Question

A first-order reaction completes 20% of its reaction in 20 minutes. How long will it take to be 30% complete?​

Answer 1

Explanation:

For first order reaction we have:-

K=

t

1

ln(

a−x

a

) −(i)

where, K= rate constant

t= time

a= initial concentration of the reactant

x= amount of reactant reacted in time t

Case I: t=20 min

x=

100

20

×a⇒x=0.2a (∵20 % reaction is complete)

⇒ a−x=0.8a

Putting the values in eq

n

1 :-

K=

20

1

ln(

0.8x

a

) −(ii)

Case II: t=? , x=0.8a

⇒a−x=0.2a

Putting the values in (i):-

⇒K=

t

1

ln(

0.2x

x

) −(iii)

From (ii) and (iii):-

20

1

ln(

8

10

)=

t

1

ln(

2

10

)

⇒t=20×

ln(S/4)

lnS

=144.25 min