The Law of Mass Action and K_c

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle before we start. Two students run the same reaction, hydrogen plus iodine giving hydrogen iodide, in sealed flasks at the same temperature. One starts with a little hydrogen, the other with a lot. At equilibrium, their concentrations are completely different. And yet, one number comes out exactly the same in both flasks. Which number? Keep thinking; by the end of this class, you will calculate it yourself. And look, this idea comes up often in JEE equilibrium questions. So, let's begin.

0:38The law of mass action

So, take a general reaction. Small a moles of capital A, plus small b moles of capital B, give small c moles of capital C, plus small d moles of capital D, okay? See the two half arrows in the middle, one pointing each way? That sign means the reaction is reversible, and here it has reached equilibrium. With me? Now, two scientists, Guldberg and Waage, found one number that describes this equilibrium. It is a fraction. So tell me, which side goes on top, the reactants or the products? The products, yes, exactly! K c, capital K with a small c below for concentration, equals the concentration of C to the power small c, times the concentration of D to the power small d, over the concentration of A to the power small a, times the concentration of B to the power small b. So each concentration is raised to its coefficient from the balanced equation. Clear? And these square brackets mean the molar concentration at equilibrium, in moles per litre; the minus one up on the litre means per litre. Not the starting amounts, and not the moles: equilibrium concentrations. Okay? Now the beautiful part. At a given temperature, K c is a constant, whatever amounts you start with. Remember our two flasks? Different starting amounts, different concentrations, but the same temperature. So the same K c! That is our number. And this is the law of mass action. Got it?

2:06Writing Kc: what goes in, what stays out

Alright, let's write one from the course. Nitrogen plus three hydrogen gives two ammonia. The small g in brackets means gas, and the little two below in N two is a subscript, two atoms. Now you write K c for it. Done? Ammonia on top, squared, because its coefficient is two. Below: nitrogen, times hydrogen cubed, because of the three. That's it! Right? Next, the things we leave out. Pure solids and pure liquids. Their concentration, more correctly their activity, stays constant, so we take it as one. Okay? For example, solid calcium carbonate, the small s means solid, breaks into solid calcium oxide and carbon dioxide gas. Both solids drop out, so K c is just the concentration of C O two. Simple! Clear? And water as the solvent, in a dilute aqueous solution, is left out too. With me? So, water is always left out of K c, right? No, no, careful! Only water as the solvent. If the water is a gas, steam, it stays in K c. And if water is a product mixed with other liquids, like an acid and an alcohol giving an ester and water, it is not the solvent and not a pure liquid, so it stays in too. Got it?

3:22K depends only on temperature

Now, a question many students get wrong. Go back to our flasks of hydrogen and iodine. If I pump more hydrogen into one flask, the concentrations change. So K c changes too, right? No! The concentrations readjust, but K c stays exactly the same. K changes only with temperature, okay? Not with concentration, not with pressure, not with volume, and not with a catalyst. Only a change of temperature can change K, nothing else. Remember this one, it is a common trap. Clear?

3:56Units of Kc from delta n

Next, units. The units of K c are moles per litre, to the power delta n. The little triangle up there is the capital Greek letter delta, okay? Delta n is the change in the number of moles: moles of products minus moles of reactants, counting gases or solutes. Right? Let's try our ammonia reaction again: one nitrogen plus three hydrogen gives two ammonia. What is delta n? Two minus four: minus two, yes! So the units are moles per litre to the power minus two, which is litre squared per mole squared. Careful with the sign: a negative delta n turns the units upside down. Clear? One honest note. Strictly, K is written with activities and has no units at all. But JEE questions often quote units anyway, so know both. Okay?

4:49Example 1: Kc for H2 + I2 to 2HI from concentrations

Now, example one, from the course. Hydrogen gas plus iodine gas gives two H I, hydrogen iodide. At equilibrium, hydrogen is zero point one zero molar, iodine is zero point two zero molar, and hydrogen iodide is zero point eight zero molar; the capital M on screen means molar, moles per litre. Find K c. Pause the video and try it first. Done? Okay, let's check. Product on top: hydrogen iodide, squared, because its coefficient is two. Below: hydrogen times iodine, each to the power one. With me? Now the numbers. Zero point eight zero squared is zero point six four. Zero point one zero times zero point two zero is zero point zero two. Zero point six four over zero point zero two: thirty two! And this is our puzzle reaction. At this temperature, whatever the starting amounts, the equilibrium mixture gives this same K c. Now, what are the units of this K c? None at all! Delta n is two minus two, zero, and anything to the power zero is one. So K c is just thirty two, a pure number. Right?

6:04Example 2: Kc for PCl5 from moles in a 2 L flask

Now a slightly harder one, also from the course. At equilibrium, a two litre flask, capital L for litre, contains zero point four zero moles of phosphorus pentachloride, P C l five, zero point two zero moles of phosphorus trichloride, P C l three, and zero point two zero moles of chlorine. Find K c for phosphorus pentachloride going to phosphorus trichloride plus chlorine. Pause the video and try it. Done? Alright, let's check. Many students put the moles straight in: zero point two times zero point two, over zero point four. That gives zero point one. So K c is zero point one, right? No, no, wait! This is the trap. Square brackets mean concentrations, moles per litre, and the flask is two litres. So divide each amount by two. Phosphorus pentachloride: zero point four over two, zero point two zero molar. Phosphorus trichloride and chlorine: zero point two over two, zero point one zero molar each. Okay? Now the expression: products on top, phosphorus trichloride times chlorine, over phosphorus pentachloride. So, zero point one zero times zero point one zero, over zero point two zero. With me? Zero point zero one over zero point two: zero point zero five. And delta n is two minus one, plus one, so the units are moles per litre. K c equals zero point zero five moles per litre. So why did the trap fail? Moles straight in gave zero point one, and that is wrong, because delta n is not equal to zero; that is what this crossed equals sign means. The volume does not cancel here. So always convert to concentrations first. Got it?

7:57Quick revision: writing Kc, what stays out, units

So, quick revision. K c is products over reactants, at equilibrium, each concentration raised to the power of its coefficient. Leave out pure solids, pure liquids, and water as the solvent. And K changes only with temperature; its units are moles per litre, to the power delta n. Now go and try the practice problems on this page. Convert to concentrations first, and you will find them easy. All the best!