EQUILIBRIUM CONSTANTS: Kc

This page explains what is meant by an equilibrium constant,introducing equilibrium constants expressed in terms ofconcentrations, Kc. It assumes that you are familiar with theconcept of a dynamic equilibrium, and know what is meant by theterms "homogeneous" and "heterogeneous" as applied tochemical reactions.

Important: If you aren't sure about dynamic equilibria it isimportant that you follow this link before you go on.

If you aren't sure what homogeneous and heterogeneousmean, you would find it useful to follow this link and read thebeginning of the page that you will find (actually on catalysis).

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

We need to look at two different types of equilibria (homogeneousand heterogeneous) separately, because the equilibrium constantsare defined differently.

A homogeneous equilibrium has everything present in thesame phase. The usual examples include reactions whereeverything is a gas, or everything is present in the samesolution.

A heterogeneous equilibrium has things present in morethan one phase. The usual examples include reactionsinvolving solids and gases, or solids and liquids.

Kc in homogeneous equilibria

This is the more straightforward case. It applies where everythingin the equilibrium mixture is present as a gas, or everything ispresent in the same solution.

A good example of a gaseous homogeneous equilibrium is theconversion of sulphur dioxide to sulphur trioxide at the heart of theContact Process:

A commonly used liquid example is the esterification reactionbetween an organic acid and an alcohol - for example:

Writing an expression for Kc

We are going to look at a general case with the equation:

No state symbols have been given, but they will be all (g), or all (l),or all (aq) if the reaction was between substances in solution inwater.

If you allow this reaction to reach equilibrium and then measure theequilibrium concentrations of everything, you can combine theseconcentrations into an expression known as an equilibriumconstant.

The equilibrium constant always has the same value (provided you

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don't change the temperature), irrespective of the amounts of A, B,C and D you started with. It is also unaffected by a change inpressure or whether or not you are using a catalyst.

Compare this with the chemical equation for the equilibrium. Theconvention is that the substances on the right-hand side of theequation are written at the top of the Kc expression, and those onthe left-hand side at the bottom.

The indices (the powers that you have to raise the concentrationsto - for example, squared or cubed or whatever) are just thenumbers that appear in the equation.

Note: If you have come across orders of reaction, don'tconfuse this with the powers that appear in the rate equationfor a reaction. Those powers (the order of the reaction withrespect to each of the reactants) are experimentallydetermined. They don't have any direct connection with thenumbers that appear in the equation

You may come across attempts to derive the expression forKc by writing rate equations for the forward and backreactions. Except in a very limited number of very simpleexamples, this can't be done! These attempts make thefundamental mistake of obtaining the rate equation from thechemical equation. That's WRONG! Deriving an expressionfor Kc is impossible at this level of chemistry.

It isn't relevant to this page, but if you want to find out moreabout orders of reaction, you might like to follow this link atsome time in the future.

Some specific examples

The esterification reaction equilibrium

A typical equation might be:

There is only one molecule of everything shown in the equation.That means that all the powers in the equilibrium constantexpression are "1". You don't need to write those into the Kcexpression.

As long as you keep the temperature the same, whateverproportions of acid and alcohol you mix together, once equilibriumis reached, Kc always has the same value. At room temperature,this value is approximately 4 for this reaction.

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The equilibrium in the hydrolysis of esters

This is the reverse of the last reaction:

The Kc expression is:

If you compare this with the previous example, you will see that allthat has happened is that the expression has turned upside-down.Its value at room temperature will be approximately 1/4 (0.25).

It is really important to write down the equilibrium reactionwhenever you talk about an equilibrium constant. That is the onlyway that you can be sure that you have got the expression the rightway up - with the right-hand substances on the top and the left-hand ones at the bottom.

The Contact Process equilibrium

You will remember that the equation for this is:

This time the Kc expression will include some visible powers:

Although everything is present as a gas, you still measureconcentrations in mol dm-3. There is another equilibrium constantcalled Kp which is more frequently used for gases. You will find alink to that at the bottom of the page.

The Haber Process equilibrium

The equation for this is:

. . . and the Kc expression is:

Kc in heterogeneous equilibria

Typical examples of a heterogeneous equilibrium include:

The equilibrium established if steam is in contact with red hotcarbon. Here we have gases in contact with a solid.

If you shake copper with silver nitrate solution, you get thisequilibrium involving solids and aqueous ions:

Writing an expression for Kc for a heterogeneousequilibrium

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The important difference this time is that you don't include anyterm for a solid in the equilibrium expression.

Taking another look at the two examples above, and adding a thirdone:

The equilibrium produced on heating carbon with steam

Everything is exactly the same as before in the equilibriumconstant expression, except that you leave out the solid carbon.

The equilibrium produced between copper and silver ions

Both the copper on the left-hand side and the silver on the right aresolids. Both are left out of the equilibrium constant expression.

The equilibrium produced on heating calcium carbonate

This equilibrium is only established if the calcium carbonate isheated in a closed system, preventing the carbon dioxide fromescaping.

The only thing in this equilibrium which isn't a solid is the carbondioxide. That is all that is left in the equilibrium constantexpression.

Calculations involving Kc

There are all sorts of calculations you might be expected to dowhich are centred around equilibrium constants. You might beexpected to calculate a value for Kc including its units (which varyfrom case to case). Alternatively you might have to calculateequilibrium concentrations from a given value of Kc and givenstarting concentrations.

This is simply too huge a topic to be able to deal with satisfactorilyon the internet. It isn't the best medium for learning how to dochemistry calculations. It is much easier to do this from a carefullystructured book giving you lots of worked examples and lots ofproblems to try yourself.

If you have found this site useful, you might like to have a look at mybook on chemistry calculations. It covers equilibrium constantcalculations starting with the most trivial cases, and graduallygetting harder - up to the moderately difficult examples which maybe asked in a UK A' level examination.

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Note: If you are interested in my chemistry calculationsbook you might like to follow this link.

Questions to test your understanding

If this is the first set of questions you have done, please read theintroductory page before you start. You will need to use the BACK BUTTONon your browser to come back here afterwards.

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© Jim Clark 2002 (modified May 2013)

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