Presentation on theme: "Chemical kinetics: accounting for the rate laws"— Presentation transcript:
1 Chemical kinetics: accounting for the rate laws 자연과학대학 화학과박영동 교수
2 The approach to equilibrium Forward: A → B Rate of formation of B = kr[A]Reverse: B → A Rate of decomposition of B = kr[B]Net rate of formation of B = kr[A] − kr[B]At equilibrium, rate = 0 = kr[A]eq − kr[B] eq
4 The net rate Forward: A → B Rate of formation of B = kr[A] Reverse: B → A Rate of decomposition of B = kr[B]Net rate d[A]/dt = − kr[A] + kr[B] = − kr[A] + kr([A]0 − [A])d[A]/dt = − (kr + kr) [A] + kr[A]0at t = 0,
5 The approach to equilibrium The approach to equilibrium of a reaction that is first-order in both directions.
8 Reaction Mechanism and elementary reactions a unimolecular elementary reactiona bimolecular elementary reactionA → P v = kr[A]A + B → P v = kr[A] [B]
9 The formulation of rate laws 2 NO(g) + O2(g) → 2 NO2(g)ν = kr[NO]2[O2]Step 1. Two NO molecules combine to form a dimer:(a) NO +NO →N2O2Rate of formation of N2O2 = ka[NO]2Step 2. The N2O2 dimer decomposes into NO molecules:N2O2 → NO + NO,Rate of decomposition of N2O2 = ka΄[N2O2]Step 3. Alternatively, an O2 molecule collides with the dimer and results in the formation of NO2:N2O2 + O2 → NO2 + NO2,Rate of consumption of N2O2 = kb[N2O2][O2]
10 The steady-state approximation 2 NO(g) + O2(g) → 2 NO2(g)Rate of formation of NO2 = 2kb[N2O2][O2]Net rate of formation of N2O2 =ka[NO]2 − ka΄[N2O2] − kb[N2O2][O2] = 0The steady-state approximation: ka[NO]2 − ka΄[N2O2] − kb[N2O2][O2] = 0[N2O2] = ka[NO]2 /( ka΄+ kb[O2] )Rate of formation of NO2 = 2kb[N2O2][O2]= 2kakb [NO]2 [O2]/( ka΄+ kb[O2] )if ka΄[N2O2]>>kb[N2O2][O2]Rate = 2kakb [NO]2 [O2]/( ka΄+ kb[O2] ) = (2kakb/ka΄)[NO]2 [O2]kr= (2kakb/ka΄)
11 The rate-determining step The rate-determining step is the slowest step of a reaction and acts as a bottleneck.The reaction profile for a mechanism in which the first step is rate determining.
12 Unimolecular Reaction and The Lindemann Mechanism Rate of formation of A* = ka[A]2A + A → A* + ARate of deactivation of A* = ka΄[A*][A]A + A* → A + ARate of formation of P = kb[A*]A* → PRate of consumption of A* = kb[A*]Net rate of formation of A* =ka[A]2 − ka΄[A*] [A]− kb[A*]= 0[A*] = ka[A]2 /( ka΄[A]+ kb)Rate of formation of P = kb[A*]=kakb [A]2 /( ka΄[A]+ kb )if ka΄[A]>>kbRate = kakb [A]2 /( ka΄[A]+ kb) = (kakb/ka΄)[A]kr= (kakb/ka΄)
13 Activation control and diffusion control Rate of formation of AB = kr,d[A][B]A + B → ABRate of loss of AB = kr,d΄ [AB]AB → A + BRate of reactive loss of AB = kr,a [AB]AB → PRate of formation of P = kr[A][B]kr= kr,a kr,d/(kr,a + kr,d΄)i) kr,a >> kr,d΄kr= kr,ddiffusion-controlled limitii) kr,a << kr,d΄kr= kr,a kr,d/ kr,d΄activation-controlled limit
14 kr,d = 8𝑅𝑇 3𝜂For a diffusion-controlled reaction in water, for which η = 8.9 × 10−4 kg m−1 s−1 at 25°C.kr,d = 8𝑅𝑇 3𝜂 = 8×( J K −1 mol −1 )×(298K) 3×8.9× 10 −4 kg m −1 s −1= 8× ×298 J mol −1 3×8.9× 10 −4 kg m −1 s −1=7.4× kg m 2 s −2 mol −1 kg m −1 s −1 =7.4× m 3 s −1 mol −1 =7.4× dm 3 s −1 mol −1kr,d = 7.4 × 109 dm3 mol−1 s−1
15 Diffusion Fick’s first law of diffusion 𝐽=−𝐷 𝑑𝑐 𝑑𝑥 Table 11.1 Diffusion coefficients at 25°C, D/(10−9 m2 s−1)The flux of solute particles is proportional to the concentration gradient.
19 DiffusionSuppose an H2O molecule moves through one molecular diameter (about 200 pm) each time it takes a step in a random walk. What is the time for each step at 25°C?Einstein–Smoluchowski equation:𝐷= λ 2 2𝜏𝜏= λ 2 2𝐷 = (200𝑝𝑚) 2 2(2.26× 10 −9 𝑚 2 𝑠 −1 ) =8.85× 10 −12 𝑠
20 CatalysisA catalyst acts by providing a new reaction pathway between reactants and products, with a lower activation energy than the original pathway.
21 Michaelis-Menten kinetics MechanismE + S ES → E + Pk2→k1k-1ES complex is a reaction intermediate
22 Michaelis-Menten Kinetics Steady state approximation
48 The DHLL for aqueous solution can be written as Debye-Huckel Limiting Law is a valid approximation when strong electrolyte ions are in the solution at low concentration.Consider the solubility of Hg2(IO3)2(Ks= 1.3×10-18 )in KCl( 0.05 M).1. Calculate the mean activity coefficient γ ± of the solution.2. Calculate solubility of Hg2(IO3)2 at this temperaturein unit of mol dm-3.The DHLL for aqueous solution can be written asln γ ± = |z+z-|I1/2.Assume DHLL applies to this solutioon.