Chemistry 100 Chapter 19

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Chemistry 100 Chapter 19

• Spontaneity of Chemical and Physical Processes
  Thermodynamics

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What Is Thermodynamics?

• Study of the energy changes that accompany
  chemical and physical processes.
• Based on a set of laws.
• In chemistry, a primary application of
  thermodynamics is as a tool to predict the
  spontaneous directions of a chemical reaction.

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What Is Spontaneity?

• Spontaneity refers to the ability of a process to
  occur on its own!
• Waterfalls
• Though the course may change sometimes, rivers
  always reach the sea Page/Plant Ten Years
  Gone.
• Ice melts at room temperature!

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The First Law of Thermodynamics

• The First Law deals with the conservation of
  energy changes.
• ?E q w
• The First Law tells us nothing about the
  spontaneous direction of a process.

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Entropy and Spontaneity

• Need to examine
• the entropy change of the process as well as its
  enthalpy change (heat flow).
• Entropy the degree of randomness of a system.
• Solids highly ordered ? low entropy.
• Gases very disordered ? high entropy.
• Liquids entropy is variable between that of a
  solid and a gas.

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Entropy Is a State Variable

• Changes in entropy are state functions
• ?S Sf Si
• Sf the entropy of the final state
• Si the entropy of the initial state

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Entropy Changes for Different Processes

• ?S gt 0 entropy increases (melting ice or making
  steam)
• ?S lt 0 entropy decreases (examples freezing water
  or condensing steam)

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The Solution Process

• For the dissolution of NaCl (s) in water
• NaCl (s) ? Na(aq) Cl-(aq)

Highly ordered low entropy
Disordered or random state high entropy
The formation of a solution is always accompanied
by an increase in the entropy of the system!
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The Entropy Change in a Chemical Reaction

• Burning ethane!
• C2H6 (g) 7/2O2 (g) ? 2CO2 (g) 3H2O (l)
• The entropy change
• ?rS? ? ? np S? (products) - ? nr S? (reactants)
• np and nr represent the number of moles of
  products and reactants, respectively.

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The Entropy Change (Contd)

• For the ethane combustion reaction
• 1 C2H6 (g) 7/2 O2 (g) ? 2 CO2 (g) 3 H2O (l)
• ?rS? ? ? np S?(products) - ? nr S?(reactants)
• 3 S? H2O (l) 2 S? CO2 (g) - (7/2 S?
  O2(g) 1 S? C2H6 (g) )

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Finding S? Values

• Appendix C in your textbook has entropy values
  for a wide variety of species.
• Units for entropy values ? J / (K mole)
• Temperature and pressure for the tabulated values
  are 298.2 K and 1.00 atm.

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Finding S? Values

• Note entropy values are absolute!
• Note the elements have NON-ZERO entropy values!
  
• e.g., for H2 (g)
• ?fH? 0 kJ/mole (by defn)
• S? 130.58 J/(K mole)

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Some Generalizations

• For any gaseous reaction (or a reaction involving
  gases).
• ?ng gt 0, ?rS? gt 0 J/(K mole).
• ?ng lt 0, ?rS? lt 0 J/(K mole).
• ?ng 0, ?rS? ? 0 J/(K mole).
• For reactions involving only solids and liquids
  depends on the entropy values of the substances.

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The Second Law of Thermodynamics

• The entropy of the universe (?univS) increases in
  a spontaneous process.
• ?univS unchanged in an equilibrium process

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What is ?univS?

• ?univS ?sysS ?surrS
• ?sysS the entropy change of the system.
• ?surrS the entropy change of the surroundings.

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How Do We Obtain ?univS?

• We need to obtain estimates for both the ?sysS
  and the ?surrS.
• Look at the following chemical reaction.
• C(s) 2H2 (g) ? CH4(g)
• The entropy change for the systems is the
  reaction entropy change, ?rS?.
• How do we calculate ?surrS?

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Calculating ?surrS

• Note that for an exothermic process, an amount of
  thermal energy is released to the surroundings!

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• A small part of the surroundings is warmed
  (kinetic energy increases).
• The entropy increases!

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Calculating ?surrS

• Note that for an endothermic process, thermal
  energy is absorbed from the surroundings!

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• A small part of the surroundings is cooled
  (kinetic energy decreases).
• The entropy decreases!
• For a constant pressure process
• qp ?H
• ?surrS ? ?surrH
• ?surrS ? -?sysH

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• The entropy of the surroundings is calculated as
  follows.
• ?surrS -?sysH / T
• For a chemical reaction
• ?sysH ?rH?
• ?surrS -?rH?/ T

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The Use of ?univS to Determine Spontaneity

• Calculation of T?univS ? two system parameters
• ?rS?
• ?rH?
• Define a system parameter that determines if a
  given process will be spontaneous?

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The Definition of the Gibbs Energy

• The Gibbs energy of the system
• G H TS
• For a spontaneous process
• ?sysG Gf G i
• Gf the Gibbs energy of the final state
• Gi the Gibbs energy of the initial state

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Gibbs Energy and Spontaneity

• ?sysG lt 0 - spontaneous process
• ?sysG gt 0 - non-spontaneous process (note that
  this process would be spontaneous in the reverse
  direction)
• ?sysG 0 - system is in equilibrium

Note that these are the Gibbs energies of the
system under non-standard conditions
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Standard Gibbs Energy Changes

• The Gibbs energy change for a chemical reaction?
• Combustion of methane.
• CH4 (g) 2 O2 (g) ? CO2 (g) 2 H2O (l)
• Define
• ?rG? ? np ?fG? (products) - ? nr ?fG?
  (reactants)
• ?fG? the formation Gibbs energy of the substance

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The Gibbs Energy Change (contd)

• For the methane combustion reaction
• 1 CH4(g) 2 O2(g) ? 1 CO2(g) 2 H2O(l)
• ?rG? ? np ?fG? (products) - ? nr ?fG?
  (reactants)
• 2 ?fG? H2O(l) 1 ?fG? CO2(g) - (2 ?fG?
  O2(g) 1 ?fG? CH4(g) )

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Gibbs Energy Changes

• ?fG? (elements) 0 kJ / mole.
• Use tabulated values of the Gibbs formation
  energies to calculate the Gibbs energy changes
  for chemical reactions.

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The Third Law of Thermodynamics

• Entropy is related to the degree of randomness of
  a substance.
• Entropy is directly proportional to the absolute
  temperature.
• Cooling the system decreases the disorder.

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The Third Law of Thermodynamics

• The Third Law - the entropy of any perfect
  crystal is 0 J /(K mole) at 0 K (absolute 0!)
• Due to the Third Law, we are able to calculate
  absolute entropy values.

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• At a very low temperature, the disorder
  decreases to 0 (i.e., 0 J/(K mole) value for S).
• The most ordered arrangement of any substance is
  a perfect crystal!

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Applications of the Gibbs Energy

• The Gibbs energy is used to determine the
  spontaneous direction of a process.
• Two contributions to the Gibbs energy change (?G)
• Entropy (?S)
• Enthalpy (?H)
• ?G ?H - T?S

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Spontaneity and Temperature
?H ?S ?G
lt 0 at high temperatures
- gt 0 at all temperatures
- lt 0 at all temperatures
- - lt 0 at low temperatures
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Gibbs Energies and Equilibrium Constants

• ?rG? lt 0 - spontaneous under standard conditions
• ?rG? gt 0 - non-spontaneous under standard
  conditions

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The Reaction Quotient

• Relationship between QJ and Keq
• Q lt Keq
• - reaction moves in the forward direction
• Q gt Keq
• - reaction moves in the reverse direction
• Q Keq
• - reaction is at equilibrium

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• ?rG refers to standard conditions only!
• For non-standard conditions - ?rG
• ?rG lt 0 - reaction moves in the forward
  direction
• ?rG gt 0 - reaction moves in the reverse direction
• ?rG 0 - reaction is at equilibrium

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Relating K to ?rG?

• ?rG ?rG? RT ln Q
• ?rG 0 ? system is at equilibrium
• ?rG? -RT ln Qeq
• ?rG? -RT ln Keq

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Phase Equilibria

• At the transition (phase-change) temperature only
  - ?trG 0 kJ
• tr transition type (melting, vapourization,
  etc.)
• ?trS ?trH / Ttr