Download Basic Concepts

Basic Concepts
• One of the fundamental ideas of chemical equilibrium is that
equilibrium can be established from either the forward or reverse
direction.

A(g)  B(g)  C(g)  D(g)
• The rates of the forward and reverse reactions can be represented as:
Rate f  k f A B which represents the forward rate.
Rate r  k r CD which represents the reverse rate.
• 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.

PCl5  PCl3  Cl2
• This reaction has a Kc=[PCl3][Cl2]/[PCl5]=0.53

PCl3  Cl2  PCl5
• 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:
K p  K c RT 
n
or K c  K p RT 
 n
n = (# of moles of gaseous products) - (# of moles of gaseous reactants)
• Heterogeneous equilibria have more than one phase present.
– For example, a gas and a solid or a liquid and a gas.
CaCO3s  
 CaOs   CO2g 
•
o
at 500 C
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:
K c = [CO 2 ]
K p = PCO 2
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.
G = G o  RT lnQ or
G = G o  2.303 RT log Q
R = universal gas constant
T = absolute temperatu re
Q = reaction quotient
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
•
1
There are three classes of strong electrolytes.
Strong Water Soluble Acids
Remember the list of strong acids from Chapter 4.
100%


HNO3( )  H 2O (  ) 
 H 3O (aq)
 NO3(aq)
2
Strong Water Soluble Bases
or
The entire list of these
was
in Chapter 4.
100bases
%
 also introduced

HNO3( )  H (aq)  NO3(aq)

2 O 100%
KOH(s) H
 K (aq)
 OH-(aq)
3
Most Water Soluble Salts
H 2 O 100%
2
Sr(OH)





Sr

2
OH
The solubility2(s)
guidelines from Chapter(aq)
4 will help you
remember these salts.
(aq)

2 O 100%
NaCl(s) H
 Na (aq)
 Cl-(aq)
2

2 O 100%
Acid
Base
Ca(NO3 ) 2s  H

 Ca (aq)
 2 NO
3(aq)
HCl
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.
Ka 
H O CH COO   1.8 10

3

3
CH3COOH
5
for acetic acid

pH = -log H 3O
+

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
a1
a2
a3
3 Ka3 = 3.0 x 10-13
K K K
• This is a general relationship.
– For weak polyprotic acids the Ka1 is always > Ka2, etc.
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
• Henderson-Hasselbach Equation
acid 
log H    log K a  log
salt 
multiply by - 1

salt 
 log H    log K a  log
acid 
salt 
pH  pK a  log
acid 

The Henderson-Hasselbach equation is one method to calculate the pH
of 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.
Buffering Action
1 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 HendersonHassselbach 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 Base
Titration 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.