Calculate the Kc Value for the a -protein Binding Reaction

Calculate the Kc Value for the a -protein Binding Reaction



This folio explains what is meant by a stability constant for a complex ion, and goes on to expect at how its size is governed in part by the entropy modify during a ligand substitution reaction.

Notation:If you aren’t happy about what a ligand exchange reaction is, it would exist useful to have a quick await at this link before you become on. There is no demand to worry nigh the item, but yous should read enough to go a experience for what nosotros are talking nigh.


What is a stability abiding?

Replacing water by ammonia around copper(II) ions

If you add together ammonia solution to a solution containing hexaaquacopper(II) ions, [Cu(HiiO)6]2+, four of the water molecules are somewhen replaced by ammonia molecules to give [Cu(NHthree)4(HtwoO)ii]2+.

This can be written as an equilibrium reaction to show the overall upshot:

In fact, the water molecules get replaced one at a time, and then this is made up of a serial of part-reactions:

Although this can wait a bit daunting at starting time sight, all that is happening is that first y’all accept one, then two, then three, and so four water molecules in total replaced by ammonias.

Individual stability constants

Let’s have a closer look at the get-go of these equilibria:

Like any other equilibrium, this one has an equilibrium constant, Kc
– except that in this case, we call it a

stability constant
. Considering this is the first water molecule to exist replaced, we call it K1.

Warning!If you aren’t happy about how to write expressions for equilibrium constants, it is
to follow this link earlier yous go any further.

Use the BACK push button on your browser to return quickly to this page.

Here is the equation again:

is given by this expression:

In that location are two points of possible confusion here – one small, one more important!

  • First, the square brackets take inverse their meaning! Square brackets are often used to keep everything in a complex ion together and tidy. Hither, they have reverted to their other apply, which implies concentrations in mol dm-3.

    In order to avoid consummate confusion, the foursquare brackets keeping the complexes together have been removed entirely.

  • More importantly, if you compare the equilibrium constant expression with the equation, you volition see that the water on the correct-hand side hasn’t been included. That is normal practice with these expressions.

    Because everything is dissolved in water, the water is present as a huge excess. Generating a little bit more during the reaction is going to make no constructive difference to the total concentration of the water in terms of moles of water per dm3.

    The concentration of the water is approximately abiding. The equilibrium abiding is divers and so that you avert having an extra unnecessary constant in the expression.

With that out of the way, let’s go dorsum to where nosotros were – but innovate a value for Gane:

The value of the equilibrium abiding is fairly large, suggesting that there is a stiff tendency to form the ion containing an ammonia molecule.

A high value of a stability constant shows that the ion is easily formed.

Each of the other equilibria above besides has its ain stability constant, One thousand2, 1000iii
and Thousand4. For instance, K2
is given by:

The ion with two ammonias is fifty-fifty more stable than the ion with one ammonia.

Yous could keep plugging away at this and come with the post-obit table of stability constants:

ion Kn
value (mol-i
log Kn
1.78 x teniv
4.07 x 10three
9.55 x 102
1.74 10 ten2

You will often find these values quoted as log Ki
or whatever. All this does is tidy the numbers up then that you tin can see the patterns more easily.

The ions proceed on getting more stable equally yous replace up to 4 water molecules, just notice that the equilibrium constants are gradually getting less big as yous supervene upon more and more waters. This is common with individual stability constants.

Overall stability constants

The overall stability abiding is simply the equilibrium constant for the total reaction:

Information technology is given by this expression:

You can see that overall this is a very large equilibrium abiding, implying a high tendency for the ammonias to replace the waters. The “log” value is 13.1.

This overall value is establish by multiplying together all the individual values of Ki, K2
and then on. To find out why that works, you volition need a big bit of paper and some patience!

Write downwardly expressions for all the individual values (the kickoff 2 are done for you above), and then multiply those expressions together. Yous will find that all the terms for the intermediate ions cancel out to get out you with the expression for the overall stability constant.



Whether you are looking at the replacement of private water molecules or an overall reaction producing the final complex ion, a stability constant is only the equilibrium abiding for the reaction you are looking at.

The larger the value of the stability constant, the farther the reaction lies to the correct. That implies that complex ions with large stability constants are more stable than ones with smaller ones.

Stability constants tend to be very large numbers. In order to simplify the numbers a “log” scale is often used. Because of the way this works, a difference of ane in the log value comes from a 10 times deviation in the stability abiding. A departure of 2 comes from a 100 (in other words, 102) times difference in stability abiding – and so on.


Stability constants and entropy – the chelate effect

What is the chelate event?

This is an consequence which happens when you supervene upon water (or other simple ligands) around the central metal ion past multidentate ligands like 1,ii-diaminoethane (often abbreviated to “en”) or EDTA.

Important!If words similar
multidentate ligand
don’t hateful anything to you, then it is
that you read the introductory page on circuitous ions. The second half of that page deals with multidentate ligands.

Apply the Dorsum push button on your browser to return apace to this page.

Compare what happens if yous replace two h2o molecules effectually a [Cu(H2O)6]2+
ion with either 2 ammonia molecules or 1 molecule of 1,2-diaminoethane.

This second structure is known as a


from a Greek give-and-take meaning a crab’south claw. You lot can picture the copper ion as being nipped by the claw of the one,2-diaminoethane molecule.

Chelates are much more stable than complex ions formed from simple monodentate ligands. The overall stability constants for the two ions are:

ion log K

The reaction with the 1,2-diaminoethane could eventually keep to produce a complex ion [Cu(en)three]2+. Simplifying the structure of this:

The overall stability constant for this (as log M) is

Another copper-based chelate comes from the reaction with EDTA.

This too has a loftier stability constant – log K is 18.viii.

Nonetheless many examples y’all take, y’all ever find that a chelate (a complex ion involving multidentate ligands) is more stable than ions with only unidentate ligands. This is known equally the

chelate result


The reason for the chelate effect

If you compare the 2 equilibria below, the one with the one,2-diaminoethane (“en”) has the college equilibrium (stability) constant (for values, meet to a higher place).

The enthalpy changes of the two reactions are fairly similar. Yous might look this because in each case yous are breaking two bonds between copper and oxygen atoms and replacing them by two bonds between copper and nitrogen atoms.

Note:This is an over-simplification. You have to consider interactions between the various species and water molecules (from the solvent) as well.

If the enthalpy changes are similar, what causes the difference in the extent to which the two reactions happen?

You demand to think virtually the

entropy change

during each reaction.

Entropy is most easily thought of as a measure of disorder. Whatsoever change which increases the amount of disorder increases the trend of a reaction to happen.

Note:If you want a more formal approach to entropy, I’m afraid y’all will accept to look elsewhere. You will notice a gentle introduction to the mathematical side of entropy in my chemistry calculations book.

If you lot look again at the two equililbria, you might notice that the 1,2-diaminoethane equilibrium does lead to an increment in the disorder of the arrangement (an increase in its entropy). There are merely two species on the left-paw side of the equation, only iii on the right.

Yous can obviously get more disorder out of iii species than out of just two.

Compare that with the other equilibrium. In this case, there is no change in the total number of species before and afterwards reaction, and and so no useful contribution to an increase in entropy.

In the case of the complex with EDTA, the increment in entropy is very pronounced.

Here, we are increasing the number of species nowadays from two on the left-hand side to seven on the right. You can get a major amount of increment in disorder by making this change.

Reversing this concluding change is going to be far more than difficult in entropy terms. You lot would have to move from a highly disordered land to a much more ordered one. That isn’t so likely to happen, and so the copper-EDTA complex is very stable.



Complexes involving multidentate ligands are more stable than those with only unidentate ligands in them.

The underlying reason for this is that each multidentate ligand displaces more than one h2o molecule. This leads to an increase in the number of species nowadays in the system, and therefore an increment in entropy.

An increment in entropy makes the formation of the chelated complex more favourable.


Questions to exam your agreement

If this is the showtime ready of questions yous have done, please read the introductory page before you first. Y’all will need to use the BACK Button on your browser to come back hither later on.

questions on stability constants



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© Jim Clark 2003 (last modified Jan 2015)

Calculate the Kc Value for the a -protein Binding Reaction


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