CHEMICAL EQUILIBRIUM

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CHEMICAL EQUILIBRIUM

• Chapter 7

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Chemical equilibrium

• Chemical reactions tend to move towards a dynamic
  equilibrium in which both reactants and products
  are present but have no further tendency to
  undergo net change.

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Spontaneous chemical reactions

• The direction of spontaneous change at constant
  temperature and pressure is towards lower values
  of Gibbs energy.
• This idea also applies to chemical reactions.
• If we can calculate the minimum value of the
  Gibbs energy for a particular reaction mixture,
  this corresponds to the location of the
  equilibrium composition.

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Spontaneous chemical reactions

• The quantity x (xi) is called the extent of the
  reaction and has units of moles.

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Spontaneous chemical reactions

• The reaction Gibbs energy DrG is defined as the
  slope of the Gibbs energy plotted against the
  extent of reaction

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Spontaneous chemical reactions
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Spontaneous chemical reactions
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Exergonic and endergonic reactions

• We can express the spontaneity of a reaction at
  constant temperature and pressure in terms of the
  reaction Gibbs energy.
• If DrG lt 0, the forward reaction is spontaneous
• If DrG gt 0, the reverse reaction is spontaneous
• If DrG 0, the reaction is at equilibrium

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Exergonic and endergonic reactions

• If a reaction for which DrG lt 0 is called
  exergonic.
• Because the process is spontaneous it can be used
  to drive another process, such as another
  reaction, or used to do non-expansion work.

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Exergonic and endergonic reactions

• In biological cells, the oxidation of
  carbohydrates acts as the heavy weight that
  drives other reactions such as formation of
  proteins from amino acids, muscle contractions
  and brain activity.

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Exergonic and endergonic reactions

• If a reaction for which DrG gt 0 is called
  endergonic.
• The reaction is not spontaneous and can only
  proceed by doing work on it, such as
  electrolyzing water to reverse its spontaneous
  formation reaction.

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Equilibrium
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Equilibrium
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Equilibrium
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Equilibrium

• A stoichiometric number is positive for products
  and negative for reactants

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Equilibrium

• If x changes by Dx, then the change in the amount
  of of any species J is nJDx

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Equilibrium

• If initially there is 10 mol of N2 present, when
  the extent of reaction changes from x 0 to x
  1 (so Dx 1 mol), the amount of N2 changes from
  10 mol to 9 mol.

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Equilibrium

• When Dx 1 mol, the amount of NH3 changes by 2
  mol and the amount of H2 changes by -3 mol.

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Equilibrium

• When Dx 10 mol, all the N2 is consumed.

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Equilibrium
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Equilibrium
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Equilibrium

• An equilibrium constant K expressed in terms of
  activities is called a thermodynamic equilibrium
  constant.
• Activities are dimensionless numbers so the
  thermodynamic equilibrium constant is also
  dimensionless.

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Equilibrium

• In elementary applications, activities can be
  replaced by numerical values of molalities,
  molarities or partial pressures.
• The resulting expressions are only
  approximations.

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Equilibrium

• In elementary applications, Kg 1 so K Kb

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How equilibria respond to pressure

• The equilibrium constant depends on the value of
  DrG?, which is defined at a single, standard
  pressure. Hence K is independent of the pressure.

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How equilibria respond to pressure

• The conclusion that K is independent of pressure
  does not necessarily mean that the equilibrium
  composition is independent of the pressure.
• It depends on how pressure is applied.

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How equilibria respond to pressure

• Consider a reaction vessel in which the pressure
  in the vessel is increased by injecting an inert
  gas.
• The presence of another gas does not alter the
  equilibrium composition because the partial
  pressure of each reacting gas molecules does not
  changed upon addition of the inert gas.

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How equilibria respond to pressure

• If however, the pressure is increased by
  confining the gases to a smaller volume.
• Consider the reaction A ?? 2B.

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How equilibria respond to pressure

• Consider the reaction A ?? 2B.

• For the right hand side of the equation to remain
  constant, pA must increase sufficiently to cancel
  out the increase in the square of pB.

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How equilibria respond to pressure

• Consider the reaction A ?? 2B.

• In order for pA to increase sufficiently, the
  equilibrium composition must shift in favor of A
  at the expense of B. The number of A molecules
  will increase as the volume is decreased.

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How equilibria respond to pressure

• The increase in the number of A molecules and the
  corresponding number B molecules in the
  equilibrium A ?? 2B is a special case of a Le
  Chateliers principle that states
• A system at equilibrium, when subject to a
  disturbance, responds in a way that tends to
  minimize the effect of the disturbance.

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How equilibria respond to pressure

• The principle implies that, if a system at
  equilibrium is compressed, then the reaction will
  adjust to minimize the pressure. It does this by
  reducing the number of particles in the gas
  phase.

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How equilibria respond to pressure

• Suppose that there is an amount n of A present
  initially (no B). At equilibrium the amount of A
  is (1-a)n and the amount of B is 2an, where a is
  the extent of dissociation of A into 2B.

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How equilibria respond to pressure

• So even though K is independent of pressure, the
  amounts of A and B do depend on pressure.

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How equilibria respond to temperature

• Le Chateliers principle predicts that a system
  at equilibrium will tend to shift in the
  endothermic direction if the temperature is
  raised.
• Conversely, an equilibrium can be expected to
  shift in the exothermic direction if the
  temperature is lowered.

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How equilibria respond to temperature

• Exothermic reactions increased temperature
  favors the reactants.
• Endothermic reactions increased temperature
  favors the products.

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How equilibria respond to temperature

• The vant Hoff equation (Justification 7.2), is
  an expression for the slope of a plot of the
  equilibrium constant as a function of
  temperature.

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How equilibria respond to temperature

• For an exothermic reaction, dlnK/dT lt 0. The
  negative slope means that ln K, and therefore K
  itself, decreases as the temperature rises.
• If K decreases, then equilibrium shifts away from
  products.

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How equilibria respond to temperature

• For an exothermic reaction, DrH?/T is negative
  and corresponds to the increase of entropy in the
  surroundings.
• Increasing entropy drives a spontaneous change.

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How equilibria respond to temperature

• When the temperature is increased, DrH?/T
  decreases and so the decreasing entropy of the
  surroundings has less importance, so there is
  less driving force for the forward reaction and
  reactants are favored.

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How equilibria respond to temperature

• For an endothermic reaction, DrH?/T is positive
  and corresponds to the decrease of entropy in the
  surroundings.
• Driving force is the increase of entropy in the
  system.

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How equilibria respond to temperature

• When the temperature is increased, DrH?/T gets
  smaller. This corresponds to less loss of entropy
  in the surroundings.
• This favors a shift towards reaction products.

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How equilibria respond to temperature

• If we assume DrH? varies little with temperature
  over the temperature range of interest, then we
  can take it outside the integral.

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Calculating an equilibrium constant

• Calculate the equilibrium constant for the
  reaction N2 3H2 ?? 2NH3 at 298 K.

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Calculating an equilibrium constant

• Calculate the equilibrium constant for the
  reaction N2 3H2 ?? 2NH3 at 298 K.

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Calculating an equilibrium constant

• Calculate the equilibrium constant for the
  reaction N2 3H2 ?? 2NH3 at 298 K.

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Calculating degree of dissociation

• The standard Gibbs energy of reaction for the
  decomposition H2O(g) ? H2(g) ½ O2(g) is 118.08
  kJ mol-1 at 2300 K. What is the degree of
  dissociation of H2O at 2300 K and 1.00 bar?

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Calculating degree of dissociation

• The standard Gibbs energy of reaction for the
  decomposition H2O(g) ? H2(g) ½ O2(g) is 118.08
  kJ mol-1 at 2300 K. What is the degree of
  dissociation of H2O at 2300 K and 1.00 bar?

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Equilibrium electrochemistry

• An electrochemical cell consists of two
  electrodes, in contact with an electrolyte.
• An electrolyte is a material that allows the
  transport of charged species or an ionic
  conductor. This may be a solution, a liquid, or a
  solid.
• An electrode and its electrolyte comprise an
  electrode compartment.

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Equilibrium electrochemistry

• There are a number of electrode configurations.
• A common electrode configuration consists of a
  metal that participates in the electrochemical
  reaction i.e. M(s)M(aq) metal/metal ion
  electrode type.
• An inert metal may make up one of the
  electrodes but is only present as a source or
  sink of electrons. It takes no other part in the
  reaction other than acting as a catalyst for it
  i.e. Pt(s)X2(g)X(aq) or Pt(s)X2(g)X(aq)
  gas electrode.

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Equilibrium electrochemistry

• M(s)MX(s)X-(aq) Metal/insoluble salt
• Pt(s)M(aq)M2(aq) - redox electrode.
• Redox Reduction Oxidation
• OIL RIG
• A redox reaction implies the transfer of
  electrons.
• Oxidizing agent (or oxidant) is the electron
  acceptor.
• Reducing agent (or reductant) is the electron
  donor.
• A redox equation may be expressed in terms of two
  half reactions. One oxidation reaction and one
  reduction equation.

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• A galvanic cell is an electrochemical cell that
  produces electricity as a result of a spontaneous
  reaction.
• An electrolytic cell is an electrochemical cell
  in which a non-spontaneous reaction is driven by
  an external source of current.
• Potential difference

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Varieties of cells

• The simplest type of cell has a single
  electrolyte common to both electrodes.
• In some cases it is necessary to immerse the
  electrodes in different electrolytes as in the
  Daniell cell in which the redox couple at one
  electrode is Cu2/Cu and at the other is Zn2/Zn.
  

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• Zn(s) ? Zn2(aq) 2e-
• Cu2(aq) 2e- ? Cu(s)
• Copper is the cathode
• Zinc is the anode

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Liquid junction potentials

• In a cell with two different electrolyte
  solutions, as in the Daniell cell, there is an
  additional source of potential difference across
  the interface of the two electrolytes.
• This potential is called the liquid junction
  potential, Elj.
• A way to reduce this potential is to use a salt
  bridge to join the electrolyte compartments.

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Notation

• Phase boundaries are represented by vertical bars
  
• CuSO4(aq)Cu(s)
• A liquid junction is represented by 3 vertical
  dots
• A double vertical line denotes an interface in
  which it is assumed the junction potential has
  been eliminated.
• Zn(s)ZnSO4(aq)CuSO4(aq)Cu(s)
• Convention is to write the anode half cell first
  and the cathode half cell second.

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The electromotive force

• The electric current produced by a galvanic cell
  arises from a spontaneous chemical reaction
  taking place inside it.
• Zn(s)ZnSO4(aq)CuSO4(aq)Cu(s)
• The cathode is where reduction takes place and
  the anode is where oxidation takes place
• Right hand electrode Cu2(aq) 2e- ? Cu(s)
• Left hand electrode Zn(s) ? Zn2(aq) 2e-

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The Nernst equation

• A cell in which the overall cell reaction has not
  reached chemical equilibrium can do electrical
  work as the reaction drives electrons through an
  external circuit.
• The work that a given transfer of electrons can
  depends on the potential difference between the
  two electrodes.
• The cell potential is measured in volts, V.
• -nFE DrG (Justification 7.3)
• n is the stoichiometric coefficient of the
  electrons in the half reactions, F is Faradays
  constant, and E is the emf.

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The Nernst equation

• E? - standard EMF of a cell.

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The Nernst equation
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Cells at equilibrium
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Cells at equilibrium

• For a Daniell cell Cu2(aq) Zn(s) ? Cu(s)
  Zn2(aq)
• n 2 and the standard emf is 1.10 V

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Cells at equilibrium

• For a Daniell cell Cu2(aq) Zn(s) ? Cu(s)
  Zn2(aq)
• n 2 and the standard emf is 1.10 V

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Standard Potentials

• A galvanic cell is a combination of two
  electrodes and each one can be considered as
  making a characteristic contribution to the
  overall cell potential.
• It is not possible to measure the contribution of
  a single electrode, so we measure the potential
  of electrodes by defining the standard hydrogen
  electrode (SHE) to be zero and then measure the
  electrode of interest in combination with the
  SHE.
• Pt(s)H2(g)H(aq) E? 0 V

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Standard Potentials

• For two redox couples Ox1/Red1 and Ox2/Red2
• Red1Ox1Red2Ox2 E? E?2 E?1
• Red1 Ox1 ? Ox2 Red2 is spontaneous if E? gt 0
• If E? lt 0 then work has to be done on the system
  for the reaction occur as written.

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Standard Potentials

• Pt(s)H2(g)H(aq)Cu2(aq)Cu(s) E?
  0.34 V
• Pt(s)H2(g)H(aq)Zn2(aq)Zn(s) E? -0.76
  V

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Determining other thermodynamic functions