Stability of Complexes

Transcript

0:00Introduction

Hello everyone! Here is a small puzzle. Take a nickel ion holding six ammonia molecules, and add a ligand called e n. Each e n grabs the nickel through two nitrogen atoms, so three of them push out all six ammonias. But the bonds are nickel to nitrogen before, and nickel to nitrogen after. So why does this reaction go almost to completion? Today we measure stability with one number, and find out what makes a complex stable. This is a useful topic for JEE, so let's begin.

0:33Stepwise and overall stability constants

So, how do we measure stability? We build the complex one ligand at a time. Capital M is the metal ion, capital L is the ligand, and the two half arrows mean an equilibrium. Its constant is K one, with a small one below, and the square brackets mean concentration. So K one is the concentration of M L, over the concentrations of M and L multiplied, okay? Then a second L joins M L to give M L two. Its constant, K two, is the concentration of M L two over M L times L, and so on. These are the stepwise constants. Right? Now everything in one go: M plus n L gives M L n, where n is the number of ligands. Its constant is beta n, the Greek letter beta with a small n below: the concentration of M L n, over M times L to the power n, the small n up top. This is the overall stability constant. With me? So, how is beta n related to K one, K two, and so on? Do we add them, or multiply them? We multiply them, yes, exactly! Beta n is K one times K two, up to K n, and the three dots stand for the constants in between. Take the log, and the product becomes a sum: log beta n is the sum of log K i, where the big Greek sigma means add them all. Constants multiply, logs add. Clear?

2:03What beta tells us: instability constant and delta G

Now run it backwards: the complex falling apart, the overall dissociation. Its constant is one over beta n, called the instability constant. Okay? So, a large beta means a stable complex; the double arrow you see on screen means implies. Got it? And the link to energy: delta G naught, with the Greek capital delta meaning change and the small circle meaning standard, equals minus R T times l n beta n, the natural log. Here R is the gas constant and T is the temperature in kelvin. So a larger beta means a more negative delta G naught. Right?

2:42What makes a complex stable

Alright, so what makes a complex stable? As ligands go on one by one, does each new ligand bind more strongly, or less strongly, than the one before? It binds less strongly, that is correct! Usually K one is greater than K two, greater than K three, and so on, which is what the three dots mean. Why? Fewer free sites remain, and each new ligand meets a more crowded, less positive species. Okay? Second, the metal ion. Higher charge and smaller size, which means higher charge density, give a more stable complex. With me? Take cobalt with six ammonias: open square bracket, C o, N H three in brackets, six, close square bracket, charge three plus. It is far more stable than the same complex with charge two plus. Same ligands; only the cobalt changes, to a higher charge and a smaller ion. Right? Third, the ligand. More basic ligands, the better sigma donors, with sigma the Greek letter on screen, give more stable complexes. And pi acceptors, pi being the other Greek letter on screen, help metals in low oxidation states. Clear?

3:55The chelate effect

Fourth, the chelate effect. Polydentate ligands hold the metal through several donor atoms, forming rings. Such ring complexes are called chelates. They give more stable complexes than the equivalent number of monodentate ligands, with one donor each. Okay? Back to our puzzle. Here e n is ethane one two diamine, a bidentate ligand with two nitrogen donors. So N i, e n three, two plus, in square brackets, is much more stable than N i, N H three six, two plus, the ammonia complex. Right? Now our puzzle reaction: the ammonia complex plus three e n gives the e n complex plus six ammonias, the arrow pointing forward. Two arms means stronger bonds, you say? But the bonds are nickel to nitrogen on both sides! So what drives it? The answer is entropy, so count the particles. On the left, one complex and three e n, four particles. On the right, one complex and six ammonias, seven particles. So delta S, the entropy change, is greater than zero. The nickel to nitrogen bonds are similar, so delta H, the enthalpy change, is small, and delta G comes out less than zero. It is mainly entropy, not stronger bonds, and that solves our puzzle. With me? And five or six membered rings are the best, while macrocyclic ligands, large ring shaped ones, are more stable still. Got it?

5:28Trap: stable is not the same as inert

Now a classic trap. Beta measures thermodynamic stability: how far the equilibrium lies towards the complex. Okay? Kinetic lability is different: how fast the ligands are exchanged. Labile means fast, inert means slow. So, must a very stable complex be slow to exchange its ligands? No, and that is exactly the trap! These are different properties. Stable complexes can still be labile. Right? And our cobalt complex with three plus charge is inert: it exchanges ligands slowly. So stable is about beta, while inert or labile is about speed. Clear?

6:10Example 1: beta2 and log beta2 from K1 = 10^5, K2 = 10^3

Now, Example one from the course. For a complex M L two, K one is ten to the power five, and K two is ten to the power three. Find beta two, and log beta two. Pause the video and try it first. Done? Okay, let's check. Some students add the two constants: ten to the power five, plus ten to the power three. Is that right? No, no, careful, the overall constant is a product, not a sum. Beta two is K one times K two, ten to the power five times ten to the power three. Add the powers, and beta two is ten to the power eight. Okay? And log beta two is log K one plus log K two: five plus three gives eight. Constants multiply, logs add. Clear?

6:59Example 2: log beta4 from four log K values, why they fall

Now a harder one, Example two. The stepwise constants for a four step complexation are given as logs. Log K one is four point zero, and log K two is three point two. Log K three is two point seven, and log K four is two point zero. Find log beta four, and explain why the values fall. Pause the video and try it first. Done? Okay, let's check. We are given logs, not the constants. So do we multiply them, or add them? We add them, exactly, because the constants multiply. Log beta four is log K one, plus log K two, plus log K three, plus log K four. Right? Four point zero plus three point two gives seven point two. Adding two point seven, we get nine point nine. Adding two point zero, log beta four is eleven point nine. With me? Now the second part. Four, then three point two, then two point seven, then two. Why do the values keep falling? It is our very first factor, very good! Each step leaves fewer free sites, and the next ligand meets a more crowded, less positive species. So the falling values are exactly what we expect. Got it?

8:19Quick revision: beta, stability factors, chelate, inert

So, quick revision. Beta n is the product of the stepwise constants: constants multiply, logs add, and a large beta means stable. Stability rises with charge density, basic ligands and the chelate effect. The chelate effect is mainly entropy, and stable is not the same as inert. Now try the practice problems on this page. All the best!