In Arrhenius equation Arrhenuis constant 'A' and Ea are 4*10^-13 and 19.6*10^3 if the reaction is of first order at what temperature will the half life period will be 10 times of its initial value ?

Question

aaronq · Answer

use the equation:  k=A*e^(-Ea/RT)  

and then use the exponential growth 

At=Ao*e^-kt

sub in k, solve for T

i'm not sure what 10 times implies, maybe 10 half-lives

anonymous · Answer

@aaronq  wat is At=Ao*e^-kt

anonymous · Answer

here t is temp or time ?

anonymous · Answer

t 1/2 = 0.693/k = ~0.7/k

aaronq · Answer

it's a exponential growth/decay formula, t is time, T is temperature

aaronq · Answer

you don't need to find the half-life

aaronq · Answer

btw, time would in terms of half-lives

anonymous · Answer

Confused*

aaronq · Answer

would be*

anonymous · Answer

So  wat to do with  "what temperature will the half life period will be 10 times"

anonymous · Answer

10 times what ?

anonymous · Answer

of its initial value ..i guess .

aaronq · Answer

okay so, you have 

 k=A*e^(-Ea/RT)  

subbing it in

At=Ao*e^(-(A*e^(-Ea/RT)*t)

How much is left after 10 half-lives, t= 10
Ao=1
At=(1/2)^10*Ao= 0.0009765625 

At/Ao= 0.0009765625 =e^(-(A*e^(-Ea/RT)*10)

you have Ea, A and R,  just need to isolate T now,