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/T Mess 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

Sadi Carnot Born: 1 June 1796 in Paris, France Died: 24 Aug 1832 in Paris, France

 E = E final - E initial = q+w The First Law The 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 = E final - E initial = q+w Constant 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.

 E = E final - E initial = q+w PATH INDEPENDENT What does that mean?

Units of energy: 1 Joule (1J) = 1kgm 2 /sec 2 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  V Enthalpy is EASY TO MEASURE: It is the heat a constant pressure system absorbs or releases.

 H is -

The Second Law “Die Energie der Welt ist Konstant; Die Entropie der Welt strebt einem Maximum zu.” - Clausius

Einstein’s desk

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 flush My hand. I fold. Probability of being dealt Klaque’s Hand?  1/2.6 x 10 6 !!!!!!!!!! Klaque’s hand

Probability of being dealt my hand?  1/2.6 x 10 6 !!!!!!!!!! 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 x10 6 The ENTROPY of a MACROSTATE IS a MEASURE of the NUMBER of MESSES (Microstates) IT CAN GET INTO

Ludwig von Boltzmann

If Entropy is against you, Ya gotta fold. Straight Flush (Klaque’s Hand) : S  ln 40 My Hand (I Fold): S  ln (2.6 x10 6 )

S = K b Ln W O (7%) Si (28%) Al (7.9%) Fe (4.5% Ca (3.5%) S = entropy of a macrostate K b is Boltzmann’s Constant, x 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

THE ENTROPY OF THE UNIVERSE IS ALWAYS INCREASING.  S system +  S s urroundings =  S universe  0

 heat   entropy  S  q/  T at constant pressure.

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 III Porous wall A A B Probability of ending up like this?

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 2 10 = A A B

Entropy, and the Air in the Room V The total # of possibilities is 2 10 = 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 VI The total # of possibilities is still 2 10 = 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!  And the numbers get bigger, fast! If each green dot represents 100 molecules.. Probability is 1000!/900!100! = 6.4 x

WHAT DRIVES THE UNIVERSE?

The Universe SPONTANEOUSLY ROLLS DOWNHILL (-  H) and makes messes (+  S) EVERYTHING ELSE TAKES WORK

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

 G is dependent on Temperature, concentration of reactants, pH...

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!).

 G f = free energy of formation from the elements: e.g. 6C + 6H 2 + 3O 2 --->

 G  f = free energy of formation from the elements under standard conditions e.g. 6C (s, 25  ) + 6H 2(g, 1atm, 25  ) + 3O 2 (g, 1atm, 25  ) ---> (s, 25  ) C 6 H 12 O 6

 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 = Nk b = J/mol K = cal/molK = 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 ) = - RTlnK eq K eq = e -  G  /RT

 G  =  G  f (products ) -  G  f (reactants )

Problem set I is there for you at: /biochemistry /New_Folder/ biochem_i_problem_set_I.htm pH Review Sessions 12-1 MTWThF

W = P  V + w’  H =  E + P  V  E = q-w  H = q-w + P  V  H = q p - (P  V + w’) + P  V  H = q p - w’

AT CONSTANT VOLUME: W = P  V + w’ work is expansion against a constant pressure + all other work.