§10.1 Typical complex reactions Chapter X Kinetics of Complex Reactions §10.1 Typical complex reactions Levine: p.559 17.9
Typical complex reactions reaction contains more than one elementary reaction Typical complex reactions 1) Opposing Reaction : 2) Parallel Reaction: 3) Consecutive Reaction:
1.1 Opposing Reaction / reversible reaction majority of the reactions are reversible, i.e., the forward and the backward / reverse reaction take place simultaneously. (1) kinetic equilibrium constant for opposing reaction consisting of elementary reactions: As reaction proceeds, r+ increases while r decreases. When r+ becomes equal to r, equilibrium is reached.
therefore In this way we arrive at a very important connection between the equilibrium constant and the rate coefficients of simple reactions. This relation, named as kinetic equilibrium constant, is correct only for elementary reactions.
t = 0 a t = t a-x x t = te a-xe xe (2) rate equation For first-first order opposing reaction: t = 0 a t = t a-x x t = te a-xe xe The total rate is Under equilibrium conditions
Principle of relaxation method for studying fast reaction which suggests that k+ and k can be determined by measuring x at t and at equilibrium concentration. Relaxation method. Similar to the rate equation of first-order reaction 1-2 opposing reaction 2-2 opposing reaction Principle of relaxation method for studying fast reaction
1.2 Parallel reaction / Competing reaction When When The rate of parallel reaction is determined mainly by the faster one.
t x = y + z a For production of B and C: A B C a a-x y z Integration of the equation yields: For production of B and C: A B C a a-x y z x = y + z
A B C t c The composition of the final products is fixed. selectivity of the reaction.
Optimum temperature for better selectivity Example A B A1 Ea, 1 A C A2 Ea, 2 logA2 1/T logA1 log k B C logA2 1/T logA1 logk B C
Using catalyst to better selectivity The selectivity of the parallel reaction can be improved by adoption of appropriate catalyst.
Selectivity: Main reaction and Side reaction: reaction with higher k is taken as the main reaction, while others side reactions. Reaction that produces the demanded product is the main reaction. Selectivity:
1.3 Consecutive reaction a = x + y + z CH4 + Cl2 CH3Cl CH2Cl2 CHCl3 Some reactions proceed through the formation of intermediate. CH4 + Cl2 CH3Cl CH2Cl2 CHCl3 CCl4 General reaction A B C t = 0 a t = t x y z a = x + y + z
C tmax t A B
At tmax, the concentration of B = ? shows that the intermediate’s concentration rises from zero to a maximum and then drops back to zero as A is depleted and C dominates in the mixture. If C is the demanded product, the reaction time should be prolonged. If B is the demanded product, the reaction should be interrupted at optimum time, i.e., tmax. At tmax, the concentration of B = ?
k2/k1 1/5 5 10 100 103 108 tmax 2.01 0.40 0.25 0.047 710-3 10-7 ymax/a 0.67 0.13 0.08 7 10-3 10-3 Ea,1Ea,2 -0.4 4.0 5.7 11.5 17.2 46.1 t y k1/k2 When k2 >> k1, ymax would be very small, and the tmax would be very short.
Steady-state approximation Physical meaning of k2 >> k1 B is a active intermediate (Such as active atom: Cl, H, etc., radicals: CH3•, H2C:, C+, C-, etc., activated molecules: A*), it is difficult to form but easy to decompose to product. For consecutive reaction with large k2/k1 ratio, once the reaction take place, the active intermediate (B) rapidly attains its maximum concentration and its concentration keeps nearly unchanged during the whole reaction. Steady-state approximation
When k2 >> k1 The total rate is determined mainly by k1 When k2 << k1 The total rate is determined mainly by k2 The rate of the overall consecutive reaction depends only on the smaller rate constant (rate-determining step).
rate-determining step (r. d. s.): the step with the slowest rate. ?? !! It’s a r.d.s patient !
Rate-determining step approximation The rate of the elementary step with the lowest rate constant, i.e., r.d.s., can be used to express the actual rate of the overall reaction. What is a eligible r. d. s.? Its activation energy should be 10 kJmol-1 more than that of other steps.