Chemical Equilibrium

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Chemical Equilibrium

• Brown, LeMay Ch 15
• AP Chemistry
• Monta Vista High School

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15.1 Chemical Equilibrium

• Occurs when opposing reactions are proceeding at
  the same rate
• Forward rate reverse rate of reaction
• Ex
• Vapor pressure rate of vaporization rate of
  condensation
• Saturated solution rate of dissociation rate
  of crystallization
• Expressing concentrations
• Gases partial pressures, PX
• Solutes in liquids molarity, X

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• Forward reaction A ? B Rate kforward A
• Reverse reaction B ? A Rate kreverse B
• or

R 0.0821 Latm molK
Forward reaction Reverse reaction
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• http//www.kentchemistry.com/links/Kinetics/Equili
  brium/equilibrium.swf

or
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• Kc kf/kr, at equilibrium, if Kgt 1, then more
  products at equilib. And if klt1, then reactants
  favored at equilb. K1 (conc. Of reactants and
  products nearly same at equilibrium)
• The magnitude of Kc gives us an indication of how
  far the reaction has proceeded toward the
  formation of products, when the equilibrium is
  achieved.
• The larger the value of K, the further the
  reaction will have proceeded towards completion
  when equilibrium is reached.

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Equilibrium

• Equilibrium is dynamic. The forward and reverse
  rxns occur at the same rate.
• There is a spontaneous tendency towards
  equilibrium. This does not mean that equilibrium
  will occur quickly, it simply means that there is
  always a drive TOWARD the equilibrium state. The
  amount of drive is measured as Free Energy (D G)
• The driving force towards equilibrium diminishes
  as equilibrium is approached. Thus the appearance
  of products actually decreases the forward
  impetus of the reaction, making the free energy
  change less negative.
• http//www.youtube.com/watch?vCMs2WhGY3NE

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Equilibrium

• The equilibrium position is the same at a given
  temperature, no matter from which direction it is
  approached.
• It is possible to force an equilibrium one way or
  the other temporarily by altering the reaction
  conditions, but once this stress is removed,
  the system will return to its original
  equilibrium.

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Figure 1 Reversible reactions
Equilibrium is established
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Reversible Reactions and Rate
Forward rate
Equilibrium is established Forward rate
Backward rate
Backward rate
When equilibrium is achieved A ? B and
kf/kr Keq
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15.2 Law of Mass Action

• Derived from rate laws by Guldberg andWaage
  (1864)
• For a balanced chemical reactionin equilibrium
• a A b B ? c C d D
• Equilibrium constant expression (Keq)

Cato Guldberg Peter Waage (1836-1902)
(1833-1900)
or

• Keq is strictly based on stoichiometry of the
  reaction (is independent of the mechanism).
• Units Keq is considered dimensionless (no units)

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Relating Kc and Kp

• Convert A into PA

where Dn change in coefficents of products
reactants (gases only!) (cd) - (ab)
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Magnitude of Keq

• Since Keq a products/reactants, the magnitude
  of Keq predicts which reaction direction is
  favored
• If Keq gt 1 then products gt reactants and
  equilibrium lies to the right
• If Keq lt 1 then products lt reactants and
  equilibrium lies to the left

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Relationship Between Q and K

• Reaction Quotient (Q) The particular ratio of
  concentration terms that we write for a
  particular reaction is called reaction quotient.
• For a reaction, A? B, Q B/A
• At equilibrium, Q K
• Reaction Direction Comparing Q and K
• QltK, reaction proceeds to right, until
  equilibrium is achieved (or QK)
• QgtK, reaction proceeds to left, until QK

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Value of K
For the reference rxn, A?gtB, For the reverse rxn, B ?gtA, For the reaction, 2A ?gt 2B For the rxn, A ?gt C C ?gt B
K(ref) B/A K 1/K(ref) K K(ref)2 K (overall) K1 X K2
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15.3 Types of Equilibria

• Homogeneous all components in same phase
  (usually g or aq)
• N2 (g) H2 (g) ? NH3 (g)

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2
1
Fritz Haber(1868 1934)
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• Heterogeneous different phases
• CaCO3 (s) ? CaO (s) CO2 (g)
• Definition What we use

• Concentrations of pure solids and pure liquids
  are not included in Keq expression because their
  concentrations do not vary, and are already
  included in Keq (see p. 548).

• Even though the concentrations of the solids or
  liquids do not appear in the equilibrium
  expression, the substances must be present to
  achieve equilibrium.

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15.4 Calculating Equilibrium Constants

• Steps to use ICE table
• I Tabulate known initial and equilibrium
  concentrations of all species in equilibrium
  expression
• C Determine the concentration change for the
  species where initial and equilibrium are known
• Use stoichiometry to calculate concentration
  changes for all other species involved in
  equilibrium
• E Calculate the equilibrium concentrations

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• Ex Enough ammonia is dissolved in 5.00 L of
  water at 25ºC to produce a solution that is
  0.0124 M ammonia. The solution is then allowed
  to come to equilibrium. Analysis of the
  equilibrium mixture shows that OH1- is 4.64 x
  10-4 M. Calculate Keq at 25ºC for the reaction
• NH3 (aq) H2O (l) ? NH41 (aq) OH1- (aq)

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NH3 (aq) H2O (l) ? NH41 (aq) OH1- (aq)
 
Initial
Change
Equilibrium
NH3 (aq) H2O (l) NH41 (aq) OH1- (aq)
X
0.0124 M
0 M
0 M
X
- x
x
x
X
0.0119 M
4.64 x 10-4 M
4.64 x 10-4 M
x 4.64 x 10-4 M
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• Ex A 5.000-L flask is filled with 5.000 x 10-3
  mol of H2 and 1.000 x 10-2 mol of I2 at 448ºC.
  The value of Keq is 1.33. What are the
  concentrations of each substance at equilibrium?
• H2 (g) I2 (g) ? 2 HI (g)

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H2 (g) I2 (g) ? 2 HI (g)
 
Initial
Change
Equilibrium
H2 (g) I2 (g) HI (g)
1.000x10-3 M
2.000x10-3 M
0 M
- x M
- x M
2x M
(1.000x10-3 x) M
(2.000x10-3 x) M
2x M
4x2 1.33x2 (-3.000x10-3)x 2.000x10-6 0
-2.67x2 3.99x10-3x 2.66x10-6 Using quadratic
eqn x 5.00x10-4 or 1.99x10-3 x
5.00x10-4 Then H25.00x10-4 M I21.50x10-3
M HI1.00x10-3 M
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15.6 Le Châteliers Principle

• If a system at equilibrium is disturbed by a
  change in
• Concentration of one of the components,
• Pressure, or
• Temperature
• the system will shift its equilibrium position
  to counteract the effect of the disturbance.
• http//www.mhhe.com/physsci/chemistry/essentialche
  mistry/flash/lechv17.swf

Henri Le Châtelier(1850 1936)
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4 Changes that do not affect Keq

• Concentration
• Upon addition of a reactant or product,
  equilibrium shifts to re-establish equilibrium by
  consuming part of the added substance.
• Upon removal of reactant or product, equilibrium
  shifts to re-establish equilibrium by producing
  more of the removed substance.

• Ex Co(H2O)62 (aq) 4 Cl1- ? CoCl42- (aq) 6
  H2O (l)
• Add HCl, temporarily inc forward rate
• Add H2O, temporarily inc reverse rate

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2. Volume, with a gas present (T is constant)

• Upon a decrease in V (thereby increasing
  P),equilibrium shifts to reduce the number of
  moles of gas.
• Upon an increase in V (thereby decreasing
  P),equilibrium shifts to produce more moles of
  gas.
• Ex N2 (g) 3 H2 (g) ? 2 NH3 (g)
• If V of container is decreased, equilibrium
  shifts right.
• XN2 and XH2 dec
• XNH3 inc

Since PT also inc, KP remains constant.
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3. Pressure, but not Volume

• Usually addition of a noble gas, p. 560
• Avogadros law adding more non-reacting
  particles fills in the empty space between
  particles.
• In the mixture of red and blue gas particles,
  below, adding green particles does not stress the
  system, so there is no Le Châtelier shift.

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4. Catalysts

• Lower the activation energy of both forward and
  reverse rxns, therefore increases both forward
  and reverse rxn rates.
• Increase the rate at which equilibrium is
  achieved, but does not change the ratio of
  components of the equilibrium mixture (does not
  change the Keq)

Ea, uncatalyzed
Ea, catalyzed
Energy
Rxn coordinate
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1 Change that does affect Keq

• Temperature consider heat as a part of the
  reaction
• Upon an increase in T, endothermic reaction is
  favored (equilibrium shifts to consume the extra
  heat)
• Upon a decrease in T, equilibrium shifts to
  produce more heat.

• Effect on Keq
• Exothermic equilibria Reactants ? Products
  heat
• Inc T increases reverse reaction rate which
  decreases Keq
• Endothermic equilibria Reactants heat ?
  Products
• Inc T increases forward reaction rate increases
  Keq

• Ex Co(H2O)62 (aq) 4 Cl1- ? CoCl42- (aq) 6
  H2O (l) DH?
• Inc T temporarily inc forward rate
• Dec T temporarily inc reverse rate

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Vant Hoffs Equation

• Vant Hoffs equation shows mathematically how the
  equilibrium constant is affected by changes in
  temp.
• ln K2 -d H0 rxn (1 1)
• K1 R T2 T1

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Effect of Various Changes on Equilibrium
Disturbance Net Direction of Rxn Effect of Value of K
Concentration Increase (reactant) Towards formation of product None
Decrease(reactant) Towards formation of reactant None
Increase (product) Towards formation of reactant None
Decrease (product) Towards formation of product None
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Effect of Pressure on Equilb.
Pressure Increase P (decrease V) Towards formation of fewer moles of gas None
Decrease P (Increase V) Towards formation of more moles of gas None
Increase P ( Add inert gas, no change in V) None, concentrations unchanged None
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Effect of Temperature on Equilb
Temperature Increase T Towards absorption of heat Increases if endothermic Decreases if exothermic
Decrease T Towards release of heat Increases if exothermic Decreases if endothermic
Catalyst Added None, forward and reverse equilibrium attained sooner None