H3C CH3 C=C H H cis-2-butene ⇄ H3C H C=C H CH3 trans-2-butene The half-life (t1/2) of the catalyzed — Kinetics Chemistry Question
Problem Context
H3C CH3
C=C
H H
cis-2-butene
⇄
H3C H
C=C
H CH3
trans-2-butene
The half-life (t1/2) of the catalyzed isomerization of cis-2-butene gas to produce trans-2-butene gas, represented above, was measured under various conditions, as shown in the table below.
Trial | Initial P(cis-2-butene) (torr) | V (L) | T (K) | t1/2 (s)
1 | 300. | 2.00 | 350. | 100.
2 | 600. | 2.00 | 350. | 100.
3 | 300. | 4.00 | 350. | 100.
4 | 300. | 2.00 | 365 | 50.
Model Answer
For a first-order reaction, the half-life is independent of reactant concentration (or pressure) at constant T, as shown in trials 1, 2, and 3.
1 point is earned for a correct explanation.
Model Answer
k = 0.693/t1/2 = 0.693/100. s = 0.00693 s^-1
1 point is earned for correct numerical answer with units.
Model Answer
The initial rate in trial 1 is less than that in trial 2 because rate = k[cis-2-butene] or rate = kP(cis-2-butene) (with reference to values from both trials). OR because the initial concentration of cis-2-butene in trial 1 is less than that in trial 2 and k is constant.
1 point is earned for the correct answer with justification.
Model Answer
The temperature is higher in trial 4, meaning that the KEavg of the molecules is greater. Consequently, in this trial a greater fraction of collisions have sufficient energy to overcome the activation energy barrier, thus the rate is greater.
1 point is earned for a correct answer with justification.