The Reaction Gibbs Energy

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					                   The Reaction Gibbs Energy


• Consider the chemical equilibrium: A  B
• rG = B - A
    – rG is the reaction Gibbs Energy
    – The reaction Gibbs energy is given by the difference in the chemical
      potentials of products and reactants at the composition of the reaction
      mixture
• rG = 0 when system is at equilibrium at constant T and P
    – This occurs when the chemical potentials of products and reactants
      are equal
• The chemical potentials vary with composition
• Equilibrium is established at a certain composition –the
  equilibrium composition

                                  Chapter 6                                 1
             Exergonic and Endergonic Reactions


• For a reaction at constant temperature and pressure:
• If rG < 0 , the forward reaction is spontaneous
    – Exergonic reaction (exergonic means work-producing)
• If rG > 0 , the reverse reaction is spontaneous
    – Endergonic reaction   (work-consuming)
•   If rG = 0 , the reaction is at equilibrium




                                Chapter 6                   2
                       Chemical Reactions


• Consider the chemical reaction: aA  bB
• rG = bB - aA
   – B = B° + RT ln aB
   – A = A° + RT ln aA
• rG = bB° + bRT ln aB - aA° - aRT ln aA
• rG = rG° + RT ln (aBb/aAa)
   – rG° is the standard Gibbs energy of reaction
   – The standard Gibbs energy is given by the difference in chemical
     potentials of products and reactants
• rG = rG° + RT ln Q
   – Q is the activity quotient
   – The activity quotient has the form Q = Activities of products divided
     by activities of reactants

                                 Chapter 6                               3
                    The Equilibrium Constant


• rG = 0 at equilibrium for a reaction at constant T and P
• Thus, 0 = rG° + RT ln Q
• rG° = -RT ln K
    – K =Q at equilibrium
• rG° is a function of temperature only
    – Independent of composition and pressure
• K is therefore a function of temperature only
    – For a given reaction, K is a true constant at a given temperature
    – K is called the thermodynamic equilibrium constant
    – K has the form: equilibrium activities of products divided by
      equilibrium activities of reactants


                                  Chapter 6                               4
                       Determination of K
                   from Thermodynamic Data

• rG° = -RT ln K
• For a reaction at 25 °C, rG° can be obtained from standard
  Gibbs energies of formation
• For a reaction at other temperatures, the standard Gibbs energy
  can be calculated from: rG° = rH° -TrS°
    – rH° is calculated from standard heats of formation
    – rS° is calculated from standard entropies
    – Reaction enthalpies and entropies can generally be assumed to be
      independent of temperature




                                 Chapter 6                               5
      Directions of Reactions at Standard Conditions


• If rG° > 0 , then K < 1
    – Reaction is nonspontaneous at standard conditions (all reactants and
      products are at standard state)
• If rG° < 0 , then K > 1
    – Reaction is spontaneous at standard conditions (all reactants and
      products are at standard state)




                                  Chapter 6                               6
              Activities of Pure Solids and Liquids


• The activity quotient, Q, and the equilibrium constant, K, are
  expressions containing activities of products and reactants
• For a pure solid, ai = 1
    – ai is the activity of species i
    – ai is exactly 1 at standard pressure (1 bar)
    – The activity of a solid is virtually independent of pressure so the
      activity of a pure solid is very close to 1 at all pressures
• For a pure liquid, ai = 1
    – The activity is exactly 1 at standard pressure
    – The activity of a liquid varies insignificantly with pressure




                                   Chapter 6                                7
                           Activity of a Gas


• For a perfect gas, ai = pi / p°
    – pi is the partial pressure of gas i
    – p° is the standard pressure (1 bar or 1 atm)
    – Note, activity has no unit, so pi must be expressed in bar or atm
• For a real gas, the fugacity, fi , of the gas is used rather than its
  partial pressure
• With good approximation we can assume that a gas behaves as an
  ideal gas at low and moderate pressures
    – Partial pressures will be used in problems on gas equilibria




                                    Chapter 6                             8
             Activities for Components in Solution


• For solvent, aA = A XA
    – aA  1 as XA  1 (in dilute solution)
    – The activity of solvent is close to 1 in dilute solutions
• For solute, aB = B b/b°
    –   b is the molality of solute
    –   b° is 1mol/kg
    –   B is the activity coefficient
    –   B  1 as b  0 (in dilute solution)
• One can also express the solute activity in terms of its mole
  fraction: aB = B XB



                                    Chapter 6                     9
            The Response of Equilibria to Pressure


• The thermodynamic equilibrium constant, K, is independent of
  pressure
    – (K/P)T = 0
• The equilibrium composition in a gas mixture may be affected by a
  change in pressure caused by a change in volume
• Consider the gas phase equilibrium: A(g)  2B(g)
• K = pB2/pA
    – pA = partial pressure of A at equilibrium
    – pB = partial pressure of B at equilibrium




                                  Chapter 6                      10
           The Response of Equilibria to Pressure


• pA = XA P and pB = XB P          (Dalton’s Law)
    – P = total pressure
• K = (XBP)2/(XAP) = Kx P
    – Kx = XB2/XA
    – Kx is inversely proportional to P
    – The higher the pressure the smaller the Kx-value and the greater the
      mole fraction of A at equilibrium
• Generally, for a gas phase reaction:
• K = Kx (P)v
    – P = total pressure
    – v = moles of gaseous products – moles of gaseous reactants


                                  Chapter 6                                  11
       Change in Pressure – Le Chatelier’s Principle


• A system at equilibrium, when subjected to a disturbance ,
  responds in a way that tends to minimize the effect of the
  disturbance (Le Chatelier’s Principle)
• If a system at equilibrium is compressed, then the reaction will
  adjust so as to minimize the increase in pressure
    – It can do this by reducing the number of particles in the gas phase
    – This implies a shift towards the side with fewest number of moles of
      gas
• Note, an increase in pressure caused by the addition of an inert gas
  to a gas phase reaction at equilibrium, will not cause a shift
    – The partial pressures of the reacting gases are unaffected by the
      addition of an inert gas – reaction remains at equilibrium


                                  Chapter 6                                  12
    Change in Temperature – Le Chatelier’s Principle


• A system at equilibrium will tend to shift in in the endothermic
  direction if the temperature is raised
    – Energy is absorbed as heat in an endothermic process
• A system at equilibrium will tend to shift in the exothermic
  direction if the temperature is lowered
    – Energy is produced as heat in an exothermic reaction
• Endothermic reactions: increased temperature favors the products
• Exothermic reactions: increased temperature favors the reactants




                                 Chapter 6                           13
                      The van’t Hoff Equation


• d ln K /dT = rH°/ RT2      or
• d ln K / d(1/T) = - rH° / R
    – The van’t Hoff equation
    – d ln K /dT > 0  rH° > 0 (endothermic reaction)
    – d ln K /dT < 0  rH° < 0 (exothermic reaction)
• Integration between temp T1 and T2:
• ln (K2/K1) = -(rH°/R) (1/T2 – 1/T1)
    –   K2 = equilibrium constant at temperature T2
    –   K1 = equilibrium constant at temperature T1
    –   rH° assumed constant in temp. interval T1 to T2
    –   Equation is similar to the Clausius-Clapeyron equation


                                   Chapter 6                     14
 The Response of Equilibria To Change in Temperature


• Endothermic reactions shift to the right when the temperature is
  raised because K increases with increasing temperature
    – greater yield of products at high temperature
• Exothermic reactions shift to the left when the temperature is
  raised because K decreases with increasing temperature
    – lower yield of products at high temperature




                                 Chapter 6                           15