How Many Half-Lives Equal a 1/8 Concentration Reduction?

[pari786]

Homework Statement

A certain first-order reaction has a rate constant of 6.70×10−3 . How long will it take for the reactant concentration to drop to 1/8 of its initial value?

Homework Equations

half life =0.693/k

The Attempt at a Solution

half life = 0.693/(6.70×10−3) = 103.43


but after that I'm confused how many half lives does 1/8 refer to?
I tried doing it by half life =4 but the answer came wrong.
any help would be appreaciated.

 

[Werg22]

Since this is a first order reaction, the function at hand is exponential, meaning the half life is constant. This means that after 1 half life, 1/2 of the reactants is left, after 2 half lives, 1/4 is left and so on. Can you do it now?

 

[pari786]

Since this is a first order reaction, the function at hand is exponential, meaning the half life is constant. This means that after 1 half life, 1/2 of the reactants is left, after 2 half lives, 1/4 is left and so on. Can you do it now?

so its 3 half lives .. right ?

 

[Werg22]

Yes it is.

 

[Smith4046]

Yup;

half of a half of a half = 1/2 x 1/2 x 1/2 = 1/8

Best of health.

Steve

 

[pari786]

Yes it is.

Thanks a lot Werg!

 

[pari786]

Yup;

half of a half of a half = 1/2 x 1/2 x 1/2 = 1/8

Best of health.

Steve

Thanks a lot Smith !