Question

1. For the reaction, CO, (g) 4 H2 (g) measured: CH4 (g) 2 HO (g), the following kinetic data are HJ 0.00500 M 0.00500 M 0.00250M 0.0100 M CO.] 0.00250 M 0.00750 M 0.00750 M 0.00250 M Temperature 500 K 500 K 500 K 450 K Rate 5.2 x 10 M/s 1.6 x 103 M/s 2.1 x 104 M/s 2x 10 M/s Based on this data, a) determine the rate law for the reaction (4 pts), b) calculate the rate constants for the first and last runs (4 pts), and c) calculate the energy of activation (6 pts). (Warning: The changes in concentrations from run to run do not reference run 1 as a "base" run.) 2. A proposed mechanism for the reaction is given below; based on a systematic approach to determining rate laws for different rate-limiting steps and comparison to the rate derived from the kinetic data, decide which step determines the reaction rate (11 pts) Step #1 Step #2 Step #3 Step #4 CO2 (g) +H, (g) HCOOH (g HCOOH (g)+ H2 (g) H,C(OH)2 (g) H,C(OH), (g) +H, (g) H,COH (gH,O (g) H,COH (g)+ H2 (g) -CH (g)+ H,O (g)

Answer 1

a) let rate law for above reaction = r = k[H₂]^a[CO₂]^b

where k = rate constant

Now, from the above given kinetic data taking ratio of different reaction rates keeping conc. of H₂ constant i.e.

r1/r2 = k[0.005]^a[0.0025]^b/ k[0.005]^a[0.0075]^b = 5.2 * 10^-4 ​​​​​​/ 1.6 * 10^-3

So, (0.0025/0.0075)^b = 13/40

(1/3)^b = 13/40

taking ln both sides,

b ln(1/3) = ln(13/40)

thus, b ~ 1

similarly, again taking ratio of different reaction rates but this timekeeping conc. of CO₂constant i.e.

r1/r2 = k[0.0050]^a[0.0075]^b/ k[0.0025]^a[0.0075]^b = 1.6 * 10^-3/ 2.1 * 10^-4

(2)^a = 7.62

taking ln both sides,

a ln(2) = ln(7.62)

thus, a ~ 3

Hence, rate law will be expressed as r = k[H₂]³[CO₂]¹

b) calculation of rate constant for 1st run,

r = k1(0.005)³(0.0025) = 5.2 * 10^-4

k1 = 1.664 * 10⁶ M^-3 s^-1

calculation of rate constant for last run,

r = k2(0.01)³(0.0025) = 1.2 * 10^-4

k2 = 4.8 * 10⁴ M^-3 s^-1

c) Calculation of Activation energy,

from Arrhenius equation,

ln(k2/k1) = (E_a/R) * (1/T₁ - 1/T₂)

where k1 and k2 are rate constants at two different temperatures T₁ and T₂

E_a = Energy of Activation

R = Gas Constant

T₁ = 500 and T₂ = 450

values of k1 and k2 obtained in part b

So, ln( 4.8 * 10⁴/1.664 * 10⁶) = (E_a/8.314) * (1/500 - 1/450)

Thus, E_a = 265.26 J/mol

2. Since the rate law for given equation depends upon the concentration of H₂ and CO₂, thus step 1 is the rate determining step here.