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Thermodynamics• First law: E = q + w
The books have to balance. Energy flows downhill. The best you can do is break even.
• Second law: S q/TMess happens. You can’t even break even.
• Free Energy, G
“A theory is the more
impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended is its area of applicability. Therefore the deep impression which classical thermodynamics made upon me…”
Albert Einstein
system: the portion of the universe with which we are concerned
The surroundings: everything else
Boundary: The “wall” separating the system from the surroundings.
Isolated system cannot exchange matter or energy
Closed system can exchange energy
Open system can exchange mass and energy both
E = Efinal- Einitial =
q+w
The First LawThe best you can do is break even. Energy flows downhill.
Energy (and matter) cannot be created or destroyed.
Work done ON the system BY the surroundings
Heat added TO the system BY the surroundings
E = Efinal- Einitial =
q+wConstant volume of the system is assumed.
HEAT: Product of random molecular motion.
World’s simplest energy. + q - Heat is absorbed from the system (enothermic).
WORK: force x distance. Force may be gravitational, tensional, electrical…
+w - Work done ON the system.
Units of energy:
1 Joule (1J) = 1kgm2/sec2
If you hold a 187 g softball 54.5 cm above the ground it has a pot’l energy of 1 joule
ENTHALPY - To warm in
H = E + PV at constant pressure
H = E + P VEnthalpy is EASY TO MEASURE: It is the heat a constant pressure system absorbs or releases.
The Second Law
“Die Energie der Welt ist Konstant; Die Entropie der Welt strebt einem Maximum zu.”
- Clausius
ENTROPY
•Drop a whole egg on the floor ---> ? (A B)
•Drop a broken egg on the floor ---> ? (B A?)
•Throw a new deck of cards in the air --->? (A B)
•Throw a random deck of cards in the air ---> ? (B A?)
•Spritz perfume into a room ---> ? (A B)
•Stand in a perfumed room with an empty bottle ---> ? (B A?)
•Put ice into a warm glass of lemonade ---> ? (A B)
•Pour warm lemonade onto some water --->? (B A?)
Second law of Thermodynamics says that spontaneous processes are characterized by the transformation of a more ordered state of system & surroundings to a more disordered state.
Entropy is time’s arrow.
Entropy is irreversible.
The Universe is a Gamble.
• Klaque’s hand.
A straight flushMy hand.
I fold.
Probability of being dealt Klaque’s Hand?
1/2.6 x 106!!!!!!!!!!
Klaque’s hand
Probability of being dealt my hand?
1/2.6 x 106 !!!!!!!!!!
But mine is junk, nada, zip, the kind of hand you get all the time… but a straight flush? That’s rare…
Micro and Macro States.
Microstate
Straight flush
“I fold”
Macrostate
# possible microstates producing the macrostate “Straight Flush” = 40
# possible microstates producing the macrostate “My Hand (I
Fold)” 2.6 x106
The ENTROPY of a MACROSTATE IS a MEASURE of the NUMBER of MESSES (Microstates) IT CAN GET INTO
If Entropy is against you, Ya gotta fold.
Straight Flush (Klaque’s Hand) :
S ln 40
My Hand (I Fold):
S ln (2.6 x106)
S = KbLn W
O (7%)
Si (28%)
Al (7.9%)
Fe (4.5%
Ca (3.5%)
S = entropy of a macrostate
Kb is Boltzmann’s Constant, 1.3807 x 10-23 J/K
W is the number of microstates in the macrostate
Whose hand has the higher entropy?
TAKE-HOME MESSAGE:Each MICROSTATE of a system is EQUALLY LIKELY.
The most likely MACROSTATE is the one with the MOST MICROSTATES.
The Macrostate with the most microstates is the one with HIGHEST ENTROPY, and
Entropy, and the
Air in the Room
wall
Box with 10 air molecules zipping about on one side, divided by a wall
Entropy, and the
Air in the Room II
Porous wall
Box with 10 air molecules zipping about on one side.
Punch hole in wall. What will happen?
Entropy, and the
Air in the Room IV
Porous wall
Each molecule can be in A or B side. So each has 2 possible states. With 10 molecules, the total # of possibilities is
210 = 1024.
A
A
B
Entropy, and the
Air in the Room VThe total # of possibilities is
210 = 1024.
Of those 1024 possible arrangements, the macrostate with 9 molecules in A has 10 microstates.
(10!/1!x9!)
A
A
B
Probability = 10/1024 =.009
Entropy, and the
Air in the Room VIThe total # of possibilities is still
210 = 1024.
The macrostate with 5 molecules in A has 252 microstates (10!/5!x5!).
Probability is 252/1024 =.246
A
A
B
Probability of ending up like this?
Probability is 252/1024 =.246
A
Probability 1s 10/1024 =.009
B Which state is most likely? Which has the highest entropy?
Probability is
1000!/500! X
500! 10299
And the numbers get bigger, fast! If each green
dot represents 100 molecules..
Probability is
1000!/900!100! =
6.4 x 10139
Will Something Happen Spontaneously?
This question is a matter of energy and entropy.Willard Gibbs answered this question in 1878, at Yale.
G = H - T S
+
G = H - T S
G < 0 The process is spontaneous
G > 0 The process takes energy to go.
G = 0 You’re at equilibrium
All those annoying little superscripts:
You’ll see:
G = Free energy change under “standard conditions”, i.e. 1.0 M, 25 C (298 K) , 1 atm.(pH is -1!).
Gf = free energy of formation from the elements under standard conditionse.g.
6C(s, 25 ) + 6H2(g, 1atm, 25 ) + 3O2 (g, 1atm,
25 )
--->
(s, 25 )
C6H12O6
G ’ = Free energy change under “standard biological conditions”, i.e. 1.0 M, 25 C (298 K) , 1 atm.pH is 7
G is concentration dependent.
For any garden-variety reaction:
aA + bB cC + dD
G = G + RTln( [C]c [D]d/[A]a [B]b)
R = Nkb = 8.3145 J/mol K =
1.9872 cal/molK =
0.08206 L atm/Kmole
At equilibrium, No NET CHANGE is occurring in the
system. G = 0
G = - RTln( [C]c [D]d/[A]a [B]b)
= - RTlnKeq
Keq = e-G/RT
Problem set I is there for you at:
http://academics.smcvt.edu/biochemistry/New_Folder/
biochem_i_problem_set_I.htm
pH Review Sessions 12-1 MTWThF
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