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

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Discussion Overview

The discussion revolves around determining how many half-lives are required for the concentration of a reactant in a first-order reaction to decrease to 1/8 of its initial value. The context is primarily homework-related, focusing on the application of half-life calculations in chemical kinetics.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant presents a homework problem involving a first-order reaction with a given rate constant and seeks clarification on how many half-lives correspond to a concentration of 1/8.
  • Another participant explains that for a first-order reaction, the half-life is constant and provides a breakdown of the concentration remaining after successive half-lives, suggesting that after 3 half-lives, the concentration would indeed reach 1/8.
  • Further confirmation is provided by multiple participants agreeing that it takes 3 half-lives to reach a concentration of 1/8.

Areas of Agreement / Disagreement

Participants generally agree that it takes 3 half-lives for the concentration to reduce to 1/8, with no significant disagreement noted in the responses.

Contextual Notes

None noted.

Who May Find This Useful

Students studying chemical kinetics, particularly those learning about first-order reactions and half-life calculations.

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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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