Problem based on chemical kinetic

Numeric problem based on chemical kinetic

Q. The half-life (t_1/2) of a first-order reaction is 0.693 minutes. Calculate the rate constant and the time required for 90% completion of the reaction.

Solution:

Given:

• Half-life, t_1/2 = 0.693 minutes

1. Calculate the rate constant (k):

For a first-order reaction, the half-life is given by:

t_1/2 = 0.693 / k

Rearranging the formula to solve for k:

k = 0.693 / t_1/2

Substitute the given value:

k = 0.693 / 0.693 = 1 min^–1

2. Time required for 90% completion:

For a first-order reaction, the formula for time (t) is:

t = (2.303 / k) × log(100 / (100 – x))

Here, x = 90%

Substitute the values:

t = (2.303 / 1) × log(100 / 10)

t = 2.303 × log(10)

t = 2.303 × 1 = 2.303 minutes

Final Answer:

• Rate constant (k) = 1 min^–1
• Time required for 90% completion = 2.303 minutes