Question

A first order reaction is takes 20 min for 25 decomposition

Answer 1

For the first order reaction

k = (2.303 / t) log (a / a – x)

When x = (25 / 100) a = 0.25 a

t = 20 minutes (given)

Therefore, k = (2.303 / 20) log (a / a – 0.25 a)

k = (2.303 / 20) log (1 / 0.75)

  = 0.013120 min-1

Hence the value of the rate constant is 0.013120 min-1

Now we need to find Time for rest 75% reaction t= ?, when x = 0.75 a

From above, k = 0.013120 min-1

Therefore, t = (2.303 / 0.013120) log (a / a – 0.75 a)

                = (2.303 / 0.013120 ) log (1 / 0.25 )

                = 105.6 min.  

The time at which the reaction will be 75% complete is 105.6 min.