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

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SUMMARY

The discussion centers on calculating the time required for a first-order reaction to reach a concentration of 1/8 of its initial value, given a rate constant of 6.70×10−3. The half-life for this reaction is determined using the formula half-life = 0.693/k, resulting in a half-life of 103.43 units of time. It is established that reaching 1/8 concentration requires three half-lives, as each half-life reduces the concentration by half: 1/2 after one half-life, 1/4 after two, and 1/8 after three.

PREREQUISITES
  • Understanding of first-order reaction kinetics
  • Familiarity with the half-life formula: half-life = 0.693/k
  • Basic knowledge of exponential decay functions
  • Ability to perform simple mathematical calculations involving fractions
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  • Study the implications of first-order kinetics in chemical reactions
  • Learn about the derivation and applications of the half-life formula
  • Explore exponential decay models in various scientific contexts
  • Investigate the impact of different rate constants on reaction times
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Chemistry students, educators, and professionals involved in chemical kinetics or reaction rate analysis will benefit from this discussion.

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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.
 
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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?
 
Werg22 said:
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 ?
 
Yes it is.
 
Yup;

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

Best of health.

Steve
 
Werg22 said:
Yes it is.

Thanks a lot Werg!
 
Smith4046 said:
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 !
 

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