22. 3. 2020

Chemical equilibrium

Thermochemistry: The study of the energy transferred as heat during the course of chemical reactions is called thermochemistry. Thermochemistry is a branch of thermodynamics because a reaction vessel and its contents form a system, and chemical reactions result in the exchange of energy between the system and the surroundings.

• a process that releases energy to the surroundings is classified as exothermic. The release of energy signifies a decrease in the enthalpy of a system (at constant pressure), H < 0.

• a process that absorbs energy from the surroundings is classified as endothermic. The absorption of energy results in an increase in enthalpy, ∆H > 0. 1

The standard enthalpy change, ∆H, the change in enthalpy of a process in which the initial and final state of the system are the standard states:

The standard state of a substance at a specified temperature is: pure form at the pressure of 1 bar.

For example, the standard state of liquid ethanol at 298 K is: pure liquid ethanol at 298 K and 1 bar

(1 bar = 100 000 Pa) 2

1 22. 3. 2020

Enthalpy of a physical change:

0 - standard enthalpy of vaporization vapH - is the enthalpy change per mole when a pure liquid at 1 bar vaporizes to a gas at 1 bar  H 0 373K   40.66kJmol 1 H 2Ol H 2Og vap

0 - standard enthalpy of fusion, fusH  H 0 273K  6.01kJmol 1 H 2Os H 2Ol fus  

0 - standard enthalpy of sublimation, subH

H 2Os H 2Og 3

0  fusH

0 vapH

0 0  fusH vapH

Another consequence of H being a state function is that the standard enthalpy changes of a forward process and its reverse differ in sign

H 0 A  B  H 0 A  B

4

2 22. 3. 2020

5

Enthalpies of a chemical change Now we consider enthalpy changes that accompany chemical reactions. aA bB  pP  rR A, B reactants P, R products Stoichiometric coefficients: reactants: A = -a, B = -b products : P = p, R = r a,b, p, r are absolute values (modulus) of stoichiometric coefficients

6

3 22. 3. 2020

0 Standard reaction enthalpy rH - is the change of enthalpy when reactants in their standard states are converted to products in their standard states  H 0  890kJmol 1 CH 4 g 2O2 gCO2 g 2H 2Ol r

Standard reaction enthalpy : 0 0 0 r H  iH m,i  jH m, j Products,i Reactants, j

For the reaction: 2A  B 3C  D 0 0 0 0 0 r H  3H m C H m D2H m A H m B 0 Hm (J) is the standard molar enthalpy of species J at given temperature 0 0 r H   j H m J  J 7

0 * Standard enthalpy of combustion cH is the standard reaction enthalpy for the complete oxidation of an

organic compound to CO2 gas and liquid H2O if the compound contains

C, H, and O, and to N2 gas if N is also present. An example is the combustion of glucose:

C6 H12O6 s 6O2 g  6CO2 g 6H 2Ol 0 1 c H  2808kJmol

8

4 22. 3. 2020

0 * Standard enthalpy of formation fH is the standard reaction enthalpy of formation of the compound from its elements in their reference states. The reference state of an element is its most stable state at the specified temperature and 1 bar. The standard ethalpies of formation of elements in their reference states are zero at all temperatures.

The reaction enthalpy in terms of enthalpies of formation: Conceptually, we can view a reaction as proceeding by decomposing the reactants into elements and then transforming those elements into the products.

0 0 0 r H  i f H  j f H Products,i Reactants, j 9

10

5 22. 3. 2020

11

The temperature-dependence of reaction enthalpies When the temperature is increased, the enthalpy of the products and the reactants both increase, but may do so to different extents.

In each case, the change in enthalpy depends on the heat capacities of the substances. T2 H T  H T  c dT  2   1   p T1 The change in reaction enthalpy reflects the difference in the changes of the enthalpies.

T2  H 0 T   H 0 T   c0 dT r  2  r  1   r p T1

Kirchhoff’s law 0 rcp is the difference of the molar heat capacities of products and reactants under 12 standard conditions

6 22. 3. 2020

0 rcp is the difference between the molar heat capacities of products and reactants under standard conditions [p = 1 bar]:

0 0 0 r cp  cp,m  cp,m Products,i Reactants, j

0 0 rcp   jcp,m J  J

13

Example: −1 The standard enthalpy of formation of gaseous H2O at 298 K is −241.82 kJ mol . Estimate its value at 100°C given the following values of the molar heat capacities at −1 −1 −1 −1 constant pressure: H2O(g): 33.58 J K mol ; H2(g): 28.84 J K mol ; −1 −1 O2(g): 29.37 J K mol . Assume that the heat capacities are independent of temperature.

0 Calculation of rcp,m : 1 H g O g  H Og 2 2 2 2

0 0 rcp,m   jcp,m J  J

0 0  0 1 0  1 1 rcp  cp,m H 2O, g cp,m H 2 , g cp,m O2 , g  9,94JK mol  2  14

7 22. 3. 2020

1 1 H g O gr H1241,82kJmol H Og T  2 9 8K 2 2 2 2 1 0 0 [cm, p T2 T1 ]P [cm, p T2 T1 ]R

1  H ? H g O gr 2  H Og T2  373K 2 2 2 2

0 0 0 0 r H1 [cm, p T2 T1 ]P  r H 2 [cm, p T2 T1 ]R

0 0 0  c0  9,94JK 1mol 1 r H 2  r H1  rcp .T r p

0 1 1 1 1 r H 373K   241,82kJmol  75K  9,94JK mol  242,6kJmol

15

aA bB  pP  rR A, B reactants, P, R products

Stoichiometric coefficients: reactants: A = -a, B = -b products : P = p, R = r State functions: at a defined state: at a standard state: 0 0 r X m   i X m i r X m   i X m i i i ( T, p =konst.)

X H G S cp V

rX rH rG rS rcp rV

0 0 0 0 0 0 rX rH rG rS rcp rV

units Jmol-1 Jmol-1 JK-1mol-1 JK-1mol-1 m3mol-1 16

8 22. 3. 2020

Chemical equilibrium, the reaction Gibbs energy. The extend of chemical reaction: A  2B 3C  D Instantaneous rate: dR The rate of consumption:  (R  A, B) dt dP The rate of formation: (P  C, D) dt dD 1 dC dA 1 dB  .     . dt 3 dt dt 2 dt …so there are several rates connected with the reaction. n  n dn The extent of the reaction:   i i0 ;d  i [mol]  i  i 17

The reaction Gibbs energy rG: is defined as the slope of the graph of the Gibbs energy plotted against the extent of reaction :  G  rG       p,T

Consider the equilibrium: A B Suppose that d =1, one mol of A turns into B:

dG   AdnA  BdnB   Ad  Bd  B   A d  G          B A rG  B   A    p,T

rG is the difference between the chemical potentials (the partial molar Gibbs energies) of the reactants and products at the composition of the reaction mixture.18

9 22. 3. 2020

rG  B   A Because chemical potential varies with composition, the slope of the plot of Gibbs energy against extent of reaction changes as the reaction proceeds.

If ∆rG < 0, the forward reaction is spontaneous. (A > B) exergonic reaction – work producing

If ∆rG > 0, the reverse reaction is spontaneous. (A < B) endergonic reaction – work consuming

If ∆rG = 0, the reaction is at equilibrium. (A = B)

19

0 The standard reaction Gibbs energy rG . The equilibrium constant K. Perfect gas equilibria (A, B gases) :

0 0 rG  B   A  B  RT ln pB   A  RT ln pA   p  0  B  rG  rG  RT ln   pA 

0 Standard reaction Gibbs energy rG is defined as the difference in the standard molar Gibbs energies of the reactants and products:

0 0 0 rG  GB,m  GA,m

At equilibrium:  rG  0

  0 0 pB 0   G  RT ln K K    r rG  RT ln K  pA equilibrium 20

10 22. 3. 2020

If the mixing of reactants and products is ignored, then the Gibbs energy changes linearly from its initial value (pure reactants) to its final value

(pure products) and the slope of the line is ΔrG .

G  rG   rG  0

However, as products are produced, there is a further contribution to the Gibbs energy arising from their mixing (lowest curve).

mixG  nRT xA ln xA  xB ln xB   0

The sum of the two contributions has a minimum. That minimum corresponds to the equilibrium composition of the system.

21

The general case of a reaction:

0 The reaction Gibbs energy: rG  rG  RT ln Q Q – reaction quotient The standard reaction Gibbs energy: 0 0 0  G0    G0 i r G   f G   f G r  i f Products Re actants i

activities of products The reaction quotient: Q = activities of reactants

 i Q  ai i

 - product of what follows it 22

11 22. 3. 2020

Example: Consider the reaction 2 A + 3 B → C + 2 D, in which case νA = −2, νB = −3, νC = +1, and νD = +2.

The reaction quotient is then:

2 2 3 2 aC aD Q  aA .aB .aC .aD  2 3 aAaB

23

At equilibrium:

0 rG  rG  RT ln K  rG  0

 a C a D  0 K   C D  rG  RT ln K  a A a B   A B equilibrium

  i  Generally: K  ai   i equilibrium

K – thermodynamic equilibrium constant

24

12 22. 3. 2020

The reaction thermodynamic state functions:

0 0 0 rG   iG i [p ] i

0 0 0 r S   i S i [p ] i 0 0 0 [T] rG  r H Tr S

0 rG  RT ln K

Response of K to conditions (p, T): Le Chatelier’s principle

A system at equilibrium, when subject to a disturbance, responds in a way that tends to minimize the effect of the disturbance. 25

The response of equilibria to temperature - the van’t Hoff equation

dG  Vdp  SdT p = const. dG  SdT dG  dH TdS (T = const.)

0 0 0 d G0  H   G T S r   S 0 r r r dT r d(RT ln K)   H 0  RT ln K  r dT T 0 0 r H  RT ln K 0  S  d(T ln K)  H r  r  ln K T dT RT

0 d(T ln K) d ln K d ln K r H van’t Hoff  ln K T  2 equation dT dT dT RT 26

13 22. 3. 2020

The response of equilibria to temperature : d ln K  H 0  r dT RT 2 d ln K dK Exotermic reactions ( H0 < 0 ):  0 (  0) r dT dT A negative slope means that ln K, and therefore K itself, decreases as the temperature rises. Increased temperature favours the reactants. d ln K 0  0 Endotermic reactions (rH > 0 ): dT A positive slope means that ln K, and therefore K itself, increases as the temperature rises. Increased temperature favours the products. 27

K2  H 0 T2 dT ln K  r  R  T 2 K1 T1

0 K2 r H  1 1  ln     K1 R T1 T2 

0 0  H  1 1   H  1 1  r r pK2      pK1 ln K2      ln K1     2,303R T2 T1  R T1 T2 

pK  log K 28

14 22. 3. 2020

Example: Calculate the standard reaction enthalpy of the decomposition :

Ag 2CO3 (s) Ag 2O(s)  CO2 (g) The data below show the temperature variation of the K : T/K 350 400 450 500 K 3,98.10-4 1,41.10-2 1,86.10-1 1,48

0  H 0 dT d ln K r H r  d ln K  2 dT RT 2  R  T  H 0 1 ln K   r .  C R T

(103K)/T 2,86 2,50 2,22 2,00 -ln K 7,83 4,26 1,68 -0,39

0 3 1 29 r H  9,5.10 K .R  79kJmol

Questions: • describe enthalpy of physical changes • describe enthalpy of chemical reactions • describe the temperature-dependence of reaction enthalpies • describe chemical equilibrium and reaction Gibbs energy • define the equilibrium constant of chemical reaction • describe the Le Chatelier ‘s principle • define the response of equilibria to temperature

30

15