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