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Thermodynamics

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Title: 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.

4
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.

5
Kinetics The reaction pathway
Thermodynamics the initial and final states
6
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.

7
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

8
Lets Look at a Simple System
  • Four atoms of an ideal gas
  • Three possible arrangements
  • How many ways can each state be achieved?

9
Examine All Possibilities (Pg 795)
10
Possibilities
  • The arrangement with two on each side is most
    likely to occur

By the ratio of 641
11
Probability of finding all the Molecules in the
Left Bulb as a function of the total number of
molecules
12
Unlikely to Occur
1 in 10 or not likely to occur
2 x 1023
But it is possible!
13
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

14
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.
15
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.

16
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.

17
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.

18
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.

19
Standard Entropies
  • Larger and more complex molecules have greater
    entropies.

20
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.
21
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
22
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.

23
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.

24
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

25
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.

26
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!

27
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.

28
Star
29
Star
Further away
30
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

31
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.

32
?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)

33
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)
34
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
35
Spontaneity
?S system ?S Surrounding ?S Universe Spontaneous?
Yes
- - - No (process in opposite direction
- ? Yes if ?Ssys gt ?Ssurr
- ? Yes if ?Ssys lt ?Ssurr
36
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?

37
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!

38
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

39
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

40
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

41
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

42
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
43
  • 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
44
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.

45
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.

46
What About Reactions?
  • Chemistry is all about the changes that occur.
    How can we use thermo and entropy to evaluate the
    changes around us?

47
Which has greater positional entropy?
48
_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?

49
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.

50
And this?
  • Cdiamond ? Cgraphite ?Go -3kJ
  • So how come we still have diamonds?

51
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.

52
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.

53
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
54
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.
55
Free Energy the Equilibrium Constant
Solving for the equilibrium constant, K ,
?G? - RT lnK
56
?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?

57
Summary of Thermo
  • 1st law says you cant win, only break even.
  • 2nd law says you cant break even.
  • Explains energy crisis!
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