# 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

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