Thermodynamics & the Hydrophobic Effect

Thermodynamics

Part 1: Thermodynamics

• General study of energy and its interconversions.

Organisms Transform Energy and Matter from Their Surroundings

• System: material or process within which we are studying the energy changes within (usually a reaction).

• Surroundings: everything else with which the system can exchange energy.

• Universe: system + surroundings.

• What we study is the exchange of energy between the system and the surroundings.

Conservation of Energy

• The law of conservation of energy: energy cannot be created nor destroyed.

• Energy can be converted from one form to another.

  • Ex. Potential Energy (PE) → Kinetic Energy (KE).

  • Chemical energy → heat.

• Total Energy (E) = PE + KE (or Chemical Energy + Heat Energy)

Energy transformation in living organisms

• First law of thermodynamics: in any physical or chemical change, the total amount of energy in the universe remains constant, although the form of the energy may change.

• Conservation of energy means that the amount of energy gained or lost by the system has to equal the amount of energy lost or gained by the surroundings.

• ΔE{universe} = ΔE{sys} + ΔE_{surr} = 0

Biosphere: Energy flow in an open system

• Radiant energy from the sun is converted into carbohydrates through photosynthesis.

• The breakdown of carbohydrates releases energy.

• Photosynthesis: 6CO2 + 6H2O —→ C6H{12}O6 + 6O2

• Breakdown of carbohydrates: C6H{12}O6 + 6O2 → 6CO2 + 6H2O + energy

Living Organisms Exist in a Dynamic Steady State

• Small molecules, macromolecules, and supramolecular complexes are continuously synthesized and broken down.

• Living cells maintain themselves in a dynamic steady state distant from equilibrium.

• Maintaining steady state requires the constant investment of energy.

• Requires Work and Energy

The 2nd Law of Thermodynamics - Entropy

• Entropy (S): a thermodynamic function that increases with the number of equivalent ways to arrange the components of a system to achieve a particular state. Roughly speaking entropy is the amount of “disorder or spreading out of energy.”

• Second law of thermodynamics: randomness in the universe is constantly increasing (conversion of order to disorder).

• This states for any spontaneous process, the total entropy of the universe (which is the “system + surroundings”) increases: ΔS{univ} = \ΔS{sys} + Δ S{surr} > 0

• \Delta S_{univ} < 0 for non-spontaneous process

• Processes that increase the entropy of the universe occur spontaneously.

• Ice melting, Radioactive decay, Iron tool rusting

Standard Molar Entropy (S°)

• Standard States

  • Gases: Pure gas at a pressure of 1 atm

  • Liquids or solids: Pure substance in most stable form at a pressure of 1 atm and a specific temperature (usually 25°C)

  • Substances in solution: Concentration of exactly 1 M

• Notation for Standard Molar Entropy = S°

• Standard molar entropy is the absolute entropy of 1 mole of a substance in its standard state at 298 K and 1 atm (or 1 bar) of pressure.

Factors That Affect Standard Entropy (S°) in Biochemistry Include:

1. Phase (s, l, g)

2. Molecular complexity

   • Ar(g) [MW 39.95] versus N2(g) [MW = 28.00]

Relative Standard Entropies: 1) Phases (States)

• $S°$ (J / mol•K)

  • $H_2O (s)$: 51.8

  • $H_2O (l)$: 70.0

  • $H_2O (g)$: 188.8

• The gas state (more arrangements, more disorder) has much larger entropy than the liquid state at a particular temp.

• The liquid state has a larger entropy than the solid state at a particular temperature (i.e. more disorder in liquid).

Relative Standard Entropies: 2) Molecular Complexity

• More complex molecules generally have larger entropy.

• Atoms: only take translational motion

• Molecules: take translational, rotational and vibrational motions

Enthalpy

• Enthalpy (H): the sum of a system’s internal energy and the product of it’s pressure and volume (H is state function):

• Heat content, roughly reflecting the number and kinds of bonds

• KEY: Change in enthalpy (ΔH); energy flows as heat at constant pressure

• If \Delta H_{rxn} > 0 then the reaction is endothermic and heat is absorbed by the system

• If \Delta H_{rxn} < 0 then the reaction is exothermic and heat is released by the system

Gibbs Free Energy (G)

• Relationship between enthalpy change in a system and temperature dependent entropy change.

• G: State function (unit of J or KJ).

• Maximum amount of “Freely available” energy for system to do useful work.

• $\Delta G = \Delta H – T\Delta S$ (at constant P & T)

• $\Delta G$ also determine spontaneity (Magnitude of ∆G says NOTHING about reaction rate!)

• \Delta G < 0 : spontaneous process / exergonic reaction (favorable)

• \Delta G > 0 : nonspontaneous process / endergonic reaction (unfavorable)

• $\Delta G = 0$ : equilibrium of spontaneity / at equilibrium, process is reversible

Energy Coupling Links Reactions in Biology

• Energy-requiring (endergonic) reactions are often coupled to reactions that release free energy (exergonic)

• The breakage of phosphoanhydride bonds in ATP is highly exergonic

Spontaneity Depends on Enthalpy & Entropy

The Effects of ΔH° and ΔS° on ΔG° and Spontaneity

• When $\Delta G°_{rxn} = 0$ (@ equilibrium)

• ΔG°{rxn} = Δ H°{rxn} - T ΔS°{rxn}

• $T = \frac{\Delta H}{\Delta S}$ IF Phase transition/ equilibrium Temp

Coupling Reactions

• ΔG3 = ΔG1 + ΔG2

• Reaction coordinate diagrams = illustrates how exergonic reactions can be coupled to endergonic reactions

• Reaction 1: endergonic; $\Delta G_1$ is positive

• Reaction 2: exergonic; $\Delta G_2$ is negative

• Reaction 3: $\Delta G_3$ is negative

Equilibrium Constant (K)

• $aA + bB \rightleftharpoons cC + dD$

• Forward rate = kf [A]a[B]b = kr [C]c[D]d = Reverse rate

• Rearrange: {kf}/{kr} = {[C]^c[D]^d}/{[A]^a[B]^b}

• Now define:

  • Equilibrium Constant, K{eq} = {kf}/{kr} = {[C]^c[D]^d}/{[A]^a[B]^b}

  • “Keq”, “Kc” or “K” “describes” which rxn (forward or reverse) is favored

What does K tell us?

• K << 1

  • Reverse direction is favored

  • Rxn does not form much product

• K >> 1

  • Forward direction is favored

  • Rxn essentially proceeds to completion

• What if K ≈ 1?

  • Neither direction is favored

  • Rxn proceeds about halfway

The Reaction Quotient - Q

• If a reaction mixture containing both reactants and products is not at equilibrium, how can we determine from which direction the reaction will reach equilibrium?

• The answer is to compare the current concentration ratios to the equilibrium constant K.

• Instead of calling “K”, we use the term Reaction Quotient “Q”

• Calculate Q, the compare to known K

• Reaction quotient (Q) = The non-equilibrium concentration ratio of the products to the reactants

Is This Reaction at Equilibrium?

• The reaction quotient (Q) is evaluated the same way as K

• K vs Q

  • Q < K, the rxn will proceed in the forward direction to reach equilibrium

    • Reactant → Products

  • Q = K, the rxn is at equilibrium

  • Q > K, the rxn will proceed in the reverse direction to reach equilibrium

    • Reactant ← Products

• $aA + bB \rightleftharpoons cC + dD$

• $Q = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

What is ΔG° rxn?

• ΔG°{rxn} = ΔH°{rxn} - T ΔS°{rxn}

• (@T = 298K , P= 1 atm (or bar))

• $\Delta G°_{rxn}$ represent the amount of energy produced by a reaction

• \Delta G°_{rxn} < 0 : It is the amount of energy theoretically available to do work.

  • Some will be lost as heat.

• \Delta G°_{rxn} > 0 : it is the amount of energy that would be required in order for the rxn to occur.

  • Minimum theoretical amount required.

ΔG° rxn Under Nonstandard Conditions

• It depends on reaction conditions relative to standard states:

• ΔG{rxn} = ΔG°{rxn} + RT lnQ

• R = 8.314 J/mol K (gas constant)

• T is temperature in Kelvin

• Q is the reaction quotient (recall from previous)

• When reaction is at equilibrium, then we know $\Delta G_{rxn} = 0$ and Q = K.

• Then, ONLY AT EQUILIBRIUM!

• $\Delta G°_{rxn} = - RT \ln K$

Relationship between ΔG° rxn and Keq

• When reaction is at equilibrium, then we know $\Delta G°_{rxn} = 0$ and Q = K. Then,

• $\Delta G°_{rxn} = - RT \ln K$

• When K < 1, $\Delta G°$ is positive, and the reaction is spontaneous in the reverse direction under standard conditions.

• When K > 1, $\Delta G°$ is negative, and the reaction is spontaneous in the forward direction under standard conditions.

• When K = 1, $\Delta G°$ is 0, and the reaction is at equilibrium under standard conditions.

Equilibrium Constant Varies with Temperature

• $\Delta G°= -RT \ln K$

• We know that $\Delta G°= \Delta H-T\Delta S$

• Substituting (1) in equation (2):

• $-RT \ln K = \Delta H-T\Delta S$

• Rearranging:

• $\ln K = -\frac{\Delta H°}{RT} + \frac{\Delta S}{R}$

• To relate K with temp with known $\Delta H°$