Vapour Pressure of Liquids

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle before we start. Up on a high mountain, water starts boiling below one hundred degrees Celsius. And at home, in a pressure cooker, food cooks faster. Same water. So why does it boil at different temperatures? Strange, right? The answer is one idea: vapour pressure. Today we will see what it is, what it depends on, and how it decides when a liquid boils. This chapter on Raoult's law is built on it, and it comes up often in JEE, so let's begin.

0:35What is vapour pressure?

So, take some liquid in a closed vessel. Molecules at the surface escape into the space above: the liquid evaporates. And some of those vapour molecules come back into the liquid: the vapour condenses. Okay? Now think. The vessel is closed. Will the liquid keep on evaporating until all of it is gone? No, it will not! It evaporates only until the rate of evaporation equals the rate of condensation. Both are still going on, at equal rates, so nothing seems to change. That is why we call it a dynamic equilibrium. Clear? And the pressure exerted by the vapour in this equilibrium is called the vapour pressure of the liquid, at that temperature. Remember those last words, at that temperature. Right? Now, vapour pressure depends on only two things: the nature of the liquid, and the temperature. Got it? So, a classic trap. I pour more water into the same closed flask, at the same temperature. More liquid, so more vapour pressure, right? No, no, careful! Vapour pressure does not depend on the amount of liquid, and not on its surface area either. Same liquid, same temperature, same vapour pressure. With me?

1:52Nature of the liquid: intermolecular forces

First, the nature of the liquid. The molecules of a liquid are held together by intermolecular forces. Now tell me, which molecules escape into the vapour more easily: those held weakly, or those held strongly? Weakly held, exactly! So, weaker intermolecular forces give a higher vapour pressure. The double arrow you see on screen means implies. Okay? Now look at this order, at a given temperature, the capital T on screen. Each sign between them means greater than. Diethyl ether has the highest vapour pressure, then acetone, then ethanol, and water has the lowest. Clear?

2:33Temperature: vapour pressure rises steeply

Next, temperature. I warm the same closed flask of water. What happens to the vapour pressure: up, down, or no change? It goes up, yes! And not just a little. Vapour pressure rises steeply with temperature. Right? The Clausius Clapeyron equation tells us how steeply. Read it with me. Natural log, written l n, of p two over p one, equals delta vap H over R, times, in brackets, one over T one, minus one over T two. The little triangle is delta, and vap written small below it means vaporisation. So delta vap H is the enthalpy of vaporisation of the liquid. Okay? Here, p one and p two are the vapour pressures at temperatures T one and T two. The small one and two written below are subscripts, just labels. And the temperatures must be in kelvin, always. Got it? Last point, where marks are often lost. R is the gas constant, eight point three one four joules per kelvin per mole. On screen, J is joules, K to the power minus one means per kelvin, and mol to the power minus one means per mole. Since R is in joules, delta vap H must also be in joules per mole, not kilojoules. Clear?

3:51Boiling: vapour pressure meets external pressure

Now, the big one: boiling. As you heat a liquid, its vapour pressure keeps rising. The liquid boils when its vapour pressure becomes equal to the external pressure. Okay? And the normal boiling point is the temperature at which the vapour pressure equals one atmosphere. The a t m on screen is short for atmosphere. Right? So, back to our mountain puzzle. High up, the external pressure is lower. Will the vapour pressure of water reach it at a lower temperature, or at a higher one? Lower, exactly! The vapour pressure only has to climb up to a smaller external pressure, so it gets there at a lower temperature. Water boils below one hundred degrees Celsius; the small circle and C mean degrees Celsius. Okay? And the pressure cooker is the opposite. Inside it, the pressure is higher, so water boils above one hundred degrees Celsius. Hotter water, so food cooks faster. Puzzle solved! Got it?

4:52Example 1: compare two liquids from boiling points

Alright, example one. Liquids X and Y have normal boiling points of three hundred and thirty kelvin and three hundred and seventy kelvin. Which has the higher vapour pressure at three hundred kelvin? And which has the stronger intermolecular forces? Pause the video, and try it first. Done? Okay, let's check. Normal boiling point means the vapour pressure equals one atmosphere. So X reaches one atmosphere already at three hundred and thirty kelvin, but Y gets there only at three hundred and seventy kelvin. With me? Now, many students see the bigger number, three hundred and seventy, and say Y has the higher vapour pressure. Is that right? No, no, careful! It is the other way round. Vapour pressure rises with temperature, and X reaches one atmosphere at a lower temperature. So at three hundred kelvin, X has the higher vapour pressure. Okay? Now the forces. Weaker forces give a higher vapour pressure, remember? So Y, with the lower vapour pressure, has the stronger intermolecular forces. So the answers are X for the vapour pressure, and Y for the forces. Got it?

6:07Example 2: enthalpy of vaporisation from two pressures

Now a harder one, example two. Read it with me: a liquid has vapour pressure one hundred millimetres of mercury at three hundred kelvin, and four hundred millimetres of mercury at three hundred and thirty kelvin. The m m H g on screen is millimetres of mercury. Estimate its enthalpy of vaporisation. Pause the video and try it. Hint: two pressures, two temperatures. Done? Okay, let's check. Clausius Clapeyron, of course. Take p one as one hundred, at T one, three hundred kelvin, and p two as four hundred, at T two, three hundred and thirty kelvin. So l n of p two over p one is l n of four hundred over one hundred, that is l n four, which is one point three eight six. Nice, right? Now the bracket: one over three hundred, minus one over three hundred and thirty. Use the common denominator: thirty over ninety nine thousand. That is three point zero three times ten to the power minus four, per kelvin. Okay? Put everything in. One point three eight six equals delta H over eight point three one four, times three point zero three times ten to the power minus four. Here delta H is just short for delta vap H, clear? So, delta H equals one point three eight six times eight point three one four, over three point zero three times ten to the power minus four. The wavy equals sign means approximately: about three point eight times ten to the power four, which is thirty eight thousand. Right? Now, the unit. Many students write thirty eight thousand kilojoules per mole. Is that correct? Oh no, careful! R was in joules per kelvin per mole, so delta vap H comes out in joules per mole. Thirty eight thousand joules per mole, that is thirty eight kilojoules per mole. With me?

8:02Quick revision: vapour pressure, boiling, Clausius-Clapeyron

So, quick revision. Vapour pressure depends only on the liquid and the temperature, not on the amount. Weaker forces give a higher vapour pressure, and a liquid boils when its vapour pressure equals the external pressure. And in Clausius Clapeyron, temperature in kelvin, and with R as eight point three one four, delta vap H comes out in joules per mole. Now go and try the practice problems on this page. All the best!