In 1845 Joule showed that mechanical energy (work) and heat were the same thing and used University of Prince Edward Island very precise temperature measurements to calculate the heat content in a foot-pound of work.

1 H Biochemistry6 7 8 C N O Barry Linkletter 15 16 P S In 1847, Helmholtz stated the law of conservation of energy, an important component of the first law. Hermann von Helmholtz James Prescott Joule Sir Benjamin Thompson, 1821-1894 1818-1889 Count Rumford 1753-1814 Lecture 10 Supplement: The Laws of Thermodynamics Benjamin Thompson fought on the Loyalist ...can be stated many ways. Here is a collection of these famous laws. They were side of the American Revolution then developed over many years and were stated by many people in many different ways decamped to Germany to start the Ther- before agreement began to form in the mid nineteenth century. Even then, the modynamic revolution in 1797. He showed third law as not formulated in it’s current form until 1906. that work could be converted to heat through friction, proving that heat was 0: If A B and B C are at equilibrium, then A C must also be at equilibrium. NOT a fluid, but was energy. 1: The increase in internal energy of a closed system is equal to the heat supplied to the system minus work done by it. Thompson also used his 2: Natural processes to lead towards spatial homogeneity of matter and energy, and especially of temperature thermodynamic powers to invent a better 3: The entropy of a perfect crystal of any pure substance approaches zero as the temperature approaches absolute zero. fireplace for Carnot, Clausius, Kelvin and Carathéodory all stated the second law in different ways. They were all correct. English homes. Thomspon married the In 1824 Carnot expressed widow of Lavoisier. the idea of the second law In 1851 Kelvin wrote down what would eventually become the in a study of steam engines. second law. He was discussing the irreversibility of heat flow In 1865 Clausius gave The Carnot cycle is well known and speculated about the heat death of the universe. entropy its name. today and is the basis for the diesel engine.. The video is available on YouTube at https://youtu.be/hE-EspsO3LI How many 17 year old students get a painted portrait? Carnot’s father was a major figure in the In 1909 Carathéodory listed French revolution. the laws of thermodynamics numerically. He could only He died young count to two at that time. from cholera. Nicholas Carnot Rudolf Clausius William Thompson, Constantin Carathéodory 1796-1832 1822-1888 Lord Kelvin 1873-1950 1824-1907 Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 1 of 13 Equilibrium The concept of equilibrium was well known to chemists when Le Chatellier encapsulated the idea in his famous principle, “If you disturb a system that is at equilibrium, it KeynoteChemistry.com will tend to return to equilibrium”. Whether we start with all α- or all β-glucose, we Keq always end up with a ratio for α/β of 1/1.78. Even if A B I dump in more α-glucose, the ratio soon returns to The specific rotation of α/β = 1/1.78. a glucose solution always B ends up at 52.5˚ no matter [ ]eq OH OH where we start. Why? Keq = O Keq O [A]eq HO HO 20 The equilibrium HO H HO OH [ ] = +52.5 OH OH D constant OH H D D = + -D-glucopyranose -D-glucopyranose = + [ ]20 112 [ ]20 18

I didn’t write out For a given set of reaction the units but they conditions, this value remains are important in constant. No matter how we [ ] = = answering the change the concentrations of Keq 1.78 question below. reactants and products, the system [ ] Berthollet first proposed the will return to the equilibrium ratio idea of chemical equilibrium over time. in 1803 when he observed that some chemical reactions were reversible

Ponder this... I have 100 mL of a solution of glucose that has been sitting around for days. I measure the optical rotation to to be 10.5˚ dm–1. What is the concentration of glucose? I then add 1g of pure α-glucose to the solution. What is the observed optical rotation immediately after addition, and what will be the optical rotation tomorrow? Tell me the final concentration of α-glucose and β-glucose in the solution. You will need to know the units of specific rotation and the molecular weight of glucose Henry Louis Le Châtelier Claude Louis Berthollet to answer this question. 1850-1936 1748-1822

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 2 of 13 Gibbs has been honoured Free Energy with a postage stamp. Willard Gibbs developed the connection between equilibrium constant and an energy difference that we now call “free energy”.

This is the change in free energy between the reactants in their standard state and the products in their standard state.

If we know the equilibrium constant then we know the difference in free energy.

Josiah Willard Gibbs G = RT ln Keq 1839-1903 These are both G the same equation. Gibbs wrote the book that was the found- RT ation of Lewis’ text- Keq = e book on chemical thermodynamics Gibbs’ father was a president of Harvard Univeristy and before that a scholar at Yale, Like his son. Gibbs had a ship named after him, He was an abolitionist and he was the USNS Josiah Willard Gibbs part of the Amistad trial in 1840.

These 5-inch guns were removed in the name of science.

USNS Josiah Willard Gibbs, 1958-1971

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 3 of 13 Enthalpy and Entropy It was a long and difficult road, filled with bitter rivalry and petty feuds. But many great minds applied the principals of thermodynamics to chemistry and eventually Lewis spent 20 years measuring and agreement was reached for concepts of free energy, calculating free energy changes in enthalpy and entropy. chemical reactions and wrote the book that defined thermodynamics Between 1888 and 1906 le Chatelier, Lewis, Richards, for our modern age in 1923. van’t Hoff, Haber, and Nernst made important contributions to this field. Today we describe free energy as being part “real energy” (enthalpy) and part statistical According to Nernst, inevitability (entropy). he himself stated the third law of thermodynamics. Others disagreed. Haber was jealous Arrhenius and Richards This is quite of van’t Hoff’s campaigned hard against G = H T S a club, isn’t it? hair (I’m kidding). Nernst in the Nobel committee. They delayed his Was Haber a hero recognition until 1920 but his or a war criminal? Richards felt that body of work could not Discuss among your Nernst didn’t give be denied. friends. him credit for his ideas. 14 01 18 20 19 19 19 19 Lewis was Richards’ doctoral student.

Lewis never met anyone that he couldn’t turn into an enemy.

Gilbert Lewis Theodore Richards Jacobus van't Hoff Fritz Haber Walther Nernst 1875-1946 1868-1928 1852-1911 1868-1934 1864-1941

“Thermodynamics (2nd Edition ed.)”, Lewis, Gilbert Newton; Randall, Merle: Revised by Pitzer, Kenneth S. & Brewer, Leo (1961). McGraw-Hill Book Co., New York, New York, United States: ISBN 0-07-113809-9. Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 4 of 13 Some Observations

Observe that the entropy term can work in Equilibrium roles downhill. The free energy of Wait a minute! Hard-core the same direction as enthalpy or in the opposite molecules in solution have been determined in the physical chemists also depending on it’s sign. standard state. demand that [H+] = 1 M. Are we in the wrong? Standard state depends on the field. In biochemistry it is usually 1M in concentration, pH 7.0, 25 ˚C. G = H T S Why not 37 ˚C? But nothing ever happens at 1M in biochemistry. What is the actual free energy difference under more likely concentrations? Imagine a change with ...and positive entropy; negative enthalpy; change is also “downhill” change is “downhill” [P] “products” over “reactants” Do you recall the The change is free energy G = G + RT ln reaction quotient, Q? will always be downhill in this case. [R] Actual free Total difference G if there Can you consider energy for a What is the ∆ ion free energy between other cases? There given system. is no product present? are 4 in total. products and reactants in their standard state.

You look these values up in published tables of thermodynamic data

Fact: when equilibrium is reached the following is true... [P] G = 0 and K = therefore 0 = G + RT ln K eq [R] eq

G = RT ln Keq G RT Keq = e

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 5 of 13 Add it Up Does ATP hydrolysis favour the products? The standard free energy change in a reaction can be combined with that of another reaction if they are Do you think phosphate coupled. Take the first step of glycolysis as an example. salt spontaneously condenses with glucose?

1 5 5.3 ATP + H 2O ADP + Pi G = 30.5 kJ mole Keq = 2.2 10 Keq =10 1 4 3.4 Glc+ Pi G6P + H 2O G = +13.8 kJ mole Keq = 3.8 10 Keq =10

1 2 2.9 ATP +Glc ADP +G6P G = 16.7 kJ mole Keq = 8.5 10 Keq =10 We make the phosphorylation of glucose highly favourable This idea is how ATP drives all Do you believe that ATP by using high energy ATP as the reactant rather than of biochemistry forward. But low energy phosphate salt. will spontaneously transfer where do we get ATP from? a phosphate group to “Nobody rides for free.” glucose? But if you add glucose and ATP to water you will never see this happen. Why? What “Nobody rides for free.” is the magic ingredient are you missing? official theme song of thermodynamics. Is it the vital force? Or something It was also the theme song for the else? Keanu Reeves/Patrick Swayze movie “Point Break” and the last single that Ratt released.

I know my hair rock. I went to school with Haywire.

These guys were sooo cool! Grunge music destroyed a treasure. Ratt It’s a classic! Skip the recent reboot. Get the bluray and compare it to “The Fast and the Furious” with Paul Walker and Vin Diesel. Discuss the similarities with your friends.

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 6 of 13 Observations Here is a table of standard free energies for the reactions of glycolysis. We can measure the concentrations of all the reactants and so we can calculate the observed chemical potential, ∆G, for each reaction. Which steps are not easily reversed? Which steps are easily reversed. Some steps have “uphill” values for ∆G. Shouldn’t they be “downhill” for glycolysis to proceed? Please explain away that observation. (remember, the ∆G values are calculated from measured concentrations and the ∆G˚ value.)

[P] G = G + RT ln [R]

Every biological pathway has a direction. What is the direction of glycolysis? What steps drive that direction? What steps could go either way?

Which enzymes would you want to make sure that you can regulate?

Gluconeogenesis is the “reverse” of glycolysis. It uses many of the enzymes available to the glycolysis pathway but cannot use them all. Which enzymes must be downregulated when we want to operate the gluconeogenesis pathway? Which steps need to use different chemistry and different enzymes?

Why does the chemistry need to change? Couldn’t we reverse a step just by using a different enzyme? table from http://www.chembio.uoguelph.ca/educmat/chm452/lecture2.htm

Are any of these reactions at or near equilibrium?

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 7 of 13 Chemical Kinetics Once we know where a reaction is going the question is how fast does it get there. A very negative ∆G indicates that a reaction would proceed forward to product but the rate towards that goal may be fast or slow. The observed reaction rate is dependant on the rate constant for the reaction.

k S P [S ] = [P] = v t t v = k [S ]

Arrhenius related the rate to an Somewhere along activation energy for the reaction. this path is the highest energy structure - Ea the transition state. RT The activation energy k = Ae defines the rate of the reaction towards product.

E a

Energy Reactants The change in standard free energy defines 1903 ∆G˚ the equilibrium constant

Products

Svante Arrhenius 1859-1927 Reaction Coordinate

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 8 of 13 Eyring was born in Mexico. His family fled during the Mexican Revolution. Thus Pancho Villa made a contribution to science.

Eugene Wigner was It was for Michael Polanyi’s physics doctoral student 196 3 Eugene Wigner contributed to the famous letter written to President Roosevelt in 1939 which led to the creation of the Manhatten Project.

Michael Polanyi Meredith Evans Henry Eyring Eugene Wigner 1891-1976 1904-1953 1901-1981 1902-1995 Transition State Theory What is the nature of the Arrhenius activation energy? In the 1930’s Henry Eyring, Michael Polanyi, Eugene Wigner and Meridith Evans Keith Laidler, one of the developed what would become to be known as transition state theory. greatest chemists Canada ever produced, was the They proposed that the reaction proceeds with structure changes, bonds breaking doctoral student of Eyring. and forming, solvation changes, etc... and moves from a low energy, stable reactant Michael Polanyi’s son, Laidler made many contributions to a low energy, stable, product. Along the way it must pass through a structure John, won a Nobel prize towards understanding the that is the highest energy point in the path. This is the transition state. for chemistry in 1986. chemistry of enzymes. He spent his career at U of Toronto. G k T RT k = B e

Anything that changes h the standard free energy difference between reactants 86 19 and the transition state will change the rate of the reaction.

How could you affect the energy of the transition state? John Polanyi Keith Laidler b. 1939 1916-2003

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 9 of 13 You will need to know how to write a rate law after inspecting a reaction Rate Laws equation. We have already seen that a reaction rate is related to the concentration of reactants by a rate constant. Consider the following reactions and their rate laws. Do these ring any bells? A reversible reaction

k k k1 A B A+ B C A+ B C At equilibrium nothing is k 1 changing. So the forward v = k [A] v = k [A][B] and reverse rates must be equal. v forward = k1 [A][B] A first order A second order reaction reaction v forward = vreverse vreverse = k 1 [C]

k1 [A][B] = k 1 [C] [C] k1 = k [A][B] 1 [C] Wow! The equilibrium Keq = constant is the ratio k1 of the forward and Keq = [A][B] reverse rate constants. k 1

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 10 of 13 Catalysis A catalyst is a reactant that accelerates a reaction but is not changed, or is regenerated, during the reaction. Many reactions are catalyzed by acid. For example, mutarotation is faster in acidic water. The more acid, the faster the rate. There is a point at which added acid will no longer increase the rate. Can you explain this observation by inspecting the rate law for the catalyzed reaction?

Rate-determining step k OH OH Split charges A B O O HO HO H HO H HO Mutarotation proceeds v = k [A] OH OH OH OH

This reaction is much faster than the one above. Positive to positive is less of an energy difference than neutral to zwitterionic. H OH OH OH H O O OH HO HO HO H HO H HO H HO Mutarotation proceeds OH OH OH OH Equilibrium OH OH association Rate-determining step with catalyst k A+ H AH AH P Ka [A][H ] Ka = v = k [AH ] How does the rate increase with [H [AH ] +]? + = These three facts [H ] [A] [AH ] [A]t will allow us to derive v = k [A] the rate law for acid t catalysis. Ka+[H ]

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 11 of 13 Summary Will a reaction go? Will it proceed towards product? That depends on the free energy of the system under the observed conditions. Combine the difference in standard free energy for the reaction with the observed concentrations of reactants and products and we can see How fast if the reaction is at equilibrium or not. If it is not at will it go? equilibrium then the difference in free energy will reveal E the direction the reaction will take under the observed a conditions. Free energy [P] includes the Energy Reactants G = G + RT ln standard free R energy and the [ ] reaction conditions. ∆G How fast will a reaction go? Just because we are out Will it go? of equilibrium does not mean that we will see observable progress towards the final state. The paper that your Products textbook is printed on should become carbon dioxide and water in our oxygen atmosphere, yet it is not chang- ing perceptably during your time in university. Reaction Coordinate

Reaction rate depends = on the rate constant v k [S ] and the reaction Why do only certain reactions go? Most biochemical reactions are Ea conditions very slow. We generally only observe the reactions that are catalyzed RT Rate constant depends by enzymes. Thus pathways can be constructed using collections of k = Ae on the energy of activation. enzymes that accelerate a series of reactions. Understanding the nature of enzyme catalysis is a major goal of this biochemistry course.

Many reactions are Again, there are many possible with these But we observe only We don’t see the products possible reactions that substrates the reaction that is of the slow uncatalyzed could happen but we only catalyzed. reactions see the product of the catalyzed reaction. Glucose + ATP Glucose-6-phosphate Fructose-6-phosphate Fructose-1,6-bisphosphate Of all the possible + ATP Biochemical reactions are organized reactions with G6P in chains of catalyzed reactions we only observe the called pathways. catalzed reaction. Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 12 of 13 This Is Only The Very Beginning... This presentation was never intended to provide all the information that you are required to digest for this course of study. By definition, university requires that you read books, think about what you have read, and ask questions. Otherwise stay at home, watch TV and save your money. Always consider the relatively brief presentation in class to be a mere apéritif for your studies. I cannot read the textbook to you but I do hope to highlight some important topics, provide stories and context to pique your interest in biochemistry and to inform you of current research challenges to which you might someday make a contribution. As you read your textbook and consider this presentation, strive to master the following essential skills of biochemistry.

Topics Highlighted in this Brief Presentation Can you define enthalpy and entropy? Can you compare and contrast the rate constant for a reaction and the equilib- rium constant for a reaction? Which one can be changed by a catalysts and which one cannot? What is free energy and how does it relate to enthalpy and entropy? How does free energy correspond to the equilibrium constant for a reaction? How can you use the difference in standard free energies between reactants and products to calculate the equilibrium constant for a reaction? Can you determine the free energy difference between reactants and products for when we do not have standard conditions? Is there a situation when the difference in free energy will be zero? What is happening when that condition occurs? Can you write a rate law for a reaction? Can you determine a rate constant from a data set of rate vs. concentration? Amaro Lucano is a What is a catalyst? popular amaro made in southern Italy. It was first produced in 1894 by Pasquale Vena, a pastry chef.

The video is available on YouTube at It became popular when https://youtu.be/hE-EspsO3LI it was adopted as the official liqueur of the royal family of Italy. The coat of arms of the House of Savoy still graces KeynoteChemistry.com the label of Amaro Lucano.

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 13 of 13 References and Notes I have used many images to decorate this presentation. Some of them are in the public domain and some are not. I claim fair use for educational purposes.

Image of Hermann Helmholtz accessed on March 15, 2015 at http://www.nndb.com/people/445/000072229/ Engraving of James Joule by C. H. Jeens (1882) accessed on March 15, 2015 at http://en.wikipedia.org/wiki/James_Prescott_Joule Image of Bejamine Thompson accessed on March 15, 2015 at http://www.historytube.org/wp-content/uploads/2013/09/Benjamin-Thompson-oil-on- Oil painting of Carnot (1813) by Louis-Léopold Boilly accessed on March 15, 2015 athttp://en.wikipedia.org/wiki/Nicolas_Léonard_Sadi_Carnot Image of Clausius accessed on March 15, 2015 at http://operamundi.uol.com.br/media/images/Rudolf_Clausius_01.jpg Image of Kelvin from accessed on March 15, 2015 at http://en.wikipedia.org/wiki/William_Thomson,_1st_Baron_Kelvin Image of Constantin Carathéodory accessed on March 15, 2015 at http://www.katohika.gr/2012/09/blog-post_5503.html

Book cover for Thermodynamics and the Free Energy of Chemical Substances (1923) by Gilbert Lewis and Merle Randall http://www.eoht.info/page/Thermodynamics+and+the+Free+Energy+of+Chemical+Substances Image of book title page accessed on March 15, 2015 athttp://en.wikipedia.org/wiki/Josiah_Willard_Gibbs#Chemical_thermodynamics Image of Berthollet accessed on March 15, 2015 at http://commons.wikimedia.org/wiki/File:AduC_198_Berthollet_(C.L.,_1748-1822).JPG Image of Le Chatellier accessed on March 15, 2015 at http://www.quazoo.com/q/Louis%20Le%20Chatelier

Image of US postage stamp honoring Gibbs accessed on March 15, 2015 at http://www.sv.vt.edu/classes/ESM4714/methods/Gibbs.html Image of Amistad poster accessed on March 15, 2015 at http://en.wikipedia.org/wiki/Amistad_(film) Image of Josiah Gibbs accessed on March 15, 2015 at http://en.wikipedia.org/wiki/Josiah_Willard_Gibbs Painting of USNS Willard J. Gibbs accessed on March 15, 2015 at http://www.navsource.org/archives/ Photo of USNS Willard J. Gibbs accessed on March 15, 2015 at http://www.amazon.com/Josiah-Willard-T-AGOR-1-1958-1971-Previously/dp/B00H07QOUG

Image of Gilbert N. Lewis accessed on March 15, 2015 at http://www.dec.ufcg.edu.br/biografias/GilbNewt.html Image of Theodore Richards accessed on March 15, 2015 at http://upload.wikimedia.org/wikipedia/commons/6/6d/Theodore_william_richards.jpg Image of Fritz haber from accessed on March 15, 2015 at http://www.figurethingsout.com/blog/2013/12/15/fritz-harber/ Image of van’t Hoff accessed on March 15, 2015 at http://commons.wikimedia.org/wiki/File:PSM_V66_D198_J_H_vant_Hoft.png Image of Walther Nernst accessed on March 15, 2015 at http://en.wikipedia.org/wiki/Walther_Nernst Image of Svante Arrhenius accessed on March 15, 2015 at http://www.lavillebrule.com/fr/svante_arrhenius

Image of John Polanyi postal stamp from http://www.news.utoronto.ca/canada-post-unveils-stamp-u-t-chemist-john-polanyi Meredith Gwynne Evans accessed on March 15, 2015 at http://www.npg.org.uk/collections/search/portrait/mw219691/Meredith-Gwynne-Evans Image of Eugene Wigner accessed on March 15, 2015 at https://thespectrumofriemannium.wordpress.com/tag/wigner/ Image of Henry Eyring accessed on March 15, 2015 at http://en.wikipedia.org/wiki/Henry_Eyring_(chemist) Painted portrait of Henry Eyring (oil on canvas, 1969) accessed on March 15, 2015 at https://www.alumni.utah.edu/continuum/fall01/gittins.htm Image of Michael Polanyi book cover from accessed on March 15, 2015 at http://www.amazon.com/Michael-Polanyi-Knowing-Library-Thinkers/dp/1932236910

Haywire album accessed on March 15, 2015 at http://en.wikipedia.org/wiki/Don't_Just_Stand_There Ratt photo accessed on March 15, 2015 at http://ultimateclassicrock.com/ratt-juan-croucier-reunion/ Point Break disk accessed on March 15, 2015 at http://www.thehut.com/blu-ray/point-break/10354532.html

Errors and Worse This presentation contains mistakes, typographical errors, crimes of grammar and worse. All mistakes are intentional – to see if you are paying attention. Report any errors that you find in the class forum. The first to spot and report an error will win a fabulous invisible prize.

Introduction To Biochemistry: Chemistry Review: Reaction Equilibrium and Kinetics Page 13 of 13