Kinetics of solution in reaction

Definition - Mechanism - Effect of dielectric constant on the rate of reactions in solutions - Salt effect - Primary salt effect - Bronsted – Bjerrum equation - Secondary salt effect - Effect of pressure on rate of reaction in solution - Volume of activation - Significance

1. Dr.P.GOVINDARAJ   Associate Professor & Head , Department of Chemistry SAIVA BHANU KSHATRIYA COLLEGE ARUPPUKOTTAI - 626101 Virudhunagar District, Tamil Nadu, India KINETICS OF REACTION IN SOLUTION

2. Kinetics of reaction in solution Reaction in solution Chemical reaction between the solute molecules present in the solvent is called Reaction in solution A (solute) + B (solute) Product Example solvent Pb(NO 3 ) 2( aq ) + K 2 CrO 4( aq ) PbCrO 4(s) + K(NO 3 ) 2( aq )

3. Mechanism for Reaction in solution There are four steps involved in the reaction in solution. Step I The reactant molecules (solute) are jumping from hole to hole (diffusion) in the solvent m atrix and occasionally finding themselves in the same solvent cage where thermal motions are likely to bring them to contact. Kinetics of reaction in solution

4. Step II As a result of step I, the two reactants form an encounter pair. If they fail to react the first time, they have many more opportunities during the lifetime of the cage eventually they undergo chemical reaction. Kinetics of reaction in solution

5. Kinetics of reaction in solution The products form from the encounter pair and begin to move away from each other Step III Finally, the solvent cage breaks up and the product diffuse away Step IV

6. Kinetics of reaction in solution Effect of solvent (or) dielectric constant on the rates of ionic reactions According to activated complex theory the ionic reaction between the reactants A and B in a solvent of dielectric constant ( ε r ) can be represented as A + B ⇌ [X * ] → Product Activated complex Initially the two ions are at infinite distance apart but they touch each other when they form t he activated complex shown in the diagram

7. The free energy change of activation per molecule is written as Kinetics of reaction in solution The work done in bringing the two ions together from infinity to a distance d AB is W = Z A e X Z B e / ε r d AB ---------(1) w here Z A e ------- charge on A Z B e ------- charge on B = + W ---------( 2)   w here ------- Molar non-electrostatic term  

8. Kinetics of reaction in solution Substituting (1) in (2) we get, = +   = + N A ---------( 3)   According to Activated complex theory, the rate constant is k = exp (- ∆G * /RT) ---------(4)  

9. Taking log on both side, gives Kinetics of reaction in solution Substituting (3) in (4) gives k = exp -( + N A ) / RT   k = exp exp N A   ln k = ln N A ----------(5)  

10. Kinetics of reaction in solution Put ln k = ln in equation (5), we get   l n k = ln k N A ----------(6)   Equation (6) is the equation of a straight line. It shows that the logarithm of the rate constant of an ionic reaction varies inversely with dielectric constant of the solvent at a given temperature. A plot of lnk versus the reciprocal of the dielectric constant for a ionic reaction is shown in the diagram The measurement of the slope, which is equal to N A , can lead to estimation of  

11. Kinetics of reaction in solution Salt effect The effect of electrolytes on the kinetics of reaction in solution is called salt effect Two types of salt effect Primary salt effect Secondary salt effect Primary salt effect The effect of ionic strength on the rate constant of the non-catalytic i onic reaction is called Primary salt effect

12. Kinetics of reaction in solution Consider a reaction involving ions in solution A + B ⇌ [X*] → Product w here Z A ------- Charge on the reactant A Z B ------- Charge on the reactant B Z A + Z B ------- Charge on the activated complex The rate of the reaction is proportional to the concentration of the activated complex X * i.e., r = k’[ X * ] -------(1) z A z B ( z A + z B ) k 1 k 2 k ’

13. The equilibrium constant ( K * ) between the activated complex and the reactants in terms of activities is written as Kinetics of reaction in solution = K * = a * / a A a B = --------(2)   [Since a = c  , where c --- concentration ] [X * ] = ----------(3)   w here a ------ Activities of the species involved  ------ Activity co-efficient of the species involved Rearranging equation (2) we get

14. Kinetics of reaction in solution r = k’K * [ A][B] ---------(4)   Substituting equation (3) in equation (1), we get Put k = k’K * in equation (4), we get r = k [A][B] ---------(5)   For a second order reaction, the rate of the reaction is expressed as r = k[A][B] ---------(6) w here k ------ r ate constant for the second order reaction

15. Equating equation (5) and (6), we get Kinetics of reaction in solution k[A][B] = k [A][B]   k = k ---------(7)   Taking log on both side of the equation (7), we get ln k = lnk + ln ---------( 8)   According to the Debye- Huckel limiting law ln  i = - AZ i 2 ---------(9)   w here A ------- Constant I ------- Ionic strength of the solution

16. Kinetics of reaction in solution Equation (8) is rewritten as Using equation (9), equation (10) can be written as, ln k = lnk + ln + ln – ln ---------(10)   ln k = lnk - AZ A 2 - AZ B 2 + A(Z A + Z B ) 2   ln k = lnk – A[Z A 2 + Z B 2 - (Z A + Z B ) 2   ln k = lnk – A[Z A 2 + Z B 2 - Z A 2 - Z B 2 - 2Z A Z B ]   ln k = lnk + 2AZ A Z B ---------(11)  

17. Kinetics of reaction in solution Equation (11) is the Bronsted – Bjerrum equation For aqueous solutions at 25 C , the constant A = 0.51, so that equation (11) becomes lnk = lnk + 1.02 Z A Z B   Equation (12) is looking as the equation of straight line, so that a plot of ln k/k versus for the following ionic reactions gives a straight line with slope = 1.02 Z A Z B shown in the diagram   1. [Co(NH 3 ) 5 Br] 2+ + Hg 2+ ( Z A Z B = 4) ln = 1.02 Z A Z B ---------(12)   2. S 2 O 3 2- + I - (Z A Z B = 2) 3 . [Co(OC 2 H 5 )N:NO 2 ] - + OH - ( Z A Z B = 1) 4 . CH 3 COOC 2 H 5 + OH - ( Z A Z B = 0) 5 . H + + Br - + H 2 O 2 ( Z A Z B = -1) 6. [Co(NH 3 ) 5 Br] 2+ + OH - ( Z A Z B = -2) 7. Fe 2+ + [Co(C 2 O 4 ) 3 ] 3- ( Z A Z B = -6)

18. Kinetics of reaction in solution From the above diagram, it was formed that I f one of the reactants is a neutral molecule, the product Z A Z B = 0 and the rate constant ( or) rate of the reaction will be independent of the ionic strength If the product Z A Z B is positive, the rate constant (or) rate of the reaction will be increased as the ionic strength increased If the product Z A Z B is negative, the rate constant (or) rate of the reaction will be decreased as the ionic strength increased

19. Secondary salt effect Kinetics of reaction in solution The effect of actual change in the concentration of reacting ions by the addition of catalytic electrolytes on the rate of a reaction is called Secondary salt effect Consider the catalytic effect of hydrogen ions produced by a mixture of weak acid and its salt at a definite concentration HA ⇌ H + + A - ----------(1) The equilibrium constant K A for the above equilibrium is K A = ----------(2)  

20. Kinetics of reaction in solution Since a= c  , equation (2) becomes K A = X ----------(3)   Rearranging the equation (3), we get [H + ] = X ----------( 4 )   Since the pH of a mixture of a weak acid (HA) and its salt ( A - ) is of constant composition, the term in equation (4) is constant   i.e., = constant = k ---------(5)  

21. Kinetics of reaction in solution Substitute equation (5) in equation (4), we get [H + ] = ---------( 6)   As per the equation (6), the activity term varies with the ionic strength of the medium , it follows that hydrogen ion (H + ) concentration and its catalytic activity will also vary with ionic strength of the medium. This is the secondary salt effect. The rate of a reaction involving hydrogen ions as catalyst is proportional to the concentration of the H + ions i.e., rate = k’ [ H + ] ---------(7)

22. Rate (r) = ---------(8)   Kinetics of reaction in solution Substitute equation (6) in equation (7), we get Taking log on both sides of equation (9), we get Put k = k’k in equation (8), we get r = ---------(9)   According to Debye- Huckel limiting law, ln = ln k + ln – ln H + – ln ---------(10)   ln H + = - 0.509 (Z H + ) 2   ln = - 0.509 (Z H+ +Z A- ) 2   ---------( 11) ln = - 0.509 (Z A- ) 2  

23. Kinetics of reaction in solution ln = ln k - 0.509 (Z H+ +Z A- ) 2 + 0.509 (Z A- ) 2   Substitute equation (11) in equation (10), we get ln = ln k - 0.509 ( Z 2 H+ + Z 2 A- + 2 Z A- ) + 0.509 (Z A- ) 2   ln = ln k - 0.509 Z 2 H + – 0.509 Z 2 A- – 0.509 X 2 Z A- + 0.509 ( Z A- ) 2   ln = ln k – 1.018 Z A- --------------(12)  

24. Kinetics of reaction in solution According to equation (13 ), as the ionic strength increases, the concentration of H + increases and therefore the rate of acid catalyzed reaction also increases . This is called Secondary salt effect. Since = +1 , Z A- = -1, equation (12) becomes   ln = ln k – 1.018 (1 X -1)   ln = ln k + 1.018 --------------(13)  

25. Kinetics of reaction in solution T = ------------(1)   According to Van’t H off , the effect of pressure on the equilibrium constant K c is w here ------- Difference between the volume of the products and reactants at standard conditions   i.e., = V p - V r ------------(2)   According to transition state theory Reactant Activated complex Product Effect of Pressure on reaction rate ------------------------------------> <-------------------------------------- k 1 k -1

26. So equation (2) becomes, Let V * -------- Partial molar volume of activated complex V * - V r -------- Partial molar volume of Products (V p ) V * - V p -------- Partial molar volume of reactants ( V r ) Kinetics of reaction in solution = (V * - V r ) – (V * - V p )   = ∆ * V 1 – ∆ * V -1 ----------(3)   w here ∆ * V 1 ------- Standard volume change in going to the activated state in the forward direction ∆ * V -1 ------- Standard volume change in going to the activated state in the backward direction

27. Kinetics of reaction in solution Substitute equation (3) in equation (1), we get The quantities ∆ * V 1 and ∆ * V -1 are called volume of activation T = -   T = - ------------(4)   Since the equilibrium constant K c is expressed as K c = ------------( 5)   w here k 1 -------- rate constant for the forward reaction k -1 -------- rate constant for the forward reaction

28. Kinetics of reaction in solution Substitute equation (5) in equation (4), we get Since the forward reaction depends only on ∆*V 1 and the backward reaction depends only on ∆*V -1 , the equation (6) can be split into the two equations T = -   T - T = - ------------(6)   T = - ------------(7)   T = - ------------( 8)  

29. The equation (11) explain the effect of pressure on the rate of a reaction. In general Kinetics of reaction in solution T = - ------------(9)   d = - d ------------( 10)   Integrating equation (10 ), we get = - ------------( 11)   w here lnk = Integrating constant i.e., the rate constant of a reaction increases with increasing pressure if is negative and decreases with increasing pressure if is positive  

30. Kinetics of reaction in solution Volume of activation and its significance Definition The difference between the partial molar volume o f the transition state and the partial molar volume o f the reactant is called volume of activation i.e., = Partial molar volume of transition state – Partial molar volume of the reactant  

31. Kinetics of reaction in solution Significance of v olume of Activation The rate constant increases with increasing pressure if is negative, that means if the activated complex has a smaller volume than the reactants. On the other hand the rate constant decreases with increasing pressure if is positive , that means if the activated complex has a higher volume than the reactant For a bimolecular reaction , is positive For a unimolecular reaction , is negative Solvent effect also plays important role in predicting the sign of Reaction between same ions lead to increase in due to repulsion Reaction between opposite charge ions lead to decrease in due to attraction   ln k = ln k -   The effect of pressure on the reaction rate is expressed in the form of equation as

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