Chemical Equilibrium      (chapter 18)

The Nature of Chemical Equilibrium

Most reactions do not go to completion but instead the products can react to re-form the reactants.  These are reversible reactions.  In reversible reactions the opposing processes eventually occur at the same time and at the same rate.  When this happens, the system is in a state of equilibrium.

For a reversible reaction:

      1.  rate expression for the forward reaction:  kf[reactants]; 

            rate expression for the reverse reaction:  kr[products]

2.      at equilibrium the forward reaction rate equals the reverse reaction rate: 

kf[reactants] = kr[products]       or    and  

The Mass-Action Expression

      1.  The mass-action expression is used to describe a system undergoing a chemical change. 

      2.  The expression is derived from the balanced equation for the reaction. 

A.     the mass-action expression is a fraction formed from the concentrations of the products in the numerator and the concentrations of the reactants in the denominator 

(products over reactants)

            B.  each concentration is raised to a power indicated by the appropriate coefficient taken from the               balanced equation  (coefficients become exponents)

            C.  if there is more than one reactant or product, multiply the concentrations

D.     the density and concentration of pure solids and liquids doesn’t change, therefore the mass-

action expression only includes (g) and (aq), do not include (s) or (l)

The Equilibrium Expression and the Equilibrium Constant

      1.  From experimentation, the mass-action expression for a system at equilibrium shows a constant                     numerical value at a particular temperature. 

2.      When the mass-action expression is set equal to this constant it is called the equilibrium

expression and the constant is called the equilibrium constant, Keq, or K.  This is called the Law of Chemical Equilibrium.

            3.  For a general reaction   mA + nB  Ö  sP + rQ ,   

            4.  The value of the equilibrium constant is not affected by the initial concentrations, only a change

in temperature will cause the value to change.

      5.  The value of the equilibrium constant indicates the extent to which the reaction proceeds in the                 forward direction (to the right) before reaching an equilibrium.

A.     if Keq > 1,  the equilibrium concentration of the products is relatively large compared with

the equilibrium concentrations of the reactants

B.     if Keq < 1,  the equilibrium concentration of the reactants is relatively large compared with

the equilibrium concentrations of the products

Shifting Equilibrium

Le Chatelier's Principle - when a system is at equilibrium and a stress is applied to that system, the system reacts to reduce the stress and re-establish equilibrium

      Consider an equilibrium reaction like a see-saw that is balanced:  if you change the weight on either side, the see-saw becomes unbalanced and you must shift the weight to make it balance again

In an equilibrium reaction, we can use Le Chatelier's principle to predict which way the reaction will shift to re-establish equilibrium:

      1.  Concentration changes

A.     if you increase the concentration of one of the reactants:  reaction shifts to the right and

favors the   forward reaction

B.     if you increase the concentration of one of the products:  reaction shifts to the left and favors

the reverse reaction

C.     if you decrease the concentration of one of the reactants:  reaction shifts to the left and favors

the reverse reaction

D.     if you decrease the concentration of one of the products:  reaction shifts to the right and

favors the   forward reaction

2.      Pressure changes - only affect substances that are gases

Pressure can be change by changing the size of the container: 

increase the volume Õ decrease the pressure;  decrease the volume Õ increase the pressure.

Adding an inert gas (like neon) won’t have any effect on the pressure of the reactants or products

because it doesn’t affect either of them.

A.     if you increase pressure:  the reaction shifts to the side with smaller number of moles  (the

side that the sum of the coefficients is the smallest)

B.     if you decrease pressure:  the reaction shifts to the side with the larger number of moles  (the

side that the sum of the coefficients is the largest)

3.      Temperature changes: 

There are two types of reactions involving temperature, exothermic and endothermic.  An

exothermic reaction releases heat, this energy can be considered as a product.  An endothermic reaction absorbs heat,  this energy can be considered as a reactant.

            A.  increase the temperature of an exothermic reaction:  reaction shifts to the left and favors the                    reverse reaction

C.     increase the temperature of an endothermic reaction:  reaction shifts to the right and favors

the forward reaction

            C.  decrease the temperature of an exothermic reaction:  reaction shifts to the right and favors the                 forward reaction

            D.  decrease the temperature of an endothermic reaction:  reaction shifts to the left and favors the                 reverse reaction 

Optimum conditions - conditions that produce the highest yield of the substance wanted;  the

conditions, such as pressure and temperature and concentrations, that are imposed to shift the equilibrium position toward that substance according to Le Chatelier's principle

Reactions that tend to go to completion include the following:

1.      reactions where a precipitate is formed

2.      reactions where a gas is formed that can escape from the container

3.      reactions where a product is formed that is slightly ionizable

Common ion effect

What happens if add a salt that has the ion of the acid?  LeChatelier's Principle: shift equilibrium

positions (the concentrations change) but the Keq remains the same. The solubility of a solid is lowered (compared to water) if the solution already contains ions common to the solid.

Equilibria of Acids, Bases, and Salts

Ionization constant of a weak acid:  Ka, a special case of the equilibrium constant, Keq

for a weak acid: HA + H2O Ö H3O+1 + A-1            or        HA  Ö  H+1 + A-1 

      Keq = [H3O+1].[A-1] / [HA].[H2O]                           or         Keq = [H+1].[A-1] / [HA] 

      Ka = Keq.[H2O] = [H3O+1].[A-1] / [HA]                   or         Ka = Keq= [H+1].[A-1] / [HA]

Dissociation (ionization) constant of a weak base:  Kb, a special case of the equilibrium       constant, Keq

for a weak base: B + H2O Ö BH+1 + OH-1

      Keq = [BH+1].[OH-1] / [B].[H2O]

      Kb = Keq.[H2O] = [BH+1].[OH-1] / [B]

For any weak acid/base and it's conjugate base/acid:  Ka * Kb = Kw.

Buffers

1.  a buffer is a substance that can absorb moderate amounts of acid or base without     significantly altering the pH

2.  a buffer is a solution of a weak acid and it's conjugate base or a weak base and it's   conjugate acid  (the common ion effect - Le Chatelier states that the equilibrium shifts but does not change the Keq)

3.  buffers are made by:

      a.  adding the salt of a weak acid/base to a solution of the weak acid/base;  example:                                                     HCH3COO and NaCH3COO  and  NH4OH and NH4Cl

  1. titrating half of a weak acid/base solution with a strong base/acid and adding it to the untitrated half of the weak acid/base 

4.  how buffers work  (think of Le Chatelier’s principle:  what is there in the solution       that the added substance can combine and how does the equilibrium shift?)

      a.  adding a acid to a buffered solution

1.      weak acid buffer:  H+1 + A-1 à HA                       

2.  weak base buffer:  H+1 + B à BH+1

      b.  adding a base to a buffered solution

            1.  weak acid buffer:  OH-1 + HA à A-1 + H2O     

2.  weak base buffer:  OH-1 + BH+1 à B + H2O

5.  Buffering systems are found in many living organisms where they are responsible for homeostatic control.  An example in humans is the blood buffering system using the HCO3-1.

Ionization of Water - review

Water ionizes only slightly according to the following equation:    H2O(l) Ö  H+1  +  OH–1 .  This

produces equal numbers of H+1 and OH–1 .  The H+1  that is produced is very reactive and attaches itself to another water molecule to form the hydronium ion, H3O+1 .  The self ionization of water can now be written as:  H2O(l)  +  H2O(l) Ö  H3O+1  +  OH–1.

In pure water [H+1] = [OH–1] and the solution is neutral.  At 25 ºC these concentrations have been measured to be [H+1] = [OH–1] = 1.00 x 10–7.  Their product is called the ion product constant of water (or the ionization constant of water) and is given the symbol Kw  and numerically at 25 ºC is 1.00 x 10–14.  Therefore: [H+1].[OH–1] = 1.00 x 10–14 .

If you add an acid to a neutral solution, the [H+1] increases and the [OH–1] decreases so [H+1] > [OH–1]  and it is now considered to be an acidic solution.  If you add a base to a neutral solution, the [OH–1] increases and the [H+1] decreases so [H+1] < [OH–1]  and it is now considered to be a basic solution.

The pH Scale - review

The pH scale is a simple way to state what the [H3O+1] is in a solution.  It identifies the relative acidity of the solution.  pH is expressed as a power of ten, usually from 100 to 10-14 . 

If [H+1] = [OH–1] = 1.00 x 10–7 is considered neutral than the pH = 7.  Definition:  pH = –log10 [H+1].

A known pH value can be used to find [H+1]. The [H+1] = 10–pH.  

The pH scale is usually expressed from 0 to 14.  A neutral solution has a pH = 7.  An acidic solution has a pH< 7 and a basic solution has a pH >7.

If there is a pH, there is also a pOH used to state what the [OH–1] is in a solution. 

Definition:  pOH = –log10 [OH–1] . The [OH–1] = 10–pOH.  Mathematically, pH + pOH = 14 .

Hydrolysis of a Salt: Acidic or basic salts – review

Hydrolysis is the reaction of a substance with the water that it is dissolved in.  Sometimes a salt will react with water to form an acidic or basic salt.  When acids and bases react, what do they produce?

1.  If a strong acid reacts with a strong base, the resulting salt is a neutral salt because    the acid and base ionize completely and all of the ions stay as ions.

2. If a weak acid, HA, reacts with a strong base, the resulting salt is a basic salt.  The anion (conjugate base), A-, of the acid reacts with water and leaves free OH- in solution.

3. If a strong acid reacts with a weak base, B, the resulting salt is an acidic salt.  The cation (conjugate acid), BH+, of the base reacts with water and leaves free H+ in solution.

4.  If a weak acid reacts with a weak base, the resulting salt could be neutral, acidic or basic depending on how weak the acid and base are in relation to each other.

You can tell if a salt is neutral, acidic or basic by looking at the acid and base that    reacted to form the salt.  Remember that a salt is made from the positive metal ion (cation) of a base and the negative nonmetal ion (anion) of an acid.

Solubility Equilibrium

A.     In a saturated solution of an ionic solid, an equilibrium exists between the ions dissolved in solution and the excess solid which hasn’t dissolved and remains in the crystal state.

B.     An insoluble solid dissolves to a limited extent in water solutions.  The solid is dissolving at the same rate at which the small number of dissolved ions are re-forming the crystal solid.

This is called solution equilibrium. 

            C.  For the reaction: AB2(s)  Ö  A+1(aq)  +  2 B-1(aq) ,   the equilibrium expression is:                                              .

            D.   Because AB2(s) is a solid, it’s concentration doesn’t change and the equilibrium expression                     becomes   Keq.[ AB2(s)] = [A+1].[ B-1]2. 

E.      The product of two constants is itself another constant.  The new constant is called the

solubility product constant, or the solubility product, and is symbolized by Ksp. 

            F.  The solubility product expression, also called the ion product, for the above reaction is

                  Ksp = [A+1].[ B-1]2. 

G.     Again this is specified for a specific temperature because solubility’s vary with temperature.

H.     The solubility of a insoluble salt is a measure of how much (in grams or moles) will dissolve in a given amount of solution.  The concentration of the ions is based on the solubility and the stoiciometric mole ratio between the salt and it’s ions as determined by a balanced equation.

Saturated solutions

1.  insoluble salt ions in solution are in equilibrium with the undissolved ionic solid

2.  solubility product constant:  Ksp, special case of equilibrium constant, Keq

            3.  if the concentrations, Q,  > Ksp the salt will not completely dissolve

if the concentrations, Q,  < Ksp the salt will dissolve

Q is determined just like Ksp, except the concentrations are not necessarily equilibrium concentrations

4.  if add common ion to saturated solution it causes the precipitation of the solute (ionic solid)

5.  solubility of substance decreases by the addition of a common ion (LeChatelier)