Thermodynamics I

Thermodynamics I Dr Una Fairbrother

General Biochemistry 2006-07 • Module Convenor: Dr Chris Bax, c.bax@londonmet.ac.uk • Lecture 1: Water (Dr Una Fairbrother). • Lecture 2: Thermodynamics I (Dr Una Fairbrother).

THERMODYNAMICS • Relationship between heat and movement • BUT better in biology to consider the relationship between energy and work • For example - can thermodynamics be used to predict whether any useful work can be achieved in a chemical reaction? • Does a reaction occur spontaneously or does energy need to be provided?

DEFINTIONS • SYSTEM • matter within a defined region of the universe • SURROUNDINGS • matter outside that defined region • BOUNDARY • A separator, real or imaginary between system and surrounding

First Law of Thermodynamics • The total energy of a system and its surroundings is a constant@ ie energy is conserved. DE = EB - EA = Q-W • DE - energy change • EB - energy of system at end of process • EA - energy of system at beginning • Q - heat absorbed by system • W - work done

NOTE about enthalpy "enthalpy is the amount of energy in a system capable of doing mechanical work" • Heat content, total heat, enthalpy, H • a thermodynamic quantity equal to the internal energy of a system plus the product of its volume and pressure DH = DE + PDV • H is ENTHALPY, P is pressure, V is volume change

THERMODYNAMICS • Unfortunately measuring DE (or DH) does not predict spontaneity of a reaction. • The next step is to consider another function of thermodynamics called ENTROPY (denoted by S) - this is the measure of randomness or disorder of system

Second Law of Thermodynamics • A process can occur spontaneously only if the sum of the entropies of a system and its surroundings increases@ • DS system + DS surroundings > 0 (for a spontaneous reaction)

Entropy • “the entropy of the universe increases during any spontaneous process” • “universe” just means “the system you’re looking at PLUS its surroundings, i.e., everything that’s close around it”. System plus surroundings. • Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so. • A rock will fall if you lift it up and then let go. • Hot frying pans cool down when taken off the stove. • Iron rusts (oxidszes) in the air. • Air in a high-pressure tire shoots out from even a small hole in its side to the lower pressure atmosphere. • Ice cubes melt in a warm room. • What’s happening in each of those processes? • Energy of some kind is changing from being localized ("concentrated" in the rock or the pan, etc.) to becoming more spread out

Iron doesn’t have to be hot to have ‘localized energy’ • Iron atoms plus oxygen molecules have more energy localized within their BONDS than iron rust (iron oxide). • Iron reacts with oxygen releasing energy from higher energy bonds and form the lower energy bonds in iron oxide • The difference in energy is dispersed to the surroundings as ‘heat’ i.e., the reaction is exothermic and makes molecules in the surroundings move faster . • Iron spontaneously, but slowly, reacts with oxygen and each spreads out some of its bond energy to the surroundings when the iron and oxygen form iron oxide. • System: iron and oxygen, iron oxide. • Surroundings: the nearby air and any moisture or salt in the air plus any object in contact with the rusting iron

Motional energy and bond energy • In chemistry the energy that entropy measures as dispersing is “motional energy”, the translational and vibrational and rotational energy of molecules • and the DH of phase change energy — both motional or phase change energy being designated either as "q" or DH in many equations. • “Bond energy”, the potential energy associated with chemical bonds that we talked about in the iron oxidation example, • measured by the potential energy of bond formation • and this is measured by entropy change in connection with a chemical reaction

FREE ENERGY • Because entropy changes are difficult to measure a third thermodynamic parameter is introduced. This is called FREE ENERGY DG = DH - TDS • DG - free energy change • DH -enthalpy change • DS -entropy change • T -temperature in Kelvin

Gibbs free energy • The Gibbs free energy was developed in the 1870s by the American mathematical physicist Willard Gibbs. • A thermodynamic potential which measures the "useful" work obtainable from an isothermal, isobaric thermodynamic system. • When a system evolves from a well-defined initial state to a well-defined final state, the Gibbs free energy DG equals the work exchanged by the system with its surroundings, less the work of the pressure forces, during a reversible transformation of the system from the same initial state to the same final state.

How do you use DG? • A reaction can only occur spontaneously if DG is negative . • If DG is 0 then the reaction is at equilibrium. • A reaction cannot normally occur if DG is positive ( an input of free energy from another reaction is required to drive it).

Consider the first step of glycolysis • Glucose + Pi Glucose 6-phosphate DG = +13.8 kJ mol-1 • Not spontaneous

If the reaction is COUPLED to the hydrolysis of ATP • ATP + H2O ADP + Pi DG= -30.5 kJ mol-1 and • Glucose + Pi Glucose 6-phosphate DG=+13.8 kJ mol-1 • Glucose + Pi + ATP + H2O Glucose 6-phosphate + ADP + PiDG = -16.7 kJ mol-1 • The net reaction is spontaneous and therefore permits the phosphorylation of glucose

Relationship between free energy (G) and the equilibrium constant (Keq) • A + B C + D • DG = DGo + RT ln [C][D] [A][B] • NOTE: ln = loge • DG0 = standard free energy change [ie change under standard conditions - A,B,C,D present at 1.0M, 298.15 K, atmospheric pressure of 101,235 Pa] • R = gas constant 8.314 JK-1mol-1 • T = temperature in K

DG0 and DG0’ • At equilibrium: DG = 0, Keq = [C][D] [A][B] • So: DG = DGo + RT ln [C][D] [A][B] • Becomes: 0 = DGo + RT ln Keq • Therefore: DGo = -RT ln Keq • In biochemistry there is a further standard free energy change which occurs at pH=7 - this is given the symbol DGo’

Reducing agents • A reducing agent is defined as a substance that will donate an electron and become oxidised • eg Fe2+ Fe3+ + e- • An oxidising agent is able to accept an electron and becomes reduced • eg Fe3+ + e- Fe2+

HALF-REACTIONS • Reactions showing the electrons being accepted (or donated) but where the electron donor (or acceptor) is not shown are called HALF-REACTIONS • eg H+ + e- H (sometimes written as 1/2 H2 ) Eo’ of -0.42 V • E0 , which is the reduction potential, • a measure of the tendency of H+ to accept electrons

Half reaction (written as a reduction)E0’ (at pH 7.0), V Fe3+ + e- Fe2+ 0.77 Dehydroascorbic acid + 2H+ + 2 e- 0.06 ascorbic acid Ethanal + 2H+ + 2 e-ethanol -0.16 NAD+ + 2H+ + 2 e- NADH + H+ -0.32

Two half reactions can be added together to obtain the full reaction • When any two half reactions are coupled the half reaction with the more positive reduction potential will proceed as written (ie as a reduction) driving the other half reaction backwards (ie as an oxidation)

Free energy is related to reduction potential as follows • DG0’ = - n FDE0’ • n = number of electrons transferred • F = Faraday’s constant (96,496 JV-1) DE0’= [E0’of half reaction containing the oxidising agent] - [E0’of half reaction containing reducing agent] [Ethanal + 2H+ + 2 e-ethanol] -[NAD+ + 2H+ + 2 e- NADH + H+]

NOTE :overall the reaction is • Ethanal + NADH + H+ ethanol + NAD+ • DE0’ = -0.16 -(-0.32) V = +0.16V Therefore • substituting in DG0 = - n FDE0’ • DG0’ = -(2)(96,496)(0.16) joules (per mole) = -30 kJmol-1

Summary • 1st Law of Thermodynamics: enthalpy • 2nd Law of Thermodynamics: entropy • FREE ENERGY, DG • Relationship between free energy and the equilibrium constant (Keq) • DG0 and DG0’ • Reducing agents • HALF-REACTIONS:Two half reactions can be added together to obtain the full reaction • Free energy is related to reduction potential

Reading list • Stryer, 5th edition Principles of Biochemistry • http://www.entropysite.com/students_approach.html

Thermodynamics I