Question

For the simple decomposition reactionAB(g)→ A(g) + B(g)Rate =k[AB]2 and k=0.2 L/mol*s . How long will it takefor [AB] to reach 1/3 of its initial concentration 1.50 mol/L?

Answer 1

6.66 s will it take for [AB] to reach 1/3 of its initial concentration 1.50 mol/L.

Step-by-step explanation:

`Rate = k[AB]^2`

The order of the reaction is 2.

Integrated rate law for second order kinetic is:

`(1)/([A_t]) = (1)/([A]_0)+kt`

Where,
`[A_0]` is the initial concentration = 1.50 mol/L

`[A_t]` is the final concentration = 1/3 of initial concentration =
`(1)/(3)* 1.50\ mol/L` = 0.5 mol/L

Rate constant, k = 0.2 L/mol*s

Applying in the above equation as:-

`(1)/(0.5) = (1)/(1.50)+0.2t`

`(1)/(1.5)+0.2x=(1)/(0.5)`

`t = 6.66\ s`

6.66 s will it take for [AB] to reach 1/3 of its initial concentration 1.50 mol/L.