Chemistry Chapter 17

Heat Flow, Entropy, and the 2nd Law

-When ice is placed in water, heat flows from the water into the ice -According to the 2nd Law, heat must flow from water to ice because it results in more dispersal of heat. The entropy of the universe increases.

DG under Nonstandard Conditions

- DG = DG only when the reactants and products are in their standard states -their normal state at that temperature -partial pressure of gas = 1 atm -concentration = 1 M - Under nonstandard conditions, DG = DG + RTlnQ -Q is the reaction quotient - At equilibrium DG = 0 DG = −RTlnK

Changes in Entropy, DS

- DS = Sfinal − SInitial • Entropy change is favorable when the result is a more random system - DS is positive • Some changes that increase the entropy are -reactions whose products are in a more random state -solid more ordered than liquid more ordered than gas -reactions that have larger numbers of product molecules than reactant molecules -increase in temperature -solids dissociating into ions upon dissolving

Melting Ice

- Endothermic - yet ice will spontaneously melt above ) degrees Celsius - More freedom of motion increases the randomness of the system -When the system becomes more random energy is released, we call this energy, entropy, S

Entropy Change and State Change

-Entropy(disorder) increases as you go from solid, to liquid, to gas -Therefore, as temperature increases, entropy increases

Increases in Entropy

-Ice to water(+DS) -Liquid to gas(+DS)

exothermic reaction

A reaction that releases energy in the form of heat • Two ways energy is "lost" from a system -converted to heat, q -used to do work, w W= FD • Energy conservation requires that the energy change in the system equal the heat released + work done - DE = q + w - DE = DH + PDV • DEisastatefunction -internal energy change independent of how done

Enthalpy Change

DH generally measured in kJ/mol • Stronger bonds = more stable molecules • A reaction is generally exothermic if the bonds in the products are stronger than the bonds in the reactants -exothermic = energy released, DH is negative • A reaction is generally endothermic if the bonds in the products are weaker than the bonds in the reactants -endothermic = energy absorbed, DH is positive • The enthalpy change is favorable for exothermic reactions and unfavorable for endothermic reactions

first law of thermodynamics

Energy cannot be created or destroyed -the total energy of the universe cannot change -though you can transfer it from one place to another DEuniverse = 0 = DEsystem + DEsurroundings D = final minus initial -As the energy of system increases, surroundings decrease and vice versa

Diamond → Graphite

Graphite is more stable than diamond, so the conversion of diamond into graphite is spontaneous - but don't worry, it's so slow that your ring won't turn into pencil lead in your lifetime (or through many of your generations)

Thermodynamics vs. Kinetics

Kinetics = intermediate states, speed Thermodynamics = Initial and finals states, spontaneity

Example 17.2a: Calculate the entropy change of the surroundings at 25oC for the reaction below C3H8(g) + 5 O2(g) 3 CO2(g) + 4 H2O(g) DHrxn = −2044 kJ Given: DHsystem =−2044kJ,T=25oC=298K Find: DSsurroundings, J/K

Solution: DSuni = DSsurr +DSsys (+) = (+) +(+) becuase more moles in products than reactants Spontaneous process at all temperatures

Comparing Potential Energy

The direction of spontaneity can be determined by comparing the potential energy of the system at the start and the end

Entropy Change in the System and Surroundings

When the entropy change in system is unfavorable (negative), the entropy change in the surroundings must be favorable (positive), and large to allow the process to be spontaneous

Practice - Predict whether DSsystem is + or − for each of the following

• A hot beaker burning your fingers DS is + • Water vapor condensing DS is − • Separation of oil and vinegar salad dressing DS is − • Dissolving sugar in tea DS is + •2PbO2(s)2PbO(s)+O2(g) DSis+ •2NH3(g)N2(g)+3H2(g) DSis+ • Ag+(aq) + Cl−(aq) AgCl(s) DS is −

Gibbs Free Energy, DG

• A process will be spontaneous when DG is negative - DGwillbenegativewhen - DH is negative and DS is positive -exothermic and more random - DH is negative and large and DS is negative but small DH is positive but small and DS is positive and large -or high temperature • DGwillbepositivewhenDHis+andDSis− -never spontaneous at any temperature • WhenDG=0thereactionisatequilibrium

Reversibility of Process

• Any spontaneous process can only proceed in one direction 4/27/2018 -Q≠K -a spontaneous process may become nonspontaneous if conditions change • A reversible process will proceed back and forth between the two conditions -any reversible process is at equilibrium, Q = K -results in no change in free energy • If a process is spontaneous in one direction, it must be nonspontaneous in the opposite direction -if Qfwd > Kfwd then Qrev < Kreverse

Calculating DG0

• At25C DGoreaction = SnDGof(products) - SnDGof(reactants) • At temperatures other than 25 C assuming the change in DHoreaction and DSoreaction is negligible 4/22/2019 Conceptual Plan: Relationships: Given: Find: Substance H2(g) O2(g) H2O(g) S, J/molK 130.6 205.2 188.8 standard entropies from Appendix IIB DS, J/K SH2, SO2, SH2O DS Solution: Check: DS is −, as you would expect for a reaction with more gas reactant molecules than product molecules DGreaction = DH0reaction - TDS0reaction DG0total = DG0reaction 1 + DG0reaction 2 + ... • or

DGo and K

• Because DGrxn = 0 at equilibrium, then DGo = −RTln(K) • When K < 1, DGo is + and the reaction is spontaneous in the reverse direction under standard conditions -nothing will happen if there are no products yet! • When K > 1, DGo is − and the reaction is spontaneous in the forward direction under standard conditions • When K = 1, DGo is 0 and the reaction is at equilibrium under standard conditions

Free Energy of an Exothermic Reaction

• C(s, graphite) + 2 H2(g) → CH4(g) • DH°rxn = −74.6 kJ = exothermic • DS°rxn = −80.8 J/K = unfavorable • DG°rxn = −50.5 kJ = spontaneous DG° is less than DH° because some of the released heat energy is lost to increase the entropy of the surroundings

Relative Standard Entropies Dissolution

• Dissolved solids generally have larger entropy • Distributing particles throughout the mixture

Entropy

• Entropy is a thermodynamic function that increases as the number of energetically equivalent ways of arranging the components increases, S -S generally J/mol

DS

• For a process where the final condition is more random than the initial condition, DSsystem is positive and the entropy change is favorable for the process to be spontaneous • For a process where the final condition is more orderly than the initial condition, DSsystem is negative and the entropy change is unfavorable for the process to be spontaneous -DSsystem = DSreaction = Sn(S°products) − Sn(S°reactants)

DG Relationships

• If a reaction can be expressed as a series of reactions, the sum of the DG values of the individual reaction is the DG of the total reaction -DG is a state function • If a reaction is reversed, the sign of its DG value reverses • If the amount of materials is multiplied by a factor, the value of the DG is multiplied by the same factor -the value of DG of a reaction is extensive

Real Reactions

• In a real reaction, some of the free energy is "lost" as heat -if not most • Therefore, real reactions are irreversible

Gibbs Free Energy and Spontaneity

• It can be shown that −TDSuniv = DHsys−TDSsys • The Gibbs Free Energy, G, is the maximum amount of work energy that can be released to the surroundings by a system -for a constant temperature and pressure system -the Gibbs Free Energy is often called the Chemical Potential because it is analogous to the storing of energy in a mechanical system DGsys = DHsys−TDSsys • Because DSuniv determines if a process is spontaneous, DG also determines spontaneity DSuniv is + when spontaneous, so DG is −

Relative Standard Entropies: Molecular Complexity

• Larger, more complex molecules generally have larger entropy • More available energy states, allowing more dispersal of energy through the states

Spontaneous Processes

• Spontaneous processes occur because they release energy from the system • Most spontaneous processes proceed from a system of higher potential energy to a system at lower potential energy - exothermic • But there are some spontaneous processes that proceed from a system of lower potential energy to a system at higher potential energy -endothermic • How can something absorb potential energy, yet have a net release of energy?

Standard Absolute Entropies

• S° • Extensive • Entropies for 1 mole of a substance at 298 K for a particular state, a particular allotrope, particular molecular complexity, a particular molar mass, and a particular degree of dissolution

Heat Transfer and Changes in Entropy of the Surroundings

• The 2nd Law demands that the entropy of the universe increase for a spontaneous process • Yet processes like water vapor condensing are spontaneous, even though the water vapor is more random than the liquid water • If a process is spontaneous, yet the entropy change of the process is unfavorable, there must have been a large increase in the entropy of the surroundings • The entropy increase must come from heat released by the system - the process must be exothermic!

The 2nd Law of Thermodynamics

• The 2nd Law of Thermodynamics says that the total entropy change of the universe must be positive for a process to be spontaneous -for reversible process DSuniv = 0 -for irreversible (spontaneous) process DSuniv > 0 • DSuniverse = DSsystem + DSsurroundings • If the entropy of the system decreases, then the entropy of the surroundings must increase by a larger amount -when DSsystem is negative, DSsurroundings must be positive and big for a spontaneous process

The 3rd Law of Thermodynamics: Absolute Entropy

• The absolute entropy of a substance is the amount of energy it has due to the dispersion of energy through its particles • The 3rd Law states that for a perfect crystal at absolute zero, the absolute entropy = 0 J/mol∙K -therefore, every substance that is not a perfect crystal at absolute zero has some energy from entropy -therefore, the absolute entropy of substances is always +

Free Energy and Reversible Reactions

• The change in free energy is a theoretical limit as to the amount of work that can be done • If the reaction achieves its theoretical limit, it is a reversible reaction

Quantifying Entropy Changes in Surroundings

• The entropy change in the surroundings is proportional to the amount of heat gained or lost q surroundings = −qsystem • The entropy change in the surroundings is also inversely proportional to its temperature • At constant pressure and temperature, the overall relationship is DSsurroundings = -q system /T = -DH system / T - The temperature must be in Kalvin

What's "Free" About Free Energy?

• The free energy is the maximum amount of energy released from a system that is available to do work on the surroundings • For many exothermic reactions, some of the heat released due to the enthalpy change goes into increasing the entropy of the surroundings, so it is not available to do work • And even some of this free energy is generally lost to heating up the surroundings

Standard Free Energies of Formation

• The free energy of formation (DGf°) is the change in free energy when 1 mol of a compound forms from its constituent elements in their standard states • The free energy of formation of pure elements in their standard states is zero

Relative Standard Entropies: States

• The gas state has a larger entropy than the liquid state at a particular temperature • The liquid state has a larger entropy than the solid state at a particular temperature

Relative Standard Entropies: Molar Mass

• The larger the molar mass, the larger the entropy • Available energy states more closely spaced, allowing more dispersal of energy through the states

Relative Standard Entropies: Allotropes

• The less constrained the structure of an allotrope is, the larger its entropy • The fact that the layers in graphite are not bonded together makes it less constrained

The Standard Entropy Change, DS

• The standard entropy change is the difference in absolute entropy between the reactants and products under standard conditions DSoreaction = (∑npSoproducts) − (∑nrSoreactants) -remember: though the standard enthalpy of formation, DHf°, of an element is 0 kJ/mol, the absolute entropy at 25 °C, S°, is always positive

Standard Conditions

• The standard state is the state of a material at a defined set of conditions • Gas = pure gas at exactly 1 atm pressure • Solid or Liquid = pure solid or liquid in its most stable form at exactly 1 atm pressure and temperature of interest -usually 25 °C • Solution = substance in a solution with concentration 1 M

Factors Affecting Whether a Reaction Is Spontaneous

• There are two factors that determine whether a reaction is spontaneous. They are the enthalpy change and the entropy change of the system • The enthalpy change, DH, is the difference in the sum of the internal energy and work energy of the reactants to the products • The entropy change, DS, is the difference in randomness of the reactants compared to the products

Thermodynamics and Spontaneity

• Thermodynamics predicts whether a process will occur under the given conditions -processes that will occur are called spontaneous -if the system after the reaction has less energy than before the reaction, the reaction is thermodynamically favorable. -Spontaneity ≠ fast or slow

Heat Exchange and DSsurroundings

• When a system process is exothermic, it adds heat to the surroundings, increasing the entropy of the surroundings • When a system process is endothermic, it takes heat from the surroundings, decreasing the entropy of the surroundings • The amount the entropy of the surroundings changes depends on its original temperature -the higher the original temperature, the less effect addition or removal of heat has

Temperature Dependence of DSsurroundings

• When heat is added to surroundings that are cool it has more of an effect on the entropy than it would have if the surroundings were already hot • Water freezes spontaneously below 0 °C because the heat released on freezing increases the entropy of the surroundings enough to make DS positive -above 0 °C the increase in entropy of the surroundings is insufficient to make DS positive

Entropy Change in State Change

• When materials change state, the number of macrostates it can have changes as well -the more degrees of freedom the molecules have, the more macrostates are possible -solids have fewer macrostates than liquids, which have fewer macrostates than gases