Principles of Reactivity: Chemical Equilibria

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Principles of Reactivity Chemical Equilibria

• Chapter 15

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Learning Objectives

• Students understand
• The nature and characteristics of chemical
  equilibria
• The significance of the equilibrium constant, K,
  and the reaction quotient, Q
• How an equilibrium will respond if the reaction
  conditions are changed (Le Chateliers principle)

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Learning Objectives

• Students will be able to
• Write the equilibrium constant and reaction
  quotient expressions for a reaction
• Calculate an equilibrium constant given the
  reactant and product concentrations
• Use Q and K in quantitative studies of chemical
  equilibria
• Derive a K value if different stoichiometric
  coefficients are used, the equation is reversed,
  or if several equations are added
• Use Le Chateliers principle

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15.1 Nature of the Equilibrium State

• All chemical reactions are reversible.
• When both the forward and reverse reactions
  continue to occur at equal rates but no net
  change is observed.
• Use a double arrow to show this situation.
• Outside forces can affect the equilibrium!

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15.2 The Reaction Quotient and Equilibrium
Constant

• For the reaction H2 I2 ?? 2HI the relationships
  among the substances has been experimentally
  established as HI2/H2I2
• This constant, K (the equilibrium constant) is
  always the same at a given temperature
• We can make an ICE table to summarize this
  relationship

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The Reaction Quotient and Equilibrium Constant
Equation H2 I2 ?? 2HI Equation H2 I2 ?? 2HI Equation H2 I2 ?? 2HI Equation H2 I2 ?? 2HI
Initial conc. (M) 0.0175 0.0175 0
Change in conc. as rxn proceeds (M) -0.0138 -0.0138 0.0276
Equilibrium conc. (M) 0.0037 0.0037 0.0276
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The Reaction Quotient and Equilibrium Constant

• Putting the equilibrium concentrations into the
  expression
• K HI2/H2I2
• (0.0276)2/(0.0037)(0.0037)
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• This quotient is always the same for all
  experiments under these conditions no matter what
  the initial concentrations.

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The Reaction Quotient and Equilibrium Constant

• The expression is commonly referred to as the
  equilibrium constant expression.
• Product concentrations always appear in the
  numerator.
• Reactant concentrations always appear in the
  denominator.
• Each concentration is always raised to the power
  of its stoichiometric coefficient in the balanced
  equation.
• When the reaction has reached equilibrium, the
  value of the constant K depends on the particular
  reaction and on the temperature. Units are never
  given for K!

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The Reaction Quotient and Equilibrium Constant

• The concentrations of reactants and products are
  always related by an expression to a value called
  the reaction quotient.
• Reaction quotient Q CcDd/AaBb
• When a reaction has reached equilibrium, the
  reaction quotient has a constant value referred
  to as the equilibrium constant, K.

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Writing Equilibrium Constant Expressions

• Reactions involving solids, water, and pure
  liquids.
• Concentrations of any solid reactants and
  products are omitted from the equilibrium
  constant expression.
• The molar concentration of water (or of any
  liquid reactant or product) is omitted from the
  equilibrium constant expression.

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Writing Equilibrium Constant Expressions

• Reactions involving gases
• If reactant and product quantities are given in
  partial pressures, then K is given the subscript
  p, as in Kp.
• H2(g) I2(g) ?? 2HI(g) Kp P2HI/(PH2PI2)

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Writing Equilibrium Constant Expressions

• For reactions concerned with substances in
  aqueous solution, the symbol K sometimes has the
  subscript c for concentration, as in Kc.
• In some cases Kc and Kp may be the same, but they
  are different when the numbers of moles of
  gaseous reactants and products are different.
• Kp Kc(RT)?n

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Practice Problem

• Write the equilibrium constant expression for
  each of the following reactions in terms of
  concentrations
• PCl5(g) ?? PCl3(g) Cl2(g)
• Cu(OH)2(s) ?? Cu2(aq) 2OH-(aq)
• Cu(NH3)42(aq) ?? Cu2(aq) 4NH3(aq)
• CH3CO2H(aq) H2O(l) ?? CH3CO2-(aq) H3O(aq)

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Meaning of the Equilibrium Constant, K

• K gtgt 1 Reaction is product-favored. Equilibrium
  concentrations of products are greater than
  equilibrium concentrations of reactants. The
  reaction has gone to completion.
• Kltlt 1 Reaction is reactant-favored. Equilibrium
  concentrations of reactants are greater than
  equilibrium concentrations of products.

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Meaning of the Reaction Quotient, Q

• If K gt Q, the system is not at equilibrium and
  some reactants will be converted to products.
• If K lt Q, the system is not at equilibrium and
  some products will be converted to reactants.
• If Q K, the system is at equilibrium.

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Practice Problem

• Answer the following questions regarding the
  butane ?? isobutane equilibrium (K 2.50 at
  298K).
• Is the system at equilibrium when butane
  0.00097 M and isobutane 0.00218 M? If it is
  not at equilibrium, in which direction will the
  reaction proceed in order to achieve equilibrium?
• Is the system at equilibrium when butane
  0.00075 M and isobutane 0.00260 M? If it is
  not at equilibrium, in which direction will the
  reaction proceed in order to achieve equilibrium?

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Practice Problem

• At 2000K the equilibrium constant, K, for the
  formation of NO(g)
• N2(g) O2(g) ? 2NO(g) is 4.0 x 10-4. If, at
  2000K, the concentration of N2 is 0.050 M, that
  of O2 is 0.025 M, and that of NO is 4.2 x 10-4 M,
  is the system at equilibrium? If not, predict
  which way the reaction will proceed to achieve
  equilibrium.

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15.3 Determining an Equilibrium Constant

• If the experimental values of the concentrations
  of all the reactants and products at equilibrium
  are known, an equilibrium constant can be
  calculated by substituting the data into the
  equilibrium constant expression.

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Determining an Equilibrium Constant

• If not all concentrations are known, use an ICE
  table to show the initial concentrations, how
  they change on proceeding to equilibrium, and the
  concentrations at equilibrium.

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Practice Problem

• A solution is prepared by dissolving 0.050 mol of
  diiodocyclohexane, C6H10I2, in the solvent CCl4.
  The total solution volume is 1.00 L. When the
  reaction
• C6H10I2 ?? C6H10 I2 has come to
• equilibrium at 35oC, the concentration of I2 is
  0.035 M.
• What are the concentrations of C6H10I2 and C6H10
  at equilibrium?
• Calculate Kc, the equilibrium constant.

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Homework

• After reading sections 15.1-15.3, you should be
  able to do the following
• P. 583a-b (1-10)

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15.4 Using Equilibrium Constants

• The value of K and the initial amounts of
  reactants are often known, and you are asked to
  calculate the quantities present at equilibrium.

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Using Equilibrium Constants in Calculations

• If the solution is a quadratic expression
• K 1.20 x2/(1.60-x)
• x2 1.20x -1.92 0
• Use appdx A to find roots to equation
• Negative values arent chemically meaningful!
  So, answer is x 0.91.

PCl5 ? PCl3 Cl2 PCl5 ? PCl3 Cl2 PCl5 ? PCl3 Cl2 PCl5 ? PCl3 Cl2
I 1.60 0 0
C -x x x
E 1.60-x x x
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Practice Problem

• Graphite and carbon dioxide are kept at 1000 K
  until the reaction
• C(graphite) CO2(g) ?? 2CO(g)
• has come to equilibrium. At this temperature, K
  0.021. The initial concentration of CO2 is
  0.012 mol/L. Calculate the equilibrium
  concentration of CO.

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Is there an easier way?

• If K is very small, then you can use another
  expression
• If 100K lt Ao the approximate expression will
  give acceptable values of equilibrium
  concentrations.
• In general, when K is about 1 or greater, the
  approximation cannot be made.
• This means you can drop the -x off of your
  expression!

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Practice Problem

• The reaction N2(g) O2(g) ?? 2NO(g) contributes
  to air pollution whenever a fuel is burned in air
  at a high temperature, as in a gasoline engine.
  At 1500 K, Kc 1.0 x 10-5. Suppose a sample of
  air has N2 0.080 M and O2 0.020 M before
  any reaction occurs. Calculate the equilibrium
  concentrations of reactants and products after
  the mixture has been heated to 1500K.

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15.5 Balanced Equations and Equilibrium Constants

• When the stoichiometric coefficients of a
  balanced equation are multiplied by some factor,
  the equilibrium constant for the new equation
  (Knew) is the old equilibrium constant (Kold)
  raised to the power of the multiplication factor.
• The equilibrium constants for a reaction and its
  reverse are the reciprocals of each other.
• When two or more chemical equations are added to
  produce a net equation, the equilibrium constant
  for the net equation is the product of the
  equilibrium constants for the added equations.

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Practice Problem

• The conversion of oxygen to ozone has a very
  small equilibrium constant.
• 3/2 O2(g) ?? O3(g) K 2.5 x 10-29
• What is the value of K when the equation is
  written using whole number coefficients?
• What is the value of K for the conversion of
  ozone to oxygen?

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Practice Problem

• The following equilibrium constants are given at
  500 K
• H2(g) Br2(g) ?? 2HBr(g) Kp 7.9x1011
• H2(g) ?? 2H(g) Kp 4.8x10-41
• Br2(g) ?? 2Br(g) Kp 2.2x10-15
• Calculate Kp for the reaction of H and Br atoms
  to give HBr.
• H(g) Br(g) ?? HBr(g) Kp ?

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15.6 Disturbing a Chemical Equilibrium

• A change in any factor that determines the
  equilibrium conditions of a system will cause the
  system to change to counteract the effect of the
  change. (Le Chateliers principle)
• Change temperature
• Change concentrations of reactants or products
• Change volume (for gas system)

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Disturbing a Chemical Equilibrium

• When temp of a system at equilibrium increases,
  rxn shifts in direction that absorbs heat energy
  (endothermic direction)
• If temp decreases, rxn shifts in direction that
  releases heat energy (exothermic direction)
• Either way, equilibrium composition will change
  and therefore K will change

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Practice Problem

• Consider the effect of temperature changes on the
  following equilibria.
• Does the concentration of NOCl increase or
  decrease at equilibrium as the temperature of the
  system is increased?
• 2NOCl(g) ?? 2NO(g) Cl2(g) ?H 77.1kJ
• Does the concentration of SO3 increase or
  decrease when the temperature increases?
• 2SO2(g) O2(g) ?? 2SO3(g) ?H -198 kJ

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Effect of Addition or Removal of Reactant/Product

• If the concentration of a reactant or product is
  changed from its equilibrium value at a given
  temperature, equilibrium will be reestablished
  eventually. The value of K will still be the
  same!

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Practice Problem

• Equilibrium exists between butane and isobutane
  when butane 0.020M and isobutane 0.050M.
  What are the concentrations of butane and
  isobutane, after equilibrium has been
  established, if 0.0200 mol/L of isobutane is
  added to the original mixture? K 2.50

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Effect of Volume Changes on Gas-Phase Equilibria

• The stress of a volume decrease (pressure
  increase) will be counterbalanced by a change in
  the equilibrium composition to one having a
  smaller number of gas molecules.
• For a volume increase (pressure decrease), the
  equilibrium will shift toward the side of rxn
  with the greater number of gas molecules.
• If there is no change in the number of gas
  molecules in the reaction, then a volume change
  will have no effect.

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Practice Problem

• The formation of ammonia from its elements is an
  important industrial process.
• 3H2(g) N2(g) ?? 2NH3(g)
• How does the equilibrium composition change when
  extra H2 is added? When extra NH3 is added?
• What is the effect on the equilibrium when the
  volume of the system is increased? Does the
  equilibrium composition change or is the system
  unchanged?

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Homework

• After reading sections 15.4-15.6, you should be
  able to do the following
• P. 583b-c (13-31 odd)