LeChatelier's Principle, The Reaction Quotient, and the Equilibrium Constant
  Gary L. Bertrand         gbert@umr.edu
Professor Emeritus of Chemistry         University of Missouri-Rolla





Writing a chemical reaction with a double arrow

A + B  C + D
indicates that the reaction is continuously occurring in both directions on the molecular level.  On the macroscopic level, we can only see that either:

(1) there is a net increase in the amounts of the compounds on the right side, products, of the written reaction (with a necessary decrease in the amounts of the compounds on the left side, reactants, of the reaction.

This indicates that on the molecular level, the forward reaction (left-to-right) is occurring more rapidly than the reverse (right-to-left) reaction.


(2) there is a net increase in the amounts of the compounds on the left side, reactants, of the written reaction (with a necessary decrease in the amounts of the compounds on the right side, products, of the reaction.

This indicates that on the molecular level, the reverse (right-to-left) is occurring more rapidly than the forward (left-to-right) reaction.


(3) there is no change in the amounts of any of the compounds.

This indicates that on the molecular level, the forward reaction (left-to-right) and the reverse (right-to-left) reaction are occurring at the same rate.
If there is no change in the amounts of the compounds, we assume that the system is at equilibrium.


In 1884, Henri-Louis LeChatelier, a French industrial chemist, made the observation (first published in 1888):
"Any change in one of the variables that determines the state of a system in equilibrium causes a shift in the position of equilibrium in a direction that tends to counteract the change in the variable under consideration."
The variables that determine the state of a system in equilibrium are the concentrations of the reactants and products of chemical reactions, the temperature, and to a lesser extent the pressure.  The effect of pressure on an equilibrium involving gases can be confusing if it is not separated from the effects of concentration.


The effect of changing the temperature:

    Some chemical systems become hotter as they react in an insulated container while others become colder, and a some show very little change in temperature.  If the system becomes hotter as the written reaction occurs from left-to-right (the forward reaction), the reaction is said to be exothermic.  Conversely, if the system becomes colder as the forward reaction occurs, the reaction is said to be endothermic.  If the forward reaction is exothermic the reverse reaction will be endothermic, and if the forward reaction is endothermic the reverse reaction will be exothermic.  A reaction that produces no change in temperature in an insulated container is said to be athermal.

    We can apply LeChatelier's Principle to a temperature change on a system at equilibrium.  If we try to raise the temperature of this system, the position of equilibrium will shift in the direction that tends to counteract this change - the direction which tends to cool the system: the direction of the endothermic reaction.

Therefore if the reaction is exothermic as written, an increase in temperature will cause the reverse reaction to occur, decreasing the amounts of the products and increasing the amounts of reactants.  Lowering the temperature will produce the opposite response.

If the reaction is endothermic as written, an increase in temperature will cause the forward reaction to occur, increasing the amounts of the products and decreasing the amounts of reactants.  Lowering the temperature will produce the opposite response.

A change of temperature has no effect on an athermal reaction.
 

The effects of adding components:

To evaluate the effect of other changes to a system at equilibrium, we must pay careful attention to the physical states of the components, and to the numbers of each of the components in the balanced reaction.  Therefore, the written reaction must indicate the physical state of each component.

2 A(s)  B(g) + C(aq)

Changing the amount of one of the reaction components can affect the equilibrium only if the concentration of that component is changed.  The concentration of a component depends on the ratio of the amount of that component (moles) to the total amount of that phase (usually the volume of the phase, but other quantities such as the total number of moles or the mass of solvent in that phase may also be used).  Theaddition of a pure solid or a pure liquid does not usually change the concentration of that component, since both the number of moles of that component and the total amount of that phase are both changed by the same factor.
 

Therefore, the addition of a pure solid component to a system at constant pressure has no effect on the amounts of the other components.  However, the addition of a liquid which is a solvent for one of the phases may have a secondary effect by lowering the concentrations of all of the reaction components dissolved in that phase.  The addition of a substantial amount of liquid or solid to a container at constant volume may also have a secondary effect of compressing the gaseous phase, thus increasing the concentrations of all gaseous compounds.

We must also pay careful attention to the conditions (constant volume or constant pressure) when a compound is added.  The addition of a gaseous reaction component at constant volume necessarily leads to an increase in the concentration of that component, while the effect of that addition at constant pressure may depend on whether or not other gases are present.  The addition of a non-reacting gaseous component (such as an inert gas) at constant volume has no effect on the concentrations of other gaseous components, but that addition at constant pressure must increase the volume of the gas phase, lowering the concentrations of all other gases.

    We can apply LeChatelier's Principle to the addition of a reaction component to a system at equilibrium.   If the addition of that component causes an increase in the concentration of that component in its indicated phase, the system will try to counteract that change by reducing that increased concentration.  This can only occur through the chemical reaction, which will reduce the amounts of other components on the same side of the reaction, and increasing the amounts of the components on the opposite side of the reaction.

Therefore, an increase in the concentration of a reactant will lead to a decrease in the amounts of all reactants and an increase in the amounts of all products.

An increase in the concentration of a product will lead to a decrease in the amounts of all products and an increase in the amounts of all reactants.

In both cases, there will be a net increase in the total amount of the added component, but the increase will be less than the amount added.
 

The effect of changing the volume:

In considering volume changes, we must pay close attention to the phases that are affected by the change.  If there are aqueous, solid, and gas phases in a container,  changing the volume of the container only changes the volume of the gas phaseAdding water to the container obviously increases the volume of the aqueous phase, but the effect on the gas phase depends on whether the addition is at constant volume or constant pressure.  If the addition is at constant pressure the volume of the gas phase is not changed, but if the volume of the container is kept constant the volume of the gas phase decreases as the volume of the aqueous phase increases.  Addition of an immiscible liquid such as mercury has no effect at constant pressure, but decreases the volume of the gas phase if the volume of the container is constant.

Addition of an inert gas has no effect if the volume of the container is constant, but increases the volume of the gas phase if the pressure is constant.

Changing the volume of a phase changes the concentrations of all components in that phase, reactants and products.  The net effect is determined by the difference in the number of molecules of reactants and products (from the balanced reaction) in that phase.

If the balanced reaction shows the same number of moles of reactants and products in the phase being changed, there is no effect on the equilibrium.

If the balanced reaction shows more moles of products than reactants in the phase being changed, the effect on the products predominates.  Therefore, if the volume of that phase is increased the concentrations of products will be decreased more than the reactants, and the equilibrium will shift to increase the amounts of products and decrease the amounts of reactants.  A decrease in the volume of that phase would have the opposite effect.

The opposite situation, more moles of reactants than products in the phase being changed, results in an increase in the amounts of reactants if the volume of the phase is increased and a decrease in the amounts of reactants if the volume of the phase is increased.

There are some circumstances in which the effect of changing the volume of one phase is counteracted by the changes in another phase.  Analysis of this situation requires a more quantitative approach.  The quantitative approach - which also applies to all of the examples discussed above - is based on a quantity called The Reaction Quotient.

About the Reaction Quotient, Q