# Half life (very very simple question)

1. Mar 21, 2007

### pari786

1. The problem statement, all variables and given/known data
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?

2. Relevant equations

half life =0.693/k

3. 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.

2. Mar 22, 2007

### 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?

3. Mar 22, 2007

### pari786

so its 3 half lives .. right ?

4. Mar 22, 2007

### Werg22

Yes it is.

5. Mar 22, 2007

### Smith4046

Yup;

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

Best of health.

Steve

6. Mar 22, 2007

### pari786

Thanks a lot Werg!

7. Mar 22, 2007

### pari786

Thanks a lot Smith !