Question

A student obtained the following data for the rearrangement of cyclopropane to propene at 500 °C. (CH2)3(g)CH3CH=CH2(g) [(CH2)3], M 0.128 6.40×10-2 3.20×10-2 1.60×10-2 time, min 0 14.4 28.8 43.2 (1) What is the half-life for the reaction starting at t=0 min? min What is the half-life for the reaction starting at t=14.4 min? min Does the half-life increase, decrease or remain constant as the reaction proceeds? _________ (2) Is the reaction zero, first, or second order? _______ (3) Based on these data, what is the rate constant for the reaction? min-1

Answer 1

Explanation:

CH2)3(g)CH3CH=CH2(g) [(CH2)3], M       time, min

0.128               0

6.40×10-2          14.4

3.20×10-2        28.8

1.60×10-2          43.2

(1) What is the half-life for the reaction starting at t=0 min? min

Half life is the amount of time required for a substance to decay by half of it's initial concentration.

Starting form 0, the initial concentration = 0.128

After 14.4 mins, the final concentration is now exactly half of the initial concentration. This means 14.4 min is the half life starting from t=0min

What is the half-life for the reaction starting at t=14.4 min?

Starting form 14.4min, the initial concentration = 6.40×10-2

After 14.4 mins (28.8 - 14.4), the final concentration is now exactly half of the initial concentration. This means 14.4 min is the half life starting from t=14.4min

Does the half-life increase, decrease or remain constant as the reaction proceeds?

The half life is a constant factor, hence it remains constant as the reaction proceeds.

(2) Is the reaction zero, first, or second order?

Because the half life is independent of the concentration, it is a first order reaction.

In a zero order reaction, the half life Decreases as the reaction progresses; as concentration decreases.

In a first order reaction, the half life Increases with decreasing concentration.

(3) Based on these data, what is the rate constant for the reaction? min-1

The realtionship between the half life and rate onstant is;

k = 0.693 / half life

k = 0.693 / 14.4

k = 0.048125 min-1