of a mixture of carbon monoxide and carbon dioxide is passed over red hot charcoal. The volume becomes forty millilitres, at the same temperature and pressure. Find the composition of the original mixture. Pause and try. Hint: use the topper's trick. Done? Okay. First, which gas reacts? Only carbon dioxide. It reacts with the carbon of the charcoal: C O two plus C gives two C O, the equation on screen, okay? Now count the volumes. One carbon dioxide plus one carbon gives two carbon monoxide. Two volumes before, two after, so no change, right? No, no, careful! The volume did change, from thirty to forty. So where is the mistake? Yes, the carbon! Charcoal is a solid, and solids count zero. So the gas goes from one volume to two volumes. Every millilitre of carbon dioxide gives one extra millilitre of gas. The measured increase is forty minus thirty, ten millilitres. One extra millilitre per millilitre of carbon dioxide, so there were ten millilitres of carbon dioxide. The rest is carbon monoxide: thirty minus ten, twenty millilitres. Quick check. Twenty millilitres of carbon monoxide pass through, and ten of carbon dioxide become twenty of carbon monoxide. Twenty plus twenty: forty. Absolutely correct. See? The volume change did all the work.

7:49Quick revision: volume ratios and volume change

So, quick revision. At the same temperature and pressure, the coefficients of the gases are their volume ratios. Liquids and solids count zero, like condensed water and solid carbon. And a change in volume is a change in the moles of gas, so it tells you exactly what reacted. Now go and try the practice problems on this page. You will find them easy, I promise. All the best!