Thermodynamics

1
Thermodynamics

• Spontaneity, Entropy, and Free Energy

2
First Law of Thermodynamics

• Law of Conservation of Energy
• Energy can change forms
• Not lost, but changed
• Discuss things like
• How much energy is exchanged?
• Where does the energy go? (calorimeter)
• What form is the energy?

3
Spontaneous Processes

• A process is spontaneous if it occurs without
  outside intervention.
• We discuss the direction of the reaction
• Says nothing of the kinetics or rate
• For example
• A ball rolls down hill, but never spontaneously
  rolls uphill.
• Iron exposed to water rusts. Rust does not
  spontaneously turn into iron
• A container will fill uniformly with a gas the
  gas does not spontaneously pool at one end.

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Spontaneous Processes

• Spontaneous processes are those that can proceed
  without any outside intervention.
• The gas in vessel B will spontaneously effuse
  into vessel A, but once the gas is in both
  vessels, it will not spontaneously return to
  vessel B.

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Kinetics The reaction pathway
Thermodynamics the initial and final states
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2nd Law of Thermo

• Entropy in the universe is increasing
• The driving force for spontaneous processes is an
  increase in Entropy
• Natural tendency is to go from ordered to
  disordered
• Take a deck of cards. Throw them into air. When
  you put them back, what are the chances they are
  all in order?
• But there is a chance, however unlikely.

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2nd Law

• Entropy is a function that describes the number
  of possible arrangements
• Available to a particular system
• Nature proceeds toward the states that have the
  highest probability of existing
• The driving force is probability

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Lets Look at a Simple System

• Four atoms of an ideal gas
• Three possible arrangements
• How many ways can each state be achieved?

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Examine All Possibilities (Pg 795)
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Possibilities

• The arrangement with two on each side is most
  likely to occur

By the ratio of 641
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Probability of finding all the Molecules in the
Left Bulb as a function of the total number of
molecules
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Unlikely to Occur
1 in 10 or not likely to occur
2 x 1023
But it is possible!
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Positional Entropy

• A gas expands into a vacuum
• Because the expanded state has the highest
  positional probability or entropy of all the
  states available to the gas
• Illustrated by changes of state
• The larger the intermolecular distances, the more
  states available
• The more states, the more entropy

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Coffee Cup

• Explain on a molecular level how a hot cup of
  coffee cools to room temperature

What is the possibility of this whole process
going in reverse?
But it is possible! Next time your coffee is
cold, just wait for it to get hot.
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Entropy on the Molecular Scale

• Ludwig Boltzmann described the concept of entropy
  on the molecular level.
• Temperature is a measure of the average kinetic
  energy of the molecules in a sample.

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Entropy on the Molecular Scale

• Molecules exhibit several types of motion
• Translational Movement of the entire molecule
  from one place to another.
• Vibrational Periodic motion of atoms within a
  molecule.
• Rotational Rotation of the molecule on about an
  axis or rotation about ? bonds.
• All of these are considered microstates of a
  system.

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Entropy on the Molecular Scale

• Each molecule has a specific number of
  microstates, W, associated with it.
• Entropy is
• S k lnW
• where k is the Boltzmann constant, 1.38 ? 10?23
  J/K.

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Entropy on the Molecular Scale

• The change in entropy for a process, then, is
• ?S k lnWfinal ? k lnWinitial

• Entropy increases with the number of microstates
  in the system.

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Standard Entropies

• Larger and more complex molecules have greater
  entropies.

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Entropy

• Kinetic-molecular view
• For an ideal gas at one atmosphere of pressure,
  as the temperature is lowered, the volume will be
  reduced.
• At 0 K, the molecules will have no energy of
  motion.
• There is only one possible arrangement for the
  molecules.

Ideal gas at one atm and 0 K.
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Entropy and temperature

• The entropy of an ideal gas at constant pressure
  increases with increasing temperature.
• This is because the volume increases.

0 K T1 T2 T3
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Entropy and temperature

• There are other reasons for entropy to increase
  with increasing temperature.
• Increased temperature will result in a greater
  distribution of molecular speeds.

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Entropy and temperature

• Increased temperature also results in more energy
  levels in atoms and molecules being occupied.
• For molecules,
• this means that
• they will be able
• rotate and their
• bonds can vibrate.
• This further
• increases entropy.

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Examples of Entropy

• What has more entropy
• Gas or liquid?
• Solid or liquid?
• Homogeneous solution or separate mixture
• sugar dissolved in water or sugar and water
• The more random or lack of order
• The more entropy
• Do you have it?
• Iodine vapor condensing on cold glass?
• Gas at 1 atm or 1 x 10-2 atm?
• ?S Sfinal Sintial

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2nd Law Restated

• In any spontaneous process, there is always an
  increase in the entropy of the universe
• ?Suniverse ?Ssystem ?Ssurroundings
• If ?S univ gt 0, process is spontaneous.
• If ?S univ lt 0, process is non-spontaneous. The
  process is spontaneous in the other direction.
• If ?S univ 0, process has no tendency to occur
  or is at equilibrium.

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How can complex molecules assemble in a bacteria?

• The created order is in the bacteria. The energy
  needed for this activity is supplied from an
  external source.
• The Universe gains entropy while the cell is
  organized.
• Most of our energy comes from the sun. The
  constant influx of energy supplies the energy to
  overcome entropy. for the time being!

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The Sun is Entropic!

• Stars produce light in all directions
• This energy is spread through the universe
• Sounds entropic
• Think about a star that is 1 million light years
  away.

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Star
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Star
Further away
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Chaos Theory

• Chaotic events tend to organize themselves
• Best example is a whirlpool. (toilet)
• The particles organize themselves in order to
  become disorganized more efficiently

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How can we determine if a process is spontaneous?

• ?Suniverse ?Ssystem ?Ssurroundings
• The sign of ?Ssurr depends on direction of heat
  flow
• exothermic process adds energy to the universe
• The universe now has more random motion
• So the universe experiences an increase in
  entropy
• ?Suniverse gt 0 or positive.

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?Ssurrounding

• Magnitude of ?Ssurr depends on the temperature
• If the surroundings have a low temp, additional
  energy makes a big difference
• If the surroundings have a high temperature,
  additional heat does not add much more energy
  (entropy) it has little effect.
• (little change, small ?Ssurr)

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Entropy Continued

• The tendency for a system to lower its energy
  becomes more important at lower temperatures.

Driving Force Provided by energy flow
Magnitude of the Entropy change of The
surroundings
Quantity of heat (J) temperature (K)
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Entropy depends on Enthalpy

• The change in Enthalpy, ?H, which is the
  direction and magnitude of heat exchanged
• Energy of system is proportional to its temp in
  kelvin in an isothermal system.

J - ?H ?Ssurr K T
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Spontaneity
?S system ?S Surrounding ?S Universe Spontaneous?
Yes
- - - No (process in opposite direction
- ? Yes if ?Ssys gt ?Ssurr
- ? Yes if ?Ssys lt ?Ssurr
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Gibbs Free Energy

• There is a war between
• order and disorder
• Enthalpy and Entropy
• The sun is the source of our energy
• It drives our enthalpic world
• If the sun were to stop, how long would live
  still exist.
• In a million years would things still look the
  same?

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G H - T S

• This war can be described mathematically
• G is Gibbs Free Energy
• Gibbs Free Energy is the energy free to do work
• We will use this to determine the force behind
  reactions
• Remember the second law!

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Free Energy

• G Gibbs Free Energy
• G H TS
• In processes where temp is constant
• ?G ?H - T ?S
• We are referring to the system
• No subscripts needed

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Free Energy

• ?G ?H - T ?Ssys If we divide by
  T
• -?G - ?H ?Ssys - ?H ?Ssurr
• T T T
  
• -?G ?Ssurr ?Ssys ?Suniv at
  constant T, P
• T
• At what value of ?G , is ?Suniv gt 0 or
  spontaneous

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Spontaneity Again

• Processes are spontaneous
• H2O(s) ? H2O (l)
• ?H 6.03 x 103 J/mol
• ?S 22.1 J/K mol
• If they have a positive ?Suniv
• If they have a negative ?G , at constant P,T
• ?G ?H - T ?Ssys
• Spontaneous processes have negative ?G

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Is Water Melting Spontaneous?

• Will this be spontaneous at -10, 0, or 10oC?
• H2O(s) ? H2O (l)
• ?H 6.03 x 103 J/mol
• ?S 22.1 J/K mol
• ?G ?H - T ?Ssys

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Calculate ?Sunv and ?G
?H 6.03 x 103 J/mol ?S 22.1 J/K mol ?G
?H - T ?Ssys
T (C) T K -?H ?Ssurr T ?S ?Ssurr?Sunv T?S X 103 ?G
-10 263 -22.9 -0.8 5.81 2.2 x102
0 273 -22.1 0 6.03 0
10 283 -21.3 0.8 6.25 - 2.2 x102
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• The spontaneity of the process depends on the temp

?S ?H Result
Positive Negative Spontaneous at All temps
Positive Positive Spontaneous at High Temps (exotherm not important)
Negative Negative Spontaneous at Low Temps (Exotherm is important)
Negative Positive Not Spontaneous Process Reverse spontaneous at all temps
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Gibbs Free Energy

1. If DG is negative, the forward reaction is
   spontaneous.
2. If DG is 0, the system is at equilibrium.
3. If ?G is positive, the reaction is spontaneous in
   the reverse direction.

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Br2(l) ? Br2(g) At what temp is the following
process spontaneous at 1 atm?What is the normal
boiling point of liquid Br2??H? 31.0 kJ/mol
?S? 93.0 J / K mol

• ?G lt 0 for spontaneous process
• ?G 0 for equilibrium process
• ?G ?H - T ?Ssys
• 0 ?H - T ?Ssys 31.0 x 103 T (93.0)
• T 333K
• T gt 333 K ?Ssys is dominant. Liquid vaporizes
• T 333 K ?G 0, liquid and vapor coexist
  (normal BP)
• (exothermic processes dominant)
• T lt 333 K ?H is dominant. Liquid forms.

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What About Reactions?

• Chemistry is all about the changes that occur.
  How can we use thermo and entropy to evaluate the
  changes around us?

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Which has greater positional entropy?
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_at_ Constant Temperature and Pressure

• Why would we use this as a constraint on a
  thermodynamic system?
• 2nd law ?Suniv ?Ssys ?Ssurr
• No temp change means no ?Ssurr
• 4NH3(g) 5O2 (g) ? 4NO(g) 6H2O(g)
• Is this process thermodynamically favored?

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How about this?

• Al2O3(s) 3H2(g) ? 2Al(s) 3H2O(g)
• Same amount of gas on both sides.
• Entropy would appear equal.
• Its actually 179J/K. Why?
• Water is more complex a molecule than hydrogen.
• More ways it can move more entropy.

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And this?

• Cdiamond ? Cgraphite ?Go -3kJ
• So how come we still have diamonds?

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Third Law of Thermodynamics

• When can perfect order be achieved?
• What conditions would have to be necessary to
  first achieve it, and the keep it that way?
• The only time the entropy is zero is when you
  have a perfect crystal at 0K
• Any rise in temperature will create movement and
  therefore raise entropy.

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Other information

• As with enthalpy which is a state function,
• ?Ho ?np ?Hf products - ?nr ?Hf reactants
• So too with entropy and free energy.
• They are both state functions
• ?So ?np ?S products - ?nr ?S reactants
• ?Go ?np ?Gf products - ?nr ?Gf reactants
• free energy of formations for an element in its
  standard state is zero.
• Also free energy and entropy for reactions can be
  added like Hesss Law.

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Free Energy the Equilibrium Constant
Recall that ?G? and K (equilibrium constant)
apply to standard conditions. However, ?G and Q
(reaction quotient) apply to any conditions. It
is useful to determine whether substances under
any conditions will react
Where R is the ideal gas constant, 8.314 J/molK
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Free Energy the Equilibrium Constant
At equilibrium, Q K and ?G 0, so
From the above we can conclude If ?G? lt 0, then
K gt 1. If ?G? 0, then K 1. If ?G? gt 0, then K
lt 1.
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Free Energy the Equilibrium Constant
Solving for the equilibrium constant, K ,
?G? - RT lnK
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?G and work

• ?G is the value of all free energy from a
  reaction.
• Therefore its value is equal to the maximum work
  possible from a reaction. (if -)
• If ?G is positive, what does it tell us?
• Used for efficiency.
• Will never be 100, why?

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Summary of Thermo

• 1st law says you cant win, only break even.
• 2nd law says you cant break even.
• Explains energy crisis!