Manipulating Equilibrium Constants

Transcript

0:00Introduction

Hello everyone! Okay, a small puzzle before we start. Three students study the same ammonia equilibrium, in the same flask, at the same temperature. Each one writes the equation in a different way. The first gets K c equal to zero point five zero. The second gets two. The third gets zero point seven zero seven. Three different numbers for one equilibrium! So, who made the mistake? Hold that thought. By the end of this class, you will find these numbers yourself. And look, questions where you flip, scale or combine reactions come up often in JEE exams. So, let's begin.

0:39Rule 1: reverse the reaction, flip K

So, start with the reaction from our puzzle. Nitrogen, N two, plus three hydrogen, H two, gives two ammonia, N H three; the small numbers below count the atoms. The two half arrows mean the reaction is reversible, okay? And from the law of mass action, K equals the concentration of ammonia squared, over nitrogen times hydrogen cubed. The square brackets mean concentrations at equilibrium. Right? Now, I write the same reaction backwards. What happens to this fraction? Yes, exactly! It turns upside down. Two ammonia gives nitrogen plus three hydrogen. Now ammonia is the reactant, so it goes below. We call the new constant K prime; the little dash just means a new constant. K prime equals nitrogen times hydrogen cubed, over ammonia squared. With me? So here is rule one. Reverse the reaction, and K prime equals one over K, as simple as that. Just flip it. Clear? And the units flip too. For the forward reaction, K c is in litre squared per mole squared; capital L is litre, and the minus two up on the mole means per mole squared. The arrow means becomes: flip the constant, and the units become mole squared per litre squared. Okay?

1:59Rule 2: multiply by n, raise K to the power n

Next, rule two. Multiply every coefficient in the equation by some number n. Then K prime equals K to the power n; that small n up top is the power. Why? Each concentration is raised to its coefficient, right? Multiply every coefficient by n, and every power gets multiplied by n, so the whole fraction goes to the power n. Okay? Now tell me. If I double every coefficient, does K also double? No, no, careful! This is the trap. Here n is two, so K prime equals K squared, not two K, okay? Many students write two K in a hurry. Don't do that! Got it? And if we halve every coefficient? Then n is one half, the small fraction in the brackets. So K prime equals K to the power half, which is the square root of K; see the root sign. Halve the equation, take the square root. Remember this one. Right?

2:54Rule 3: add or subtract reactions

Now, rule three. Suppose reaction one has constant K one, and reaction two has constant K two. I add the two reactions to get a new reaction. So I add K one and K two too, right? No! We multiply them. K equals K one times K two; K one is capital K with a small one below, the constant of reaction one. Why multiply? When you multiply the two fractions, anything made in one reaction and used up in the other cancels out, just as it cancels in the equations. Okay? And reaction one minus reaction two? Subtracting reaction two is just adding its reverse. The reverse has constant one over K two, so K equals K one over K two. Subtract the reactions, divide the constants. Clear? Whenever you change the equation, the units of K change accordingly, so work them out again for the new equation. With me? But here is the key point. The position of equilibrium does not change. Same flask, same temperature, same mixture; only the way we wrote the equation changed. So maybe our three students made no mistake at all! We will check in example one. Right?

4:04Topper's trick: build the target reaction

Now let me share a trick that toppers use. Step one: write the target reaction, the one the question asks about, and compare it with the reactions you are given. Okay? Step two: is a species on the wrong side? Reverse that reaction, and flip its constant. The coefficients do not match? Multiply the reaction by n, and raise its constant to the power n. Right? Step three: add the pieces, cancel whatever appears on both sides, and multiply all the constants. Three steps, and the question is done. Got it?

4:37Example 1: K for reversed and halved ammonia equations

Now, example one, from the course. For nitrogen plus three hydrogen giving two ammonia, K c is zero point five zero, in litre squared per mole squared, at some temperature. Find K c for: part a, two ammonia giving nitrogen plus three hydrogen; part b, half nitrogen plus three halves hydrogen giving one ammonia; and part c, one ammonia giving half nitrogen plus three halves hydrogen. Pause the video and try it first. Done? Okay, let's check. Part a is the original reaction, written backwards. So, rule one: flip it. One over zero point five zero is two point zero. Easy one. With me? Now part b. Every coefficient is halved. Halve the equation, so halve K c: zero point five zero over two, zero point two five, right? No, no, wait! Halving the equation means the power one half. So K c equals the square root of zero point five zero: zero point seven zero seven. Clear? And part c? Look closely: it is part b, written backwards. So flip it: one over zero point seven zero seven is one point four one. Now, remember our three students? Zero point five zero, two, and zero point seven zero seven. All three were right! Same flask, same mixture, just different ways of writing the equation.

6:06Example 2: combine K1 and K2 for N2, O2 and NO2

Got it? Now a harder one, also from the course. Nitrogen plus oxygen gives two N O, nitric oxide, with constant K one. Two N O plus oxygen gives two N O two, nitrogen dioxide, with constant K two. Find the constants for: part a, nitrogen plus two oxygen giving two N O two; and part b, one N O two giving half nitrogen plus one oxygen. Pause the video and try it. Use the topper's trick! Done? Okay, let's check. Part a. Add the two given reactions. Two N O is made in the first and used up in the second, so it cancels. What is left? Nitrogen plus two oxygen gives two N O two. Exactly our target! With me? So we added the reactions. What do we do with K one and K two? Multiply them, yes! K equals K one times K two. Not plus: times. Right? Now part b. Look: N O two is on the left now, so start by reversing part a. Two N O two gives nitrogen plus two oxygen, and its constant is one over K one K two. Okay? But the target has only one N O two, not two. So what is the last step? Halve it, exactly! Halving means the square root. So K equals one over the square root of K one K two, which is the same as K one K two to the power minus one half; that is the minus half up top. Reversed, then halved: two rules in one answer. See how neat that is?

7:40Quick revision: reverse, multiply, add and subtract

So, quick revision. Reverse the reaction: one over K, and multiply the coefficients by n: K to the power n; halving means the square root. Add reactions: multiply the constants; subtract: divide them. And the units change, but the position of equilibrium does not. Now go and try the practice problems on this page. Build the target reaction step by step, and you will find them easy. All the best!