# Equilibrium

Dynamic equilibrium occurs when two opposing processes take place at equal rates and there are no net change in composition. Thus the rate Forward is equal to the rate Reverse. And the amounts of product equals amounts of reactant in both forward and reverse reactions.

### Types of Equilibrium

Chemical Equilibrium Physical Equilibrium
Chemical equilibrium occurs when reaction changes chemically such as in decomposition Dynamic equilibrium when rates of forward and reverse reactions are equal
Example of Decomposition: When gaseous phosphorus pentachloride is heated, it decomposes to phosphorus trichloride and chlorine gas: PCl5(g)=> PCl3(g) +Cl2(g) Vapor Pressure- Example: in a closed container, vapor molecules condense to the liquid state at the same rate which liquid molecules vaporize. This is a dynamic equilibrium, because the molecules exchange phases at the same rate and the pressure exerted by the vapor remains constant with time.
Solubility- Example: In a saturated solution, a solute is added to a solvent and the system reaches a point at which the rate of dissolution is equal to the rate at which the dissolved solute crystallizes.
Distribution Coefficient- Example: When iodine,I2, is shaken with pure carbon tetrachloride, CCl4(l), the I2 molecules move into the CCl4 layer . As concentration of I2 builds up in the CCl4, the rate of I2 in which in returns to the water layer becomes significant. When the I2 molecules pass the two liquids at equal rates, dynamic equilibrium is reached, the concentration of I2 in each layer is constant.

### For a general reaction:

$aA + bB \rightleftharpoon cC + dD \tag{2}$

$Kc = \dfrac{[C]^c * [D]^d}{[A]^a * [B]^b} \tag{2}$

### Why does K (constant) have no unit?

Because K is the activities of the reaction, it has no units.
Example:
Consider the reaction: CO(g)+ 2H2 (g)<=>CH3OH (g) at T=483K
[CO]=1.03M, [CH3OH]=1.56M
What is the equilibrium constant of H2?

Solution Calculations
First write the equilibrium constant expression in terms of activities K= (CH3OH/ (CO(H2)2))eq =14.5
Assume that reaction conditions are activities that can be replaced by their concentration values,
therefore concentration units are canceled out. K=([CH3OH]/CO([H2])2)eq =14.5
Substitute given concentrations into the equilibrium constant expression K= [CH3OH]/(CO[H2]2)=1.56/(1.03 [H2]2)=14.5
Solve for the unknown concentration, [H2]=activity(H2) x c° =0.322 x 1.00M=0.322 M [H2]2 =1.56/(1.03 x 14.5)=0.104
[H2]=Square Root of 0.104= 0.322M

### Determining the equilibrium constant, K

Example:
2O3 (g) <=> 3O2(g)
K=Product/Reactant
Product: O2
Reactant: O3
Notice how the coefficients become the powers, so you get [O2]3 for products and [O3]2 for the reactants.
Therefore you have:
K=[O2]3 / [O3]2

### An Example of Equilibrium

Methanol is synthesized from a carbon monoxide-hydrogen mixture called sythesis gas in the following reaction:
CO(g) + 2H2 ---> CH3OH (g)
Methanol synthesis is a reversible reaction because at the same time CH3OH (g) is being formed, it decomposes to:
CH3OH(g)-->CO(g) +2H2(g) (Chemical Equilibrium)
When methanol synthesis decomposes to CO(g) and 2H2(g), it is classified as a chemical equilibrium. Because the forward and reverse reactions of methanol synthesis occur at equal rates it is a dynamic equilibrium and therefore can be represented with a double arrow <=>.
Rewritten as: CO(g)+ 2H2 (g)<=>CH3OH (g)

### Le Chatlier's principle

Le Chatlier's Principle: When an equilibrium system is affected by changes in temperature , pressure, or concentration of a reacting species, the system responds by attaining a new equilibrium that corresponds to the impact of the changes.

### Effect of Adding More of a Reactant to an Equilibrium Mixture

Predict the effect of adding more H2(g) to a constant-volume equilbrium mixture of N2, H2, NH3.

N2(g)+ 3H2(g) <=> 2NH3(g)

Notice that increasing [H2] stimulates the forward rection and a shift in the equilibrium concentration to the right. To learn more about Le Chatlier's Principle, please click the following link : http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch16/lechat.html

### References

1. Petrucci, R., Harwood, W., Herring, F., Madura, J., General Chemistry, 9th ed., Pearson, New Jersey, 2007
2. Zumdahl, Steven; Zumdahl, Susan; DeCoste, Don, World of Chemistry, McDougal Littell, Boston, 2002
3. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch16/lechat.html

### Contributors

• Jackie Xie (UCD)