Physical Biochemistry

Physical Biochemistry

Kwan Hee Lee, Ph.D.

Handong Global University

Week 3

CHAPTER 2

The Second Law: Entropy of the Universe increases

 Definition: measure of disorder

 The greater the disorder, the greater is the entropy.

 Disorder occurs spontaneously and thus entropy tends to increase.

 In an isolated system, every change within the system increases its entropy.

 Fluctuations may decrease the entropy of an isolated system slightly for a short time.

What is entropy

 If the system is not isolated from the

surroundings, then the entropy of the system can decrease.

 This decrease is accompanied by a larger increase in entropy of the surroundings.

 So the entropy of the universe always increases.

 Gibbs free energy always decreases or does not change, in a process that occurs

spontaneously at constant temperature and pressure.

Concepts

 The purpose of science is the prediction of the future.

 However, the first laws does not tell us whether a particular reaction can spontaneously occur.

 Key questions: which reactions are impossible under given conditions and how the conditions can be changed to make impossible reactions probable.

 Thermodynamics does not tell us how fast a reaction occur or how the rate depends on the reaction conditions.

Applications

 Carnot cycle: an ideal engine that undergoes a particular cycle of four steps to return to its original state.

 All steps are here are reversible.

 Steps I and III are isothermal.

 Steps II and IV are adiabatic

Carnot cycle

 In step I, a hot ideal gas at T_hot expands isothermally and reversibly in a cylinder.

 In step II, the gas expands adiabatically and

reversibly. The engine does work (w₂ is negative) without heat input, its energy drops and the

temperature of the gas reduced to T_cold.

 In step III, the gas is compressed isothermally and reversibly.

 In step IV, the gas is compressed adiabatically and reversibly (w₄ is positive, q₄=0) to return to its

original condition.

Carnot cycle

 Total work (w) = w1 + w2 + w3 + w4

 Total heat absorbed (q) = q1 + q2 + q3 + q4

 Since the initial and final states are the

same and the energy is a state function, ΔE

= o = q + w

 So it is important to know the work and heat in each step.

Carnot cycle

PV diagram

Carnot cycle heat engine

 For step I( isothermal)

 w₁ = -∫PdV = -nRT_hot ln (V₂/V₁)

 E₂-E₁ = 0, q₁ + w₁ = E₂-E₁ = 0

 Therefore q₁ = nRT_hot ln (V₂/V₁)

 For step II (adiabatic)

 q₂ = 0 (adiabatic)

 w₁ = E₂-E₁ = C_V (T_hot-T_cold)

Work and heat in Carnot cycle

 dV will result in dT

 The energy change ΔE is C_VdT

 In adiabatic, energy change is equal to the work.

C_VdT = - PdV = - nRT/V ∙ dV

 C_V∫dT/T = -nR ∫dV/V (from V₂-V₃)

C_V ln T_cold/T_hot = -nR lnV₃/V₂ = nR lnV₃/V₂

Work and heat in carnot cycle

 q₃ = -w₃ = nRT_cold lnV₄/V₃

 q₄ = 0, w₄ = C_V (T_hot-T_cold)

 -CV ln T_cold/T_hot = nR lnV₄/V₁

 Total heat absorbed (q) = q₁+q₂+q₃+q₄ = nRT_hotlnV₂/V₁ + 0 + nRT_coldlnV₄/V₃ + 0

 Total work (w): -w = -(w₁+w₂+w₃+w₄)

=nRT_hotlnV₂/V₁ + nRT_coldlnV₄/V₃

=> w= -q

Work and heat in carnot cycle

 New finding: sum of q for the reversible is not zero, but the sum of q_rev/T is zero

 In step I, ∫dq_rev/T = 1/T_hot∫dq_rev = q₁/T_hot

 In step III, ∫dq_rev/T = 1/T_cold∫dq_rev = q₃/T_cold

 In step II, IV, ∫dq_rev/T =0

 The sum of dq_rev/T = q₁/T_hot + q₂/T_cold =

nRlnV₂/V₁ + nRlnV₄/V₃ = nRlnV₂V₄/V₁V₃ = 0 (3.1a, 3.1b)

 q₁/T_hot + q₃/T_cold = 0

New state function, Entropy

 ΔS=∫dS = ∫dq_rev/T = q_rev/T

 Efficiency = -w/q_hot = -w/q₁

 q₁/T_hot = -q₃/T_cold

 -w = q₁ + q₃

 Efficiency = -w/q_hot = (q₁+q₃)/q1

= 1+ q₃/q₁

q₃/q₁ = -T_cold/T_hot

Efficiency = 1 + q₃/q₁ = 1- T_cold/T_hot

Entropy

 Entropy is an extensive variable

 Entropy is a state function

 ΔS (system) + ΔS (surrounding) ≥ 0

 For an isolated system, ΔS ≥0

Second Law of Thermodynamics:

Entropy is not conserved

 The more disorder, the higher is the entropy.

 The universe is becoming more disordered.

 Biological processes involve decreases of entropy for the organism itself but they are always coupled to other processes that

increase the entropy, so the sum is always positive.

 Entropy depends on the phase of the materials.

Molecular interpretation of

Entropy

 Liquid molecules have larger entropy than solid ones.

 For monoatomic elements. entropy can be qualitatively related to the hardness of an element (diamond is more ordered than graphite)

 All entropies increase as the temperature go up.

Molecular interpretation of

Entropy

 In the gas phase, if the number of product

molecules is less than the number of reactant molecules, entropy

decreases.

 For reactions in solution, it is more

difficult to predict the entropy change

because of the large effect of the solvent.

Molecular interpretation of

Entropy

 For the first four reactions, neutralization of charges occurs. Because a charged species tends to orient the water molecules around it, charge neutralization

results in disorientation of some of the solvent

molecules and an increase in entropy

Molecular interpretation of

Entropy

 The next two reactions involve transfer of charge but no neutralization. The entropy changes are small as a consequence.

 The last reaction involves the transfer of a nonpolar methane molecule from a polar solvent to a nonpolar solvent. The large positive ΔS is primarily the result of the ordering of water molecules around a nonpolar molecules.

 In figure a, pressures tend to be uniform.

 In figure b, compositions tend to be uniform.

 These processes can take place without changing the surroundings.

 The reverse of them can only be done if the surroundings are also changed.

Fluctations

 In a system of uniform pressure, there will be very slight increases of pressure on one side and decreases on the other side, owing to the random motion of the molecules.

 A system of uniform composition will have fluctuations in composition in any volume of the system.

 The second law of thermodynamics does not work in fluctuations.

Fluctuations

 ΔS = S₂-S₁ = ∫ dS = ∫dq_rev/T

 Entropy is a state function which

depends on the initial and final states.

 For irreversible path, the entropy change is not equal to the heat absorbed divided by T. It is greater ΔS = S₂-S₁ > ∫dq_rev/T

Measurement of Entropy

 n_AA + n_BB → n_CC + n_DD

 ΔS = n_CS_C + n_DS_D – n_AS_A – n_BS_B

 The entropy of each reactant or product depends on T and P, so ΔS of a given

reaction is dependent on T and P.

 For convenience and comparison,

standard state (reference) is defined as 1 atm and 25℃.

 Standard molar entropy

Chemical reactions

 The entropy of any pure, perfect crystal is zero at 0K. S_A(0K) = 0

 Near 0K, the disorder of a substance can approach zero, the number of microstate approaches 1.

 For this to happen, the substance must be pure.

Third law of thermodynamics