The Reaction Quotient, and What K Tells Us

Transcript

0:00Introduction

Hello everyone! Okay, one small puzzle before we start. Take a mixture of hydrogen and oxygen gas at room temperature, two hundred and ninety eight kelvin. For making water, the equilibrium constant K is about ten to the power eighty. That is a one followed by eighty zeros! So it should turn into water, right? But it just sits there. Why? By the end of this class, you will answer it yourself. In JEE, comparing the reaction quotient with K comes up often. So, let's begin.

0:36The reaction quotient Q

So, remember: K is built from the concentrations at equilibrium. But a flask you have just mixed is usually not at equilibrium yet. So how do we know which way it will go? We use a twin of K, okay? Meet capital Q, the reaction quotient. Same form as K: the same products on top, the same reactants below, the same powers. Only one difference. Q uses the concentrations, or pressures, at any instant, not necessarily at equilibrium. It tells you where the mixture stands now. Clear? Now tell me. Suppose Q is smaller than K, okay? Which way must the reaction go? Forward, yes, exactly! That sign on screen is the less than sign. Q smaller means too little product compared with equilibrium, so more product forms, and Q climbs up towards K: the reaction proceeds forward. And when Q is greater than K, the greater than sign, there is too much product, so the reaction proceeds backward, and Q comes down. See, Q always moves towards K; that is the whole trick. Right? And when Q equals K, nothing is left to change: the system is at equilibrium. Got it? But one careful point. K is fixed only at a given temperature. So compare Q with the K at that same temperature, written for the same balanced equation. With me?

2:06What the size of K tells us

Now the second big idea: what the size of K tells us. When K is greater than ten to the power three, more than a thousand, the mixture at equilibrium is mostly products. Okay? When K is less than ten to the power minus three, one over a thousand, it is mostly reactants. Right? And in between, you get appreciable amounts of both. Clear? Now, back to our puzzle. Two hydrogen plus oxygen gives two water; the two half arrows mean a reversible reaction. At two hundred and ninety eight kelvin, K is about ten to the power eighty; the wavy sign means about. So at equilibrium it is almost all water. Then why does the mixture just sit there? Because K gives the position, not the rate! It tells you where the reaction ends up, not how fast it gets there. Without a spark, this reaction is far too slow at room temperature. Huge K does not mean fast. Don't fall for that trap. Got it? And the opposite case. Nitrogen plus oxygen gives two N O, nitric oxide, with K about ten to the power minus thirty. Tiny! So almost no nitric oxide exists at equilibrium, and air is thermodynamically stable. With me?

3:20Links with rates and with ΔG

So K is about position. Now let's link it with rates. Take an elementary reversible reaction, a single step: at equilibrium, the rate forward equals the rate backward. Okay? And that gives K equals k f over k b. Small k with a small f below is the forward rate constant; small k with a small b below is the backward one. Remember, this is for an elementary reaction. Right? Now thermodynamics. The triangle is capital delta, meaning change; G is the Gibbs energy; the small circle on top, read nought, means standard. Delta G nought equals minus R T l n K, or minus two point three zero three R T log K, okay? R is the gas constant, T the temperature in kelvin; l n is the natural log, and log is to base ten. So, if K is more than one, the log is positive, and with the minus sign, delta G nought is negative. The double arrow means each gives the other. And delta G nought equal to zero goes with K equal to one. Clear? Now take a mixture at any instant. Delta G, without the nought, equals delta G nought plus R T l n Q, for the mixture as it is now. Put in minus R T l n K for delta G nought, and it becomes R T l n of Q over K, got it? Now see the beauty. If Q is less than K, then Q over K is less than one. So what is the sign of delta G? Negative! The log of a number below one is negative. So delta G is less than zero exactly when Q is less than K: the forward change is spontaneous. Same answer as our Q rule, by a completely different road!

5:00Example 1: which way will H2, I2 and HI react?

Alright, example one, from the course. Hydrogen plus iodine gives two H I, hydrogen iodide. K c, capital K with a small c below, is fifty seven at seven hundred kelvin. Hydrogen is zero point one zero, iodine zero point two zero, and hydrogen iodide zero point five zero molar; the square brackets mean concentration, and capital M means moles per litre. Which way will it react? Pause the video and try it first. Done? Okay, let's check. Q has the same form as K c: the concentration of H I, squared, over hydrogen times iodine. Squared because of the two in front of H I, okay? Now the numbers. Zero point five zero squared is zero point two five; zero point one zero times zero point two zero is zero point zero two zero. So Q equals twelve point five. Right? Q is twelve point five, K c is fifty seven. So, which way? Forward, yes, exactly! Q is less than K c, so the reaction proceeds forward, forming more hydrogen iodide. That's it!

6:10Example 2: is the SO2, O2, SO3 mixture at equilibrium?

Now a harder one. Two S O two plus O two gives two S O three, and K c is eighty litres per mole; on screen, L mol to the power minus one. We have zero point five zero molar S O two, zero point one zero molar oxygen, and one point five molar S O three. Is it at equilibrium? Pause the video and try it. Done? Okay, let's check. Some students write one point five, over zero point five zero times zero point one zero. That gives thirty, less than eighty, so forward, right? No, no, careful! This is the trap. Q has the same form as K, so every coefficient becomes a power: S O three squared, over S O two squared, times O two. Okay? Now the numbers. One point five squared is two point two five. Zero point five zero squared is zero point two five, times zero point one zero gives zero point zero two five. So Q equals ninety. With me? So, ninety against eighty. Is it at equilibrium, and if not, which way will it go? Not at equilibrium! Q is greater than K c, so it shifts backward. See? The trap gave exactly the wrong direction. Write the powers, always. And the delta G check. Q over K is more than one, so delta G for the forward change is positive; forward is not spontaneous here. Both roads agree. Got it?

7:39Quick revision: Q vs K, size of K, and ΔG

So, quick revision. Q less than K, forward; Q greater than K, backward; Q equal to K, at equilibrium, at the same temperature. K above ten to the power three, mostly products; below ten to the power minus three, mostly reactants; and K gives the position, not the rate. Delta G nought equals minus R T l n K, and delta G equals R T l n of Q over K, okay? Now go and try the practice problems on this page. All the best!