4 chemical equilibrium

8/9/2019 4 Chemical Equilibrium

1/94

Equilibrium

Nothing ever changes. Does it?

1/28/15 1


2/94

Phase Equilibrium

The laws of thermodynamics determine equilibrium

between phases.

.

The fundamental fact of phase equilibrium is that atequilibrium the chemical potential of any substance must

have the same value in all phases in which that

substance appears.

1/28/15 2


3/94

Phase Equilibrium

Phasea portion of a system

or an entire system

wherein the intensiveproperties do not

chan!e abruptly as a

function of position.

"ne of the many

homo!eneous portions

of a hetero!eneous

system1/28/15 #

$ hetero!eneous system


4/94

Equilibrium

between phases

1/28/15 %


5/94

At constant temperature and pressure, any substance

tends to move spontaneously from a phase of higher

chemical potential to a phase of lower chemical potential.

1/28/15 5

&onequilibrium phases


6/94


7/94

The coe,istence of two phases in equilibrium

implies that

This means that the two intensive variables

needed to describe the state of a system are

now related and no lon!er independent.

1/28/15


8/94

1/28/15 8

Thermodynamic at says The 'ibbs phase

rule is one of the most ele!ant deductions of

the whole of chemical thermodynamics and

one of the truly !reat !enerali0ations of the

physical sciences.

here fis the 3e!rees of freedom

4ariance the number of independent intensive

variables in a simple system that can have a

number of phases and components.


9/94

1/28/15

6ut how do we count the

number of components7 s

number of components 9number of chemical

species7

$ctually+

&":


10/94


11/94

E,ample

3etermine the number of components in$n aqueous solution containin! &a*+ l@+ and

6r@.

$n aqueous solution containin! &a*+ A*+ Bi*+

l@+ and 6r@.$ !aseous system containin! &"2 and &2"%

at chemical equilibrium with each other.

$n aqueous solution containin! a2* ions and

l@ ions.

1/28/15 11

3, 5, 1, 2


12/94

Phase equilibria in one)component systems

f = 1 C 1 * 2 9 2


13/94

E,amples

$ system composed of solid sucrose in equilibrium with an aqueous

solution of sucrose.

?"2+ ?"#+ and "2in a one)phase !aseous system+ with the

chemical reaction amon! these substances at equilibrium

ce and liquid water.

"+ "2+ and "2in a sin!le !as phase+ with no catalyst present so

that the chemical reaction cannot equilibrate+ and with each

substance added separately.

$n aqueous solution of acetic acid. Dae a list of the maFor species

present in the solution.

1/28/15 1#


14/94

aterGs phase dia!ram

1/28/15 1%


15/94

1/28/15 15

f helium has

many different

phases+ cursed

humans alsohave different

phases.


16/94

lapeyron equation

1/28/15 1-


17/94

E,ample

Estimate the pressure on a system of liquid and solidwater if the equilibrium meltin! temperature is equal to

@>.1>>. The density of ice is >.1 !/cm#+ the densityof liquid water is 1.>>> !/cm#+ and the molar enthalpy

chan!e of fusion is ->>8 H/mol.

nte!rate the lapeyron equation for a solidCsolid or

liquidCsolid phase transition under the assumption that

IVmis constant and that IHm


18/94

lausius)lapeyron Equation

The lausiusClapeyron equation is obtained by

inte!ratin! the lapeyron equation in the case that one

of the two phases is a vapor

condensed phase


19/94

lausius)lapeyron equation

1/28/15 1

This is &"T the lausius)lapeyron equation


20/94

E,ample

alculate the enthalpy chan!e of vapori0ation of water

!iven the followin! values 4apor pressure of water at 25.> 9 2#.5- torr

4apor pressure of water at 1>>.> 9 ->.> torr

1/28/15 2>


21/94

'ibbs Ener!y and Phase Transitions

1/28/15 21


22/94

lassification of Phase Transitions

Phase transitions are classified accordin! to the partial derivatives of

the 'ibbs ener!y "rdinary phase transitions such as vapori0ations etc are called first)

order phase transitions.

This means that at least one of the first derivatives and is discontinuous

at the phase transition.

1/28/15 22


23/94

'iven the relationships below+ at the discontinuity the

!p,mand Tmust have a sin!ularity+ a point where it

becomes infinite.

1/28/15 2#


24/94

?econd order phase

transitions

$ transition wherein both of the first

derivatives of the 'ibbs ener!y are

continuous but at least one of the

second derivatives is discontinuous.

The order of a phase transition must

be determined e,perimentally

throu!h careful measurements of the

isothermal compressibility and heat

capacity at the phase transition.

$n e,ample of a second)order phase

transition is the transition between

normal and superconductin! states

1/28/15 2%


25/94

"ther inds of transitions

Parama!netic)to)ferroma!netic transitions

in some ma!netic

materials

"rder)disorder transitions

in certain alloys such as

beta brass

1/28/15 25


26/94

Bambda transitionThis taes place when the heat capacity rises

smoothly toward infinity instead of risin!abruptly

E,ample transition between normal+ liquid

helium + and liquid helium .

1/28/15 2-


27/94

?urfaces

Dany of the thermodynamic equations discussed are

valid only when surface contributions to the ener!ycan be ne!lected.

$lthou!h this is ordinarily an e,cellent appro,imation+

there is a si!nificant contribution to the ener!y of aliquid by the surface of the phase in the case of a

small droplet or a liquid in a small capillary tube.

Dany products and reactions involve surface effects+such as colloids+ biolo!ical cell membranes+

lubrication+ corrosion+ adhesion+ deter!ency+

lubrication+ and electrochemical cell reactions.1/28/15 2


28/94

Ener!y attributed to a surface

The surface contribution to the ener!y of a liquid is

primarily due to intermolecular attractions.

$lthou!h this is ordinarily an e,cellent appro,imation+

there is a si!nificant contribution to the ener!y of a

liquid by the surface of the phase in the case of asmall droplet or a liquid in a small capillary tube.

Dany products and reactions involve surface effects+

such as colloids+ biolo!ical cell membranes+lubrication+ corrosion+ adhesion+ deter!ency+

lubrication+ and electrochemical cell reactions.

1/28/15 28


29/94

&anoscale Thermodynamics

Thermodynamic

properties chan!e asobFects become smaller+

si!nificantly so in

nanoscale.

Deltin! point andenthalpy of fusion

decreases as the si0e of

a nanoparticle decreases.

Thermodynamicsbecomes less and less

applicable as particle

si0es become smaller.

1/28/15 2


30/94

&anoparticles

#>

Jrom

http//cfpub.epa.!ov/ncerKabstracts/inde,.cfm/fuseaction/display.abstract3etail/abstract/1#-/report/J

http//cheed.nus.edu.s!/LcheleeFy/'allery.html

n nanoparticles and

other nanoscale obFects+

their properties be!in to

depend more and more

on surface effects+electrostatic interactions+

molecular interactions+

and even quantum

mechanics.


31/94

&anoparticles

#1

Jrom

http//upload.wiimedia.or!/wiipedia/commons/-/-b/olloidal'oldKaq.pn!

http//www.topnews.in/files/stained)!lass.Fp!6u0ea+ 2>>


32/94

&anoparticles Jabrication

'as phase methods

4apor deposition synthesis

Dechanical processes

Biquid phase methods

#2

Jrom

http//cheed.nus.edu.s!/LcheleeFy/'allery.html

http//www.ptl.eth0.ch/research/resKtopKJ?P

http//www.manmadediamondinfo.com/cvd.shtmlhttp//www.cuttin!toolssite.com/2>11/>2/25/ball)millin!)2/


33/94

&anoparticles $pplications

##

Jrom

http//www)ibmc.u)strasb!.fr/ict/vectorisation/nanotubesKen!.shtml

http//www.voyle.net/E,traM2>2>>5M2>ma!es/21)>1)2>>5)2.Fp!

http//www.pharmacy.ac.u/uploads/pics/3ru!K3eliveryKPolymer.Fp!

http//www.brid!at.com/files/antiN4Ka!ent.Fp!http//ic.tweaim!.net/e,t/i/ima!enormal/12-5##>.Fpe!


34/94

&anoparticles lassification

#%

Jrom6u0ea+ 2>>


35/94

Ouantum dots

nor!anic semiconductor nanocrystals.

ave many possible applications due to their optical

properties.

n solar cells+ biosensors and bioima!in!+ BE3s+ quantum

computin!


36/94

nterphase re!ion

The #)3 re!ion of contact

between 2 phases whereinmolecules interact with

molecules of both phases

is called the interfacial

layer+ surface layer+ orinterphase re!ion.

This re!ion is a few

molecules thic if ions are

not present.

This re!ion is a transition

re!ion between the two

bul phases and is not

homo!eneous1/28/15 #-


37/94

olloids

$ colloid or disperse phase is a dispersion of

small particles of one material in another.This means typically around less than 5>> nm

particles.

n !eneral+ colloidal particles are a!!re!ates ofnumerous atoms or molecules.

Ainds of colloids?ol C solid in liquid

$erosol C liquid in !asEmulsion C liquid in liquid

1/28/15 #


38/94

olloids

olloids are

thermodynamicallyunstable with respect to

the bul+ but inetically

nonlabile

Even thou!h colloidsappearto attract each

other to coalesce into

lar!er particles+ there are

factors that oppose these.

$ maFor source of inetic

nonlability of colloids is

the electrical double layer

1/28/15 #8


39/94

olloids

The theory of the stability of

colloids is nown as the 3B4"theory+ which assumes that there is

a balance between the repulsive

interaction between the char!es of

the electric double layers on

nei!hborin! particles and the

attractive interactions arisin! from

van der aals interactions

between the molecules in the

particles.

1/28/15 #


40/94

The 'ibbs phase rule allows phase dia!rams to be

understood.

The lausius and lausiusClapeyron equations !overn

the curves in phase dia!rams.

Thermodynamics allows analysis of the stability of

phases in systems.

?urface effects must be included in a complete

thermodynamic treatment+ but are usually ne!li!ible.

1/28/15 %>


41/94

hemical Equilibrium

1. The principles of thermodynamics determine the state of chemical

equilibrium for any reaction.

2. The equilibrium constant e,pression of elementary chemistry is

equal to a constant at constant temperature when it is e,pressed in

terms of activities.

#. The principle of Be hatelier can predict how a chemical system at

equilibrium responds to chan!es in temperature+ pressure+ or

amounts of substances.

%. The couplin! of biochemical reactions can be understood throu!h

thermodynamics and the use of postulated mechanisms.

1/28/15 %1


42/94

1/28/15 %2Qumdahl hapter 2

Qer! at chemical equilibrium.


43/94

1/28/15 %#


44/94

1/28/15 %%

$t constant T and PR

= extent of reaction


45/94

1/28/15 %5

e now have the e,pression of #for our

reaction system as a function of the e,tent of

reaction at constant T and P


46/94

1/28/15 %-

ant equilibrium7

Hoin the Darines:


47/94

1/28/15 %

here activity can be defined as


48/94

here activity can be defined as

he activity is a dimensionless$uantity that is e$ual to unity if

the substance is in its standard

state.

1/28/15 %8


49/94

Jor every mole of reaction

1/28/15 %


50/94

'ibbs Ener!y han!e at a definite composition

O is called the activity quotient. The factors for the

reactants have ne!ative e,ponents.

1/28/15 5>


51/94

$t equilibrium

Beadin! to

hich !ives us

1/28/15 51


52/94

1/28/15 52

This is one of the

!reatest or most

si!nificant equations

in science $n article in?cientific $merican

states that this is

one of the only two

equations you

should now


53/94

(eactions involvin! !ases and pure solids or

liquidse now that

?o for an ideal !as reaction

e define this as the pressure equilibrium constant+ or

%p

1/28/15 5#


54/94

E,ampleonsider the reaction > 9 2&"2

volume of 2%.%- B at 28.15 A. $ssume ideal !ases.

If#S


55/94

aA + bB cC + dD

The same equilibrium stateis achieved whether

startin! with pure reactants

or pure products.

The equilibrium state can

chan!e with temperature.

The Equilibrium ondition


56/94

The Equilibrium ?tate


57/94

As the equilibrium state is approached, the

forward and backward rates of reaction

approach equality. At equilibrium the ratesare equal, and no further net change occurs

in the partial pressures of reactants or

products.

1. o macroscopic e!idence of change.

". #eached through spontaneous processes.

$. %how a dynamic balance of forward and backward processes.

&. %ame regardless of the direction from which they are approached.

'undamental characteristics of equilibrium states(

Chemical #eactions and )quilibrium

*. o change o!er time.

$ h i l ? b li


58/94

se this in an

equilibrium e-pression.

se this to indicate

resonance.

$rrows hemical ?ymbolism


59/94

Chemical #eactions and )quilibrium

he equilibrium condition for everyreaction can be

described in a single equation in which a number, theequilibrium constant (K)of the reaction, equals an

equilibrium expression, a function of properties of the

reactants and products.

/"0l2 /"0g2 3 "*oC emperature

oC2 4apor 5ressure atm2

1*.6 6.6178$ 19.6

6.61:1" 1:.6 6.6"178 "1.6

6.6"&*& "$.6 6.6"99"

"*.6 6.6$1"7 $6.6 6.6&189

*6.6 6.1"19

/"0l2 /"0g2 3 $6oC

; < 6.6$1"7

; < 6.6&189

L f M A ti (1)


60/94

5artial pressures and concentrations of products appear in the

numerator and those of the reactants in the denominator.

)ach is raised to a power equal to its coefficient in the

balanced chemical equation.

aA + bB cC + dD

Law of Mass Action (1)

if gases

PC( )c PD( )d

PA( )

a

PB( )

b= K

if concentrations

C[ ]c D[ ]d

A[ ]a

B[ ]b=K

L f M A ti ()


61/94

1. =ases enter equilibrium e-pressions as partial pressures, in

atmospheres. ).g., 5C0"

". Dissol!ed species enter as concentrations, in molarity >2

moles per liter.E.g., ?a+@

$. 5ure solids and pure liquids are represented in equilibrium

e-pressions by the number 1 unity2 a sol!ent taking part in a

chemical reaction is represented by unity, pro!ided that the

solution is dilute. E.g., I(s) ! I(aq) "I(aq) # $ K

Law of Mass Action ()

)#("1

)#("

)#("

)#("

)()(

aqIaqI

sI

aqIK

aqIsI


62/94

The Equilibrium ?tate


63/94

2" (g)* " (g) 2(g)* "2(g)

q

COOH

COHp

PPPPK

"

""=

h ) ilib i ) i


64/94

he )quilibrium )-pressions

n a chemical reaction in which amoles of species A and bmoles of

species B react to form cmoles of species C and dmoles of species D,

he partial pressures at equilibrium are related through

; < 5cC

5dD

5aA

5bB

aA + bB cC + dD

f


65/94

rite equilibrium e,pressions for the

followin! reactions

$ /"g2 + %0"g2 /"%g2 + " /"0g)

" C"'*Clg2 + & 0"g2 Cl"g2 + & C0"g2 + * '"g2

/ t ) ilib i


66/94

ases an

*olis

CaC0$s2 Ca0s2 + C0"g2

;


67/94

Liquis

*olutions

/"0l2 /"0g2

;


68/94

#elationships Among the ;s of #elated #eactions

E1( he equilibrium constant for a re!erse reaction is always

the reciprocal of the equilibrium constant for thecorresponding forward reaction.

" /" g2 + 0" g2 " /"0 g25/"02

"

5/"2"50"2

< ;1

" /"0 g2 " /" g2 + 0" g25/"2

"50"2

5/"02" < ;"

;1< 1;"

E1

E"

aA + bB cC + dD cC + dD aA + bBversus

1;;or;

1; re!for

re!

for ==

# l ti hi A th ; f # l t d # ti


69/94

E "( Fhen the coefficients in a balanced chemical

equation are all multiplied by a constant factor, thecorresponding equilibrium constant is raised to a power

equal to that factor.

5/"02

5/"250"2G

< ;$ ;$< ;1G

#elationships Among the ;s of #elated #eactions

" /" g2 + 0" g2 " /"0 g2 #-n 1E1

/" g2 + G 0" g2 /"0 g2 #-n $ < #-n 1 times 1"E$

5/"02"

5/"2"50"2

< ;1

# l ti hi A th ; f # l t d # ti


70/94

E $( when chemical equations are added to gi!e a new

equation, their equilibrium constants are multiplied togi!e the equilibrium constant associated with the new

equation.

" BrCl g2 Br" g2 + Cl" g2

5Br"25Cl"2

5BrCl2"

Br" g2 + " g2 " Br g2

5Br2"

5Br"2 5"2

" BrCl g2 + " g2 " Br g2 + Cl"g2 < ;1;"

< 6.&*26.6*12


71/94

Calculating )quilibrium Constants

Consider the equilibrium & 0"g2

" "0g2 + $ 0"g2 he three gases are introduced into a containerat partial pressures of $.7 atm for 0"2, *.1 atm for "02, and 8.6 atm

for 0"2 and react to reach equilibrium at a fi-ed temperature. he

equilibrium partial pressure of the 0"is measured to be ".& atm.

+alculate te equilibrium constantof the reaction at this temperature,

assuming that no competing reactions occur.

- /(g) ! /(g) 0 & /(g)

initial partial pressure atm2

change in partial pressure atm2equilibrium partial pressure atm2

+alculate te equilibrium constant of te reaction at tis temperature


72/94

- /(g) ! /(g) 0 & /(g)

initial partial pressure atm2 $.7 *.1 8.6

change in partial pressure atm2 I &x +"x +$x

equilibrium partial pressure atm2 ".& *.1 + "x 8.6 + $x

$.7 I &x< ".& atm 0"

- < 6.$ atm

*.1 + "6.$ atm2 < *.9 atm "0

8.6 + $6.$ atm2 < 8.: atm 0"

;

6.&62

x xx

=

check assumption

"- "&.$-16J$2< - 166 < "."O

6.&6 6.&6

assumpiton !alid, less than *O

At a particular temperature, ; < ".6 - 16J7 molM for the reaction


79/94

p p ,

+/(g) +/ (g) 0 /(g)

f ".6 mol C0"is initially placed into a *.6JM !essel, calculate te equilibrium

concentrations of all species.

initial partial pressure mol/B2 6.& 6 6

change in partial pressure mol/B2 I "x +"x +1-

equilibrium partial pressure mol/B2 6.& J"- "x 1x

+/(g) +/ (g) 0 /(g)

"J7"

p "

"

"

"

J$

?C0@ ?0 @; < < ".6-16

?C0 @

" 2 2

6.&6 " 2

- < &.$-16 >

x x

x=

"

J$

?C0 @ < 6.&6 J "-

onJ)quilibrium Conditions(


80/94

K (te Equilibrium +onstant)uses equilibrium

partial pressures

: (te reaction quotient)usesprevailing partial

pressures, not necessarily at equilibrium

he #eaction Puotient 12

wrong arrowdDcCbBaA +

+ reverse

forward

( ) ( )

( ) ( ) K

PP

PP

bB

aA

d

c

C =( ) ( )

( ) ( ) !

PP

PPb

B

a

A

d

c

C =

KQ

;

he #eaction Puotient "2


81/94

f P N ;, reaction proceeds in aforward direction toward

products2

f P Q ;, reaction proceeds in a backward directiontoward reactants2

f P < ;, the reaction is in equilibrium.

he #eaction Puotient "2

wrong arrow

KQ ; ( ) ( )

( ) ( )K

PP

PPb

B

a

A

d

c

C=

dDcCbBaA +

+

reverse

forward

( ) ( )

( ) ( ) !

PP

PPb

B

a

A

d

c

C =

The equilibrium constant for the reaction )4g! !2 )2g! is


82/94

q 4g! 2g!

1.# at %>>o. ?uppose that 2.5 mol of P%8 mol of

P2 B container at %>>o. ompute

O


83/94

*enri +ouis +e hYtelier1850-193'!

*ihlihts 188% Be hatelierZs Principle $ system in

equilibrium that is subFected to a stressreacts in a way that counteracts the stress

f a chemical system at equilibrium

e,periences a chan!e in concentration+temperature or total pressure theequilibrium will shift in order to minimi0ethat chan!e.

ndustrial chemist involved with industrialefficiency and labor)mana!ement

relations

oments in a +i$e Be hatelier was named [chevalier[

2.

hallen!e my

moustache7

thin not:

ff f l ilib i


84/94

)ffects of )-ternal %tresses on )quilibria(

Me ChRteliers 5rinciple

A system in equilibrium that is subSected to a

stress reacts in a way that counteracts the stress.

". )ffects of Changing the 4olume or 5ressure2 of the %ystem

$. )ffects of Changing the emperature

1. )ffects of Adding or #emo!ing #eactants or 5roducts

Me ChRteliers 5rinciple pro!ides a way to predict theresponse of an equilibrium system to an e-ternal

perturbation, such asT

Effects of Aing or


85/94

g g

5Cl*g2 5Cl$g2 + Cl"g2 ; < 11.* 3 $66oC < P

add e-tra 5Cl*g2

add e-tra 5Cl$g2

remo!e some 5Cl*g2

remo!e some 5Cl$g2

A system in equilibrium that is subSected to a stress reacts in a

way that counteracts the stress. In tis case aing or

remo2ing reactants or proucts

Effects of +anging te =olume of te *5stem


86/94

Effects of +anging te =olume of te *5stem

5Cl*g2 5Cl$g2 + Cl"g2

Mets decrease the !olumeof the reaction container

Mets increase the !olumeof the reaction container

Mess room (( less amount fewer moles2

*ifts reaction to restore equilibrium

>ore room (( more amount greater moles2

*ifts reaction to restore equilibrium

1 mole 1+1 < " moles

A system in equilibrium that is subSected to a

stress reacts in a way that counteracts the stress.

In tis case a cange in 2olume


87/94

)ff t f Ch i th t


88/94

)ffects of Changing the emperature

Endothermic: eat is aborbe b5 a reaction


89/94


Let@s ecrease te temperature of te reaction

Mets increase the temperature of the reaction, what

direction does the equilibrium reaction shift

Endothermic: absorption of eat b5 a reaction


90/94

Mets decrease the temperature of the reaction

Mets increase the temperature of the reaction


Exothermic: eat liberate b5 a reaction


91/94

n"othermi(ea(tion

absorb heat!

Equilibrium shift ri!ht


92/94

Dri!ing #eactions to Completion ncreasing Uield

ndustrial %ynthesis of Ammonia /aber2

"g2 + $/"g2 "/$ g2

'orward reaction is exotermic

at conitions o we nee to increase te 5iel, i.e.,

prouce more ammonia;

olume e(rease" olume n(rease"

)ressure n(rease"! )ressure e(rease"!

rea(tants

#ro"u(ts

quilibrium shi$t

rihttoar" #ro"u(ts!

quilibrium ;hi$ts le$t

toar"rea(tants!

6em#erature aise" 6em#erature +oere"

:othermi(ea(tion

liberate heat!

quilibrium ;hi$ts le$ttoar"

rea(tants!

quilibrium shi$t rihttoar"

#ro"u(ts!

Problem


93/94

ello Aitty has concocted a vile !as+ 2(g),to combat the forces of

Aeroeropi the 'reen. This !as is harmless+ but when in contact with

sunli!ht+ it decomposes into the to,ic nerve !as 2

liquid (l).

22(g) 2

$t equilibrium+ the partial pressures of 2(g) and 2.>2 and >.8

atm at #2C, the usual temperature in Isengard.

3etermine the !as equilibrium constant of the reaction.

3etermine the standard reaction 'ibbs ener!y of the reaction.

n (ohan+ the temperature is a cooler 2C and hen !aruman"s #ru$%&ai arriors deplo'ed the gas there, the partial pressures of2(g)

and 2.>5 and >.- atm at equilibrium.

3etermine the standard reaction 'ibbs ener!y of the reaction when it

taes place in (ohan.

hat is the standard reaction enthalpy chan!e of the reaction7

#


94/94

Than you for listenin!:

4 chemical equilibrium

Documents