§10.1 Typical complex reactions Chapter X Kinetics of Complex Reactions §10.1 Typical complex reactions Outside classroom reading: Levine: p.559 17.9
Typical complex reactions 1) Opposing Reaction 2) Parallel Reaction 3) Consecutive Reaction
1.1 Opposing Reaction / reversible reaction The forward and the backward / reverse reaction take place simultaneously. for opposing reaction consisting of elementary reactions: As reaction proceeds, r+ increases while r decreases. When r+ becomes equal to r, equilibrium is reached.
Can we extend this discussion to ammonia synthesis? therefore The connection between the equilibrium constant (Kc) and the rate coefficients of simple reactions. This relation, named as kinetic equilibrium constant. Can we extend this discussion to ammonia synthesis? It is correct only for elementary reactions!
Under equilibrium conditions (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 The first equilibrium gives a; the second equilibrium gives xe. k+ and k can be determined by measuring x at t and at equilibrium concentration. Principle of relaxation method for studying fast reaction
Why? 1-2 opposing reaction 2-2 opposing reaction Other opposing reactions 1-2 opposing reaction 2-2 opposing 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
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.