John A. Schreifels

1
Chapter 19

• Thermodynamics and Equilibrium

2
Overview

• First Law of Thermodynamics
• Spontaneous Processes and Entropy
• Entropy and the Second Law of Thermodynamics
• Standard Entropies and the Third Law of
  Thermodynamics
• Free Energy Concept
• Free Energy and Spontaneity
• Interpretation of Free Energy
• Free Energy and Equilibrium Constants
• Relating DG to the Equilibrium Constant
• Change of Free Energy with Temperature

3
First Law of Thermodynamics

• First law can be written as
• DE q w
• where q heat involved in the process and w
  work done by or to the system.
• Work can be electrical or pressure volume
• Work force acting over some distance w ? d x
  F (referenced to the system).
• During reactions often there is an expansion of
  gases against some pressure where pressure is
  equal to the force per unit area
• or .
• Work is obtained by substitution
• w ? d x F ? d x (PxA) or
• w ? P?V.
• The first law can be restated as E q ? P?V.

4
Energy and Enthalpy

• From the first law q ?E P?V.
• With no change in volume the equation simplifies
  to qV ?E.
• At constant pressure qP ?E P?V.
• There are times when both volume and pressure can
  change the heat involved in the reaction is then
  a more complicated function of ?E.
• Enthalpy the heat output at constant pressure.
  H E PV.
• In general, ?H ?E P?V V?P.
• At constant pressure, a change in enthalpy is
  given by
• ?H ?E P?V qP.
• Normally, ?H and ?E are fairly close to each
  other in magnitude. In the combustion of propane
  (see book), ?E ?2043 kJ, ?H ?2041 kJ and w
  ?P?V ?2kJ.

5
Spontaneous Processes

• Spontaneous process one that occurs without any
  continuous external influence it may not occur
  rapidly.
• E.g. combustion of hydrogen with oxygen
  spontaneous decomposition of water never occurs
  spontaneously.
• H2(g) O2(g) ? ½H2O(l)
• E.g.2 Weak acid
• HF(aq) H2O(aq)? F?(aq) H3O(aq) Ka
  3.52x10?4
• E.g. 3 Solubility of solids.
• AgCl(s) ? Ag(aq) Cl?(aq) Ksp 1.8x10?10
• Moves to equilibrium amounts of reactants and
  product.
• Rate of spontaneous change related to ratio of
  rate constants for forward and reverse reactions.
  
• Extent of reaction related to energy difference
  between forward and reverse reactions (?H).
• Goal Determine criteria necessary to predict
  spontaneity.

6
Enthalpy, Entropy, and Spontaneous Processes
Review.

• Negative value for enthalpy thought to be
  criterion for spontaneity since most reactions
  with negative ?H are spontaneous, but exceptions
  exist
• The reverse of the spontaneous reaction in not
  spontaneous. Reactions can only be spontaneous
  in one direction.
• Qc compared to Kc indicates the direction of the
  reaction (will be related to the thermodynamic
  quantity soon).
• E.g. determine the direction of reaction when
  0.100M acetic acid (Ka 1.75x10?5), 0.100 M
  sodium acetate, and 0.100 M HCl are mixed
  together.
• Solution LeChateliers principle says reaction
  shifted to the left. What about when the
  reaction is reversed?

7
ENTROPY

• Entropy thermodynamic quantity that is measure
  of randomness of system.
• All changes tend to increase in randomness
  (second law of thermodynamics).
• ?Stotal Sfinal ? Sinitial
• ?Stotal ?Ssys ?Ssurr ? 0.
• ?Ssys is sometimes negative, but is more than
  offset by ?Ssurr.
• ?S is positive for a transition from ordered to
  less ordered system (such as with melting and
  vaporization) and negative for the reverse.
• E.g. determine the sign of ?S for the following
  changes (what about the reverse of these?)
• N2(g) 3H2(g) ? 2NH3(g)
• CaCO3(s) ? Ca(s) CO2(g)
• H2(g) O2(g) ? H2O(l)
• H2O(l) ? H2O(s)

8
Entropy and the Second Law

• Second Law all systems tend towards an increase
  in the randomness of the system. In terms of
  entropy, the total entropy of the universe always
  increases.
• ?Stotal ?Ssys ?Ssurr ? 0.
• ?Srev ??Sfwd.
• ?S of phase change determined from heat of phase
  change. ?S ?H/T.
• E.g. Determine ?S of melting and vaporization
  for water. ?Hfus 6.0kJ/mol and ?Hvap 40.8
  kJ/mol.
• Generally, ?Sfus lt ?Svap. Entropy of s lt l lt g.
• Since ?S ?H/T, we can determine temperature of
  phase change (mp or bp) if ?H and ?S of phase
  change are known.
• E.g. Determine boiling point of chlorine if
  ?Hvap 6.41kJ/mol ?Svap 37.3 J/K?mol.

9
Entropy and Probability

• Randomness is related to the probability of
  finding a molecule in a particular microstate
• E.g. determine the probability of having
  perfectly order system (HH) when
• Two microstates (heads, H, and tails,T) of same
  exact energy (same likelihood of existing).
• Two particles. Then the possible states are HH,
  TT, TH, HT. Probability, P, of perfectly order
  system 25 (PHH 2-2100).
• E.g.2 determine PHHH for 3 particles.
• Possible states HHH, TTT, HHT, HTH, THH,
  HTT,THT, TTH. (PHHH 2-3100).
• Ludwig Boltzmann statistical approach to
  entropy, S, given by S k?lnW where k
  Boltzmann's const. R/N 1.38x10?23J/K.
• W total of ways that all atoms in a sample
  can be arranged and still have same energy.
• E.g. Determine molar entropy of CO (2 states)
  and HCl (1 state) molecules in a crystal.

10
Entropy and Probability

• Third Law perfectly ordered crystal has zero
  entropy.
• entropy change when molecules filling a container
  after expansion is related probability of this
  expansion and is given by the relationship
  (constant T and n)
• E.g. determine the entropy change that occurs
  when a gas expands to twice its initial volume.
• E.g.2 twice its initial pressure.

11
Entropy and Temperature

• At absolute zero there is no molecular motion and
  the S of a perfectly order system is zero.
• Entropy expressed in absolute quantities.
• Entropy increases with temperature.
• Entropy increases dramatically as the melting and
  boiling points.
• Standard Molar Entropies, So, ?So.
• Standard molar entropy, So entropy of 1 mol of a
  compound at 1 atm and 25C.
• Entropy of a compound is the total entropy. Not
  relative to the reference state.
• As with ?Ho it is convenient to present all
  entropies at reference set of conditions.
• As with ?Ho, ?So of the reaction can be
  determined. For general reaction
• aA bB cC ... ? mM nN oO ...
• ?So (mSM nSN ...) ? (aSA bSB ...).
• E.g. determine ?So of the reaction using data in
  the table from the text.
• NH3(g) ? 3/2 H2(g) ½ N2(g)

12
GIBB'S FREE ENERGY

• Spontaneity can also be expressed without ?Ssurr.
  
• Recall ?Stotal ?Ssys ?Ssurr ? 0 and
• ?Ssurr ??H/T.
• Combining ?Stotal ?Ssys ? ?H/T ? 0 or
• ?T?Stotal ?G ?H ? T?Ssys ? 0
• Gibb's Free Energy, ?G and in general terms is G
  H ? TS. Criterion for spontaneity is ?G ? 0.
  Always found to be true.
• If ?H and ?S are known, spontaneity of reaction
  can be determined.
• Possible signs of enthalpy and entropy
• E.g. determine ?Go for the melting of water.
  ?Ho 6.03 kJ/mol ?So 22.1 J/K at ?10C.

13
?G Temperature Dependence

• Spontaneity Reaction becomes spontaneous when ?G
  goes from to ?. We use ?G 0 to tell us when
  reaction just becomes spontaneous or 0 ?H ? T?S
  or T ?H/?S.
• E.g. determine the temperature at which the
  synthesis of HI(g) becomes spontaneous.
• ?Ho 52.96 kJ and ?So 166.4 J/mol
• H2(g) I2(g) ? 2HI(g)

14
Standard Free Energy Changes for Reactions

• Free Energy is a state function and an extensive
  property so that its value is dictated by the
  number of moles appearing in the equation.
• ½ N2(g) 3/2 H2(g) ? NH3(g) ?Go ?16.5 kJ
• N2(g) 3 H2(g) ? 2 NH3(g) ?Go ?33.0 kJ

15
Standard free energies of formation, DGfO.

• ?Go 0 for elements in most stable form (as with
  enthalpy).
• Free Energies are listed in tables and can be
  used to determine ?G of reaction and spontaneity.
• For general reaction aA bB cC ... ? mM nN
  oO ...
• E.g. Determine ?G for
• 4NH3(g) 5O2(g)? 4NO(g) 6H2O(g).
• As with enthalpy reactions can be coupled to
  determine ?G for unknown reaction.
• Determine ?G Fe2O3(s) 3/2C(g) ? 3/2CO2
  2Fe(s).
• Given
• Fe2O3(s) ? 2Fe(s) 3/2O2(g) ?Go 742 kJ
• 3/2 C(gr) 3/2O2(g) ? 3/2CO2(g) ?Go ?592 kJ.

16
EQUILIBRIUM CONSTANTS AND ?G

• Equilibrium constant for a reaction aA bB ...
  ? mM nN ... is defined as
• Tells how far to right reaction proceeds.
• Large value ? mostly products.
• Small value ? mostly reactants.
• At equilibrium this equation must always be
  obeyed no matter what relative amount of reactant
  and was started with.
• Reaction quotient, Q, defined in same way as K
  but refers to some initial condition that might
  not be at equilibrium.
• These two are related to ?G by the equation
• ?G RTln(Q/K).
• When Q K equilibrium exists and ?G 0.

17
EQUILIBRIUM CONSTANTS AND DG

• K and Q often separated by rewriting
• ?G ?Go RTlnQ and ?Go ?RTlnK.
• From initial conditions and ?Go, the free energy
  of the reaction can be determined.
• E.g. determine ?G at 25C for the reaction
• H2O(l) ? H (aq) OH?(aq) if the concentration
  of H 1.00x10?5 M OH? 1.00x10?5 M
• K can be determined under standard conditions if
  ?G is known.
• E.g. Determine K for 3NO(g) ? N2O(g) NO2(g)
• E.g.2 Determine K for NH4NO3(s) ? N2O(g)
  2H2O(g).
• ?Go can be determined if K is known.
• E.g. determine ?Go for the solubility of AgCl(s)
  if its Ksp 1.8x10?10
• E.g. 2 determine ?Go for ionization of HF in
  water. Ka 3.5x10?4.