Answer to Question #198135 in Physical Chemistry for bienvenido marmol

Question

A reaction 𝐴 + 𝐵 → 𝑃 has been studied with the half-time method to determine a total order of a reaction and the rate constant. The experimental measurements determined the following characteristic equation:

log6𝑡!/#7 = 0.290618 + 0.500 ∗ log(𝐴$)

(a) Find the total order, and the rate constant of the reaction.

(b) State if and when one has to be cautious using the half-time method to determine the order or the rate constant of a reaction.

(c) State if the method can be used to determine orders of reaction with respect to individual reactants. If yes, briefly describe what needs to be done to determine these orders.

Answer 1

(a)

a plot of log(t1/2) vs log(Ao) will have, slope = 1 - n

we have, 1-n = 1.200

n = - 0.200

==>

we have intercept , log {(2^n-1 -1)/k*(n-1) } = 0.228958

{(2^n-1 -1)/k*(n-1) } = 10^0.228958 = 1.694

0.4706/k = 1.694

k = 0.2778

(b)   

Usually, this method applies with rate law involving only one concentration term (when the rate law has the form r = k[A]n).

c) When order of reaction is half this method cannot be applied.

for n=1 , t1/2 is independent of [A]o.