For the reaction A + B → products, the following initial rates were obtained at various given initial concentrations

Determine the half-life period.

OR

A first-order reaction is 50 % complete in 50 minutes at 300 K and the same reaction is again 50 % complete in 25 minutes at 350 K. Calculate activation energy of the reaction.

The half-life of a reaction is the time in which the concentration of a reactant is reduced to one half of its initial concentration. It is represented as t_1/2.

In the given data, it is observed that when the concentration of reactant [A] is doubled, the initial rate is doubled. On the other hand, there is no change in the rate when [B] is doubled. Hence, this reaction depends on the concentration of only one reactant and thus the reaction follows first-order kinetics.

Rate = k[A]^α[B]^β

=

=

α = 1

Carrying out the same calculation for equation 1 and 3,

(2)^β = 1

ln1 = ln(2)^β

= βln(2)

Dividing both sides by ln1, and since ln1 = 0 and ln2 = 0.693,

β = 0/0.693 = 0.

Now, according to the rate law,

r = k[A]¹[B]⁰

0.05 = k[A]

k(0.1) = 0.05

k = 0.5 s^-1

t_1/2 = = = 1.38 s.

OR

Using the half-life equation for first order reactions,

t_1/2 = 50 mins

k₁ = = min^-1

k₂ = = min^-1

Activation energy is calculated as

log = ()

= 2

Log2 = ()

E_a = log2 × 2.303 × 8.314 × 3000 ×

E_a = 0.3021 x 19.147 x 300 x 7 = 12,104.5 J mol^-1 OR 12.014 kJ mol^-1