thermodynamics spontaneity, entropy, and free energy
TRANSCRIPT
Thermodynamics
Spontaneity, Entropy, and Free Energy
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?
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.
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.
KineticsThe reaction pathway
Thermodynamics the initial and final states
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.
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”
Let’s Look at a Simple System
• Four atoms of an ideal gas
• Three possible arrangements
• How many ways can each state be achieved?
Examine All Possibilities (Pg 795)
Possibilities
• The arrangement with two on each side is most likely to occur
By the ratio of 6:4:1
Probability of finding all the Molecules in the Left Bulb as a function of the total number of molecules
Unlikely to Occur
1 in 10 or not likely to occur2 x 1023
But it is possible!
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
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.
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.
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.
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 1023 J/K.
Entropy on the Molecular Scale
• The change in entropy for a process, then, is
S = k lnWfinal k lnWinitial
Wfinal
Winitial
S = k ln
• Entropy increases with the number of microstates in the system.
Standard Entropies
Larger and more complex molecules have greater entropies.
Entropy• Kinetic-molecular viewKinetic-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.
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
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.
speed
num
ber
T3
T2
T1
T1 < T2 < T3T1 < T2 < T3
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.
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
2nd Law Restated• In any spontaneous process, there is always an
increase in the entropy of the universe
Suniverse = Ssystem + Ssurroundings
If S univ > 0, process is spontaneous.If S univ < 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.
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!
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.
Star
Star
Further away
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
How can we determine if a process is spontaneous?
Suniverse = Ssystem + Ssurroundings
The sign of Ssurr depends on direction of heat flowexothermic process adds energy to the universeThe universe now has more random motion So the universe experiences an increase in entropy
Suniverse > 0 or positive.
Ssurrounding
Magnitude of Ssurr depends on the temperatureIf 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)
Entropy Continued
• The tendency for a system to lower its energy becomes more important at lower temperatures.
Driving ForceProvided by energy flow
Magnitude of the Entropy change ofThe surroundings
Quantity of heat (J) temperature (K)
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
Change in enthalpy exotherm = neg endotherm = pos
SpontaneityS
system
S
Surrounding
S
Universe
Spontaneous?
+ + + Yes
- - - No (process in opposite direction
+ - ? Yes if Ssys > Ssurr
- + ? Yes if Ssys < Ssurr
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?
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!
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
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 > 0 or “spontaneous”
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
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
Calculate Sunv and G
T (°C)
T
K
-H = Ssurr
T
S + Ssurr=Sunv TS
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
H = 6.03 x 103 J/mol S = 22.1 J/K • mol
G = H - T Ssys
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
The spontaneity of the process depends on the temp
Gibbs Free Energy
1. If G is negative, the forward reaction is spontaneous.
2. If G is 0, the system is at equilibrium.
3. If G is positive, the reaction is spontaneous in the reverse direction.
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 < 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 > 333 K Ssys is dominant. Liquid vaporizesT = 333 K G = 0, liquid and vapor coexist (normal BP)
(exothermic processes dominant)T < 333 K H is dominant. Liquid forms.
What About Reactions?
• Chemistry is all about the changes that occur. How can we use thermo and entropy to evaluate the changes around us?
Which has greater positional entropy?
@ 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?
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.
And this?
• Cdiamond → Cgraphite ∆Go = -3kJ
• So how come we still have diamonds?
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.
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 Hess’s Law.
Free Energy & the Equilibrium ConstantFree 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:
QRTGG lnWhere R is the ideal gas constant, 8.314 J/mol•K
Free Energy & the Equilibrium ConstantFree Energy & the Equilibrium Constant
At equilibrium, Q = K and G = 0, so
.ln
.ln0
ln
KRTG
KRTG
QRTGG
From the above we can conclude:If G < 0, then K > 1.If G = 0, then K = 1.If G > 0, then K < 1.
Free Energy & the Equilibrium ConstantFree Energy & the Equilibrium Constant
Solving for the equilibrium constant, K ,
G = - RT lnK
K = e- Gº
RT
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?
Summary of Thermo
• 1st law says you can’t win, only break even.
• 2nd law says you can’t break even.
• Explains energy crisis!