Basic Concepts• One of the fundamental ideas of chemical equilibrium is that

equilibrium can be established from either the forward or reverse direction.

(g)(g)(g)(g) D C B A• The rates of the forward and reverse reactions can be represented as:

rate. reverse therepresents which DCkRate

rate. forward therepresents which BAkRate

rr

ff

• When system is at equilibrium:

Ratef = Rater

Equilibrium constants are dimensionless because they actually involve a thermodynamic quantity called activity.

Activities are directly related to molarity

The Equilibrium Constant

• Kc is the equilibrium constant .

• Kc is defined for a reversible reaction at a given temperature as the product of the equilibrium concentrations (in M) of the products, each raised to a power equal to its stoichiometric coefficient in the balanced equation, divided by the product of the equilibrium concentrations (in M) of the reactants, each raised to a power equal to its stoichiometric coefficient in the balanced equation.

Variation of Kc with the Form of the Balanced Equation

• The value of Kc depends upon how the balanced equation is written.

• This reaction has a Kc=[PCl3][Cl2]/[PCl5]=0.53

235 ClPClPCl

523 PClCl PCl• This reaction has a Kc=[PCl5]/=[PCl3][Cl2]=1.88

The Reaction Quotient• The mass action expression or reaction quotient has the

symbol Q.

– Q has the same form as Kc

• The major difference between Q and Kc is that the concentrations used in Q are not necessarily equilibrium values.

• Why do we need another “equilibrium constant” that does not use equilibrium concentrations?

• Q will help us predict how the equilibrium will respond to an applied stress.

• To make this prediction we compare Q with Kc.

• Q<K products favored

• Q>K reactants favored

• favored Q=K equilibrium

Disturbing a System at Equlibrium: Predictions

• LeChatelier’s Principle - If a change of conditions (stress) is applied to a system in equilibrium, the system responds in the way that best tends to reduce the stress in reaching a new state of equilibrium.

– We first encountered LeChatelier’s Principle in Chapter 14.

• Some possible stresses to a system at equilibrium are:

1. Changes in concentration of reactants or products.

2. Changes in pressure or volume (for gaseous reactions)

3. Changes in temperature.

Relationship Between Kp and Kc

• The relationship between Kp and Kc is:

reactants) gaseous of moles of (#-products) gaseous of moles of (#=n

RTKKor RTKK npc

ncp

• Heterogeneous equilibria have more than one phase present.

– For example, a gas and a solid or a liquid and a gas.

• How does the equilibrium constant differ for heterogeneous equilibria?– Pure solids and liquids have activities of unity.– Solvents in very dilute solutions have activities that are essentially unity.– The Kc and Kp for the reaction shown above are:

2COp2c P=K ][CO=K

C500at CO CaO CaCO og2ss3

Relationship Between Gorxn and the

Equilibrium Constant G (notice no o indicating standard state) is the free energy change

at nonstandard conditions

• For example, concentrations other than 1 M or pressures other than 1 atm.

G is related to Go by the following relationship.

quotientreaction =Q

re temperatuabsolute = T

constant gas universal =R

Q log RT 303.2G=G

or lnQ RTG=Go

o

Relationship Between Gorxn and the

Equilibrium Constant

• The relationships among Gorxn, K, and the spontaneity of a

reaction are:

Gorxn K Spontaneity at unit concentration

< 0 > 1 Forward reaction spontaneous

= 0 = 1 System at equilibrium

> 0 < 1 Reverse reaction spontaneous

• There are three classes of strong electrolytes.

1 Strong Water Soluble Acids

Remember the list of strong acids from Chapter 4.

2 Strong Water Soluble Bases

The entire list of these bases was also introduced in Chapter 4.

3 Most Water Soluble SaltsThe solubility guidelines from Chapter 4 will help you remember these salts.

Acid

HCl

Base

NaOH

Arrhenius Produces H+ Produces OH-

Brönsted-Lowery Donates H+ Accepts H+

Lewis Accepts e- pair Donates e- pair

Ionization Constants for Weak Monoprotic Acids and Bases

• We can define a new equilibrium constant for weak acid equilibria that uses the previous definition.

– This equilibrium constant is called the acid ionization constant.

– The symbol for the ionization constant is Ka.

acid aceticfor

108.1COOHCH

COOCH OHK 5

3

33a

pH = -log H O3+

Polyprotic Acids• Many weak acids contain two or more acidic hydrogens.

– Examples include H3PO4 and H3AsO4.

• The calculation of equilibria for polyprotic acids is done in a stepwise fashion.

– There is an ionization constant for each step.

• Consider arsenic acid, H3AsO4, which has three ionization constants.

1 Ka1 = 2.5 x 10-4

2 Ka2 = 5.6 x 10-8

3 Ka3 = 3.0 x 10-13

• This is a general relationship.

– For weak polyprotic acids the Ka1 is always > Ka2, etc.

a3a2a1 KKK

Polyprotic Acids• Calculate the concentration of all species in 0.100 M arsenic acid, H3AsO4,

solution.

1 Write the first ionization step and represent the concentrations.

Approach this problem exactly as previously done.2 Substitute the algebraic quantities into the expression for Ka1.

3. Use the quadratic equation to solve for x, and obtain both values of x.

4 Next, write the equation for the second step ionization and represent the concentrations.

5 Substitute the algebraic expressions into the second step ionization expression.

6 Finally, repeat the entire procedure for the third ionization step.

7. Substitute the algebraic representations into the third ionization expression.

The Common Ion Effect and Buffer Solutions

• There are two common kinds of buffer solutions:

1 Solutions made from a weak acid plus a soluble ionic salt of the weak acid.

2 Solutions made from a weak base plus a soluble ionic salt of the weak base

1. Solutions made of weak acids plus a soluble ionic salt of the weak acid

• One example of this type of buffer system is:

– The weak acid - acetic acid CH3COOH

– The soluble ionic salt - sodium acetate NaCH3COO

The Common Ion Effect and Buffer Solutions

The Henderson-Hasselbach equation is one method to calculate the pHof a buffer given the concentrations of the salt and acid. The Henderson-Hasselbach Equation can be used for bases by substituting OH- for H+ and base for acid.

acid

saltlogpKpH

acid

saltlogKlogHlog

1-by multiply

salt

acidlogKlogHlog

a

a

a

• Henderson-Hasselbach Equation

Buffering Action1 Calculate the pH of the original buffer solution.

2 Next, calculate the concentration of all species after the addition of the gaseous strong acid or strong base.

– This is another limiting reactant problem.3 Using the concentrations of the salt and base and the Henderson-

Hassselbach equation, the pH can be calculated.4 Finally, calculate the change in pH.

Strong Acid/Strong Base Titration Curves

• We have calculated only a few points on the titration curve. Similar calculations for remainder of titration show clearly the shape of the titration curve.

Weak Acid/Strong Base Titration Curves• We have calculated only a few points on the titration curve. Similar calculations

for remainder of titration show clearly the shape of the titration curve.

Strong Acid/Weak BaseTitration Curves

• Titration curves for Strong Acid/Weak Base Titration Curves look similar to Strong Base/Weak Acid Titration Curves but they are inverted.

• Weak Acid/Weak Base Titration curves have very short vertical sections.

• The solution is buffered both before and after the equivalence point.

• Visual indicators cannot be used.