Question

In the second-order decomposition of substance X at 750 K, it is found that 15 % of the sample has decomposed in 45 seconds. If the initial concentration of the substance X is 0.046 M Calculate the rate constant. Calculate the half-life. How long will it take for 65 % of X to decompose?

Answer 1

we know that

for a second order reaction

1/[A] = 1/[Ao] + kt

given

15 % of the compound is decomposed

so

85% left

[A] = 0.85 [Ao]

[A]= 0.85 x 0.046 = 0.0391

now

1/0.0391 = 1/0.046 + ( k x 45)

k = 0.085

so

the rate constant is 0.085

now

we know that

half life = 1 / k[Ao]

so

half life = 1 / 0.085 x 0.046

half life = 255

so

the half life is 255 sec

now

given

[A] = 0.35 Ao

so

[A] = 0.35 x 0.046 = 0.0161

so

1/0.0161 = 1/0.046 + ( 0.085 x t)

t = 474.97

so

the time taken is 474.97 sec