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Chemical Equilibrium Definitions

Le Chatelier’s
Rule · The Equilibrium Constant · The Reaction Quotient · Temperature
Dependence · Mole
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There is a rule called * Le Chatelier’s Rule* that says that, once a
reaction reaches

For a general *elementary* chemical reaction,

The concentrations of the reactants and products are related to each other according to

The number K_{c} is called the * equilibrium constant*,
and is a function of temperature only (i.e., its numerical value doesn’t change
unless the temperature changes – we’ll hold the temperature constant for now).
Note the word

the equilibrium constant is defined

Notice that the units of K_{c} in this case are M^{-1}=
L/mol.

There is another useful definition of the equilibrium constant based on pressure rather than concentration. The ideal gas law reads

Here P is the total pressure. In the case of several components, each has a partial pressure, all of which sum up to the total pressure:

For each component, we can write the ideal gas law (putting a subscript where applicable)

This works for the other components, too, and gives us the
relation between the concentrations and the partial pressures. If we plug in the partial
pressures in the definition of K_{c} above, we get

In the more general case where the reaction is

And K_{c} is

Then the new equilibrium constant becomes

Where

Is the change in number of moles in the gas phase. These numbers come from the balanced equation and are basically the sum of the stoichiometric coefficients of the products minus the sum of the stoichiometric coefficients of the reactants.

Problems using K_{P} instead of K_{c} are solved
the same way, except we are looking for the partial pressures P_{X} instead of the
concentrations [X], X = A, B, C, etc. is particularly useful for gas phase problems since
the pressure is usually more convenient to measure than the concentration. Also, there is
a direct relationship between K_{P} and the Gibbs energy of the reaction, DG^{0}_{rxn} .

Before getting into more complicated types of equilibrium problems, it’s a good
idea to look a bit more closely at why a reaction goes forward or backward. This is just a
more mathematical way of looking at Le Chatelier’s rule. Suppose our reaction is * not*
at equilibrium. We can still calculate the ratio of products to reactants, we just
won’t get the equilibrium constant. This number is Q

For the example reaction we have been considering,

The reaction quotient is defined as

Please remember that we put "0" subscripts on our
initial amounts of components to emphasize that they are *not equilibrium concentrations*.

Here’s how Q_{c} should be used:

There is an equivalent notion with respect to pressure:

That works the same way

The Gibbs Free Energy of Reaction is related to the equilibrium constant K_{P}
by the relation

It should be noted that this equation is approximate and good for gases only. The relation between two equilibrium conditions at two temperatures is given by the Van’t Hoff equation (also approximate)

Where the K’s can be either K_{P} or K_{c}
‘s.

The mole fraction of a component X is the moles of X divided by the total number of moles:

By the ideal gas law,

And so substituting for each component yields

A similar relation holds for the other components, and it should be easy to prove (for our three-component system) that

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