Characteristic functionsCharacteristic functions. . Thermodynamics of chemical equilibriumThermodynamics of chemical equilibrium

PlanPlan

1. 1. Criterion of the Criterion of the Process’sProcess’s DirectionDirection..

2. 2. Gibbs Gibbs Helmholtz equation and equation and

thermodynamics gas’s functiionthermodynamics gas’s functiion..

3. 3. The third law of thermodynamicsThe third law of thermodynamics..

Prepared by Kozachok S.S.

Definition of the process’s direction according to the

caracteristic functions (internal energy)

UU is the function of the isochoric-is the function of the isochoric-isoentropic processisoentropic process:: UU

dU = TdS – pdVdU = TdS – pdV

dWdWmaxmax = = -dU -dU

For the random processFor the random process::

UU00directiondirection

spontaneous no

nsp

on

tan

eou

s

Definition of the process’s direction according to the

enthalpy

НН is the function of the isobaric-is the function of the isobaric-isoentropic processisoentropic process:::: НН

ddНН = TdS = TdS ++ Vdp Vdp

dWdWmaxmax = = -d -dННFor the random processFor the random process:: НН00

directiondirection

sponta

neous

nonsp

onta

neous

Definition of the process’s direction according to the

entropy

SS is the function of isolated system is the function of isolated system::

SS

dWdWmaxmax = = TdS TdSFor the random processFor the random process:: SS00

directiondirection

sp

on

tan

eou

s

nonsp

onta

neous

Determination of a direction of a process using Helmholtz’ energy energy

FF is the function of isochoric- is the function of isochoric-isothermal processisothermal process:: FF

dF = dU - TdSdF = dU - TdS

dWdWmaxmax = = -dF -dF

For randomFor random

processprocess:: FF00Direction of a processDirection of a process

Sponta

neous

Forc

ed p

roce

ss

Determination of a direction of a process using Gibbs’ free energyGibbs’ free energy

GG is the function of isobaric-isothermal is the function of isobaric-isothermal process process :: GG

dG = dH- TdSdG = dH- TdS

dWdWmaxmax = = -dG -dG

For spontaneousFor spontaneous

processprocess:: GG00Direction of a processDirection of a process

Sponta

neous

Forc

ed p

roce

ss

Helmholtz’ equation:Helmholtz’ equation:F = F = U - TU - TSS

Gibbs’ equation:Gibbs’ equation:G = G = H - TH - TSS

Thermodynamic functions Thermodynamic functions of the ideal gasesof the ideal gases

F = kF = kFF - RTlnV - RTlnV,,

wherewhere kkFF is the is the constantconstant, , which depends from which depends from

temperaturetemperature

(k(kF F = U – Tk = U – TkSS))

GGii = k = kG,IG,I + RTlnP + RTlnPii

For real gasesFor real gases::G = GG = G00 + RTlnf + RTlnf, , wherewhere ff - - a fugacitya fugacity;; f = f = γγ · P; · P;γγ is a coefficient of a fugacity is a coefficient of a fugacity;; γγ = P/P = P/Pidealideal..

Nernst’ heat theorem:Nernst’ heat theorem:

NearNear Т = 0Т = 0::G = G = НН - T - TS = S = HH

НН

GG

TTSS

EE

TT00

0limlim 0

dT

Gd

dT

HdToT

THIRD LAW OF THERMODYNAMICS:

tthe entropy of a perfectly pure crystal at absolute zero T=273 K is zero.

Ludwig Boltzmann’ equation::

S = klnW,S = klnW,

wherewhere k is k is Boltzmann’s constant k= k= R/NR/Na a

k=k=1.38 *10-23 J/K.

AtAt Т Т→0→0: : W = 1; S = 0.W = 1; S = 0.

Calculation of a standard and an Calculation of a standard and an absolute meaning of Entropyabsolute meaning of Entropy

298

0

lnTdCS p

CCpp

ln Tln T

∫∫

T

pT S

T

dTCSS

0

0298

, if S0 = 0

Chemical equilibriumChemical equilibrium

PlanPlan

1.1. Chemical potentialChemical potential..

2.2. Calculation of the chemical equilibriumCalculation of the chemical equilibrium..

3.3. Phase equilibriumPhase equilibrium. . Gibb’s phase ruleGibb’s phase rule..

The calculation of the chemical The calculation of the chemical potentialpotential

For ideal gas :

For real gas:

For ideal solution:

For real solution:

jjjj nTVi

nTpi

nTVi

nTpi

i dn

dF

dn

dH

dn

dU

dn

dG,,,,,,,, )()()()(

iii PRT ln0 iii fRT ln0

iii CRT ln0

iii aRT ln0

CHEMICAL EQUILIBRIUM The state reached when the concentrations of reactantsand products remain constant over time

A mixture of reactants and products in the equilibrium state is called anequilibrium mixture.

According to the balanced equation, 2.0 mol of NO2 forms for each mole of N2O4

that disappears, so the concentration of N2O4 at any time equals the initial concentration

of N2O4 minus half the concentration of NO2. As time passes, the concentration of N2O4 decreases and the concentration of NO2 increases until both

concentrations level off at constant, equilibrium values:

The Equilibrium Constant Kc

Calculation of the equilibrium Calculation of the equilibrium constantconstant

The equilibrium constant for a reaction at a particular temperature always has the same value.

аА + аА + bbВ = сС + В = сС + dDdD

;][][

]][[ba

dc

cBA

DCK

;][][

]][[ba

dc

cBA

DCK

;bB

aA

dD

cC

PPP

PPK

Pi = CiRT, that Kp = Kc (RT)n,

хi = CiRT/Ptotal, that

where n is the change of moles of gases

bB

aA

dD

cC

xK

n

totalcx P

RTKK

The physical content of the equilibrium constants

If n = 0 that Kp=Kc=Kx

N.B. This equations are true for ideal gases or solutions.

For the real systems the equilibrium constant is expressed by using activity and is named thermodynamic equilibrium constant

bB

aA

dD

cC

aaa

aaK

Heterogeneous EquilibriaThus far we’ve been discussing homogeneous

equilibria, in which all reactants

and products are in a single phase, usually either gaseous or solution.

Heterogeneous equilibria, by contrast, are those in which reactants and products

are present in more than one phase.

Because both CaO and CaCO3 are pure solids, their molar “concentrations” are constants. In general, the concentration of any pure solid (or pure liquid) is independent

of its amount because its concentration is the ratio of its amount (in moles)

to its volume (in liters). If, for example, you double the amount of CaCO3 you also

double its volume, but the ratio of the two (the concentration) remains constant.

Rearranging the equilibrium equation for the decomposition of CaCO3 to combine the constants [CaCO3], [CaO], and “Kc”, we obtain

N.B. As a general rule, the concentrations of pure solids and pure liquids are not includedwhen writing an equilibrium equation because their concentrations are constants thatare incorporated into the value of the equilibrium constant. We include only theconcentrations of gases and the concentrations of solutes in solutions because onlythose concentrations can be varied.

Judging the Extent of Reaction

Predicting the Direction of ReactionThe reaction quotient Qc is defined in the same way

as the equilibrium constant Kc

except that the concentrations in are not necessarily equilibrium values.

Altering an Equilibrium Mixture:Changes in Concentration

In general, when an equilibrium is disturbed by the addition or removal of any reactant or product, Le Châtelier’s principle predicts that

• The concentration stress of an added reactant or product is relieved by net reaction

in the direction that consumes the added substance.• The concentration stress of a removed reactant or

product is relieved by netreaction in the direction that replenishes the

removed substance.

If these rules are applied to the equilibrium

then the yield of ammonia is increased by an increase in the N2 or H2 concentration

or by a decrease in the NH3 concentration

Altering an Equilibrium Mixture:Changes in Pressure and Volume

Altering an Equilibrium Mixture:Changes in number of mokes

If n < 0 at increasing pressure

↑ p → ↑ increasing in the equilibrium constant K → ↑ increasing in product’s quantity (products predominate over reactants)

If n > 0 at ↑ p → ↓ K → ↓ decreasing in product’s quantity (reactants predominate over reactants)

If n = 0 pressure doesn’t influence on the the equilibrium constant K

Altering an Equilibrium Mixture:Changes in Temperature

Van't Hoff'sVan't Hoff's isotherm equationsotherm equationG = -RT ln KG = -RT ln K

G = G = GG0 0 + RT ln K+ RT ln K

Isobar equationIsobar equation )(ln21

12

1

2

TT

TT

R

H

K

K

Isochor equationIsochor equation )(ln21

12

1

2

TT

TT

R

U

K

K

Van't Hoff'sVan't Hoff's isotherm equationsotherm equationG = G = GG0 0 + RT ln K+ RT ln KG = RT lnG = RT ln - RT lnKp - RT lnKpb

BaA

dD

cC

PP

PP

Predicting the Direction of Reaction according to isotherm equationG <G < 0, when < lnKp, the spontaneous process of < lnKp, the spontaneous process of

net reaction goes from left to rightnet reaction goes from left to rightG >G > 0, when >> lnKp, the spontaneous process of lnKp, the spontaneous process of

net net reaction goes from right to leftreaction goes from right to leftG = 0 that is equilibrium stateG = 0 that is equilibrium state

bB

aA

dD

cC

PP

PP

ln

bB

aA

dD

cC

PP

PP

ln