Question

Physical Chemistry II

2. Hydrogen iodide can be synthesized from the elements in a gas-phase reaction. One proposed mechanism for the process is (20 pts) 1, 21(1" order) and E= 320kJ/mol ki k 21—1, (20 order) and E, = 440kJ/mol 21+H, → 2HI (36d order) and E, = 210kJ/mol Derive a differential rate law for the rate of production of HI if a) 1, and I are in equilibrium throughout the reaction (Rapid Equilibrium) b) Derive the differential rate law if a steady state approximation can be applied to I atoms and indicate what type of conditions in terms of rate constant and concentration of I required to make a SSA. c) How could you determine experimentally which of these two assumptions a or b is correct. d) Calculate the overall activation energy for the formation of HI using both methods.

Answer 1

d) By assumption a, Ea = E3 + E1 - E2 = (210 + 320 - 440)KJ/mol = 90 KJ/mol

by assumption b, when the concentration of hy
2 I a) In < K2 kz 2 I + H2 2 HI k, [1 2] kz [+]2 ki [I 2] 1/2 [I] k2 of HI - d[HE at rate of production I d [] kg [] ² [m2] 2. dt at K2 d [HI 2kzk [12] [12 ke HI rate of production of 2k3 ki [f₂] [ H₂] b) by applying SSA to I, Iz 2I , → 12 ki 2 I + H₂ 2HI. 21 k2 k3 37 0 at 2 2 [1] 2k1 [12] - 2k2 [F]1 2kg [D] [142] = 0 2kg [I2 2kg + 2k3 [H2 rate of production of HI = 2kg [+] ² [H2 2k3 x 2k, [F2 2k2 +263 [42] 4k, k3 [fa] [H2 2kg + 2k3 [22]

Delete lowo when [M2] is rate = 2kq > 2k₃ [he] 4 kq k3 [I2] [H2 2 rate = 2k2 K2 241 kg [12] [hz] (same as a when [H2] is very high, 2k3 [H2] x 2k2 2 rate. sik, kg [12] [43] 243 Lyh]

when the rate constant kz is greater than kz than SSA can be applied. When the Concentration of I vanisher within a short time then the SSA has to be applied Ez is less c) if kz is greater than ky then SSA should be applied that is if Ez is less than E2 thin SSA should be applied. if ky is greater than ky that is crouct. the consumption than Ez then stion bis correct since Fz 2 E2 - here aussump an dy for assumption 2kzki K2 m ki dlnk. dT d dT In 2t Inkz + Ez RT2 Ea + RT2 R72 RT2 Ea when [H2 Ez + E, - E for assumption by very lew then came with when [he] a very high then, brate = {x, ky [12] [3] 2k, [I2 pk/3 ["} 2k1 d - dink (In 2ki) 3 & Fa = Ej dT dt
drogen is very high then activation energy = E1 = 320 KJ/mol