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

In summary, for a first-order reaction with a rate constant of 6.70×10−3, it will take 3 half lives for the reactant concentration to drop to 1/8 of its initial value. The half life for this reaction can be calculated using the equation half life = 0.693/k.
  • #1
pari786
29
0

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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  • #2
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
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 ?
 
  • #4
Yes it is.
 
  • #5
Yup;

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

Best of health.

Steve
 
  • #6
Werg22 said:
Yes it is.

Thanks a lot Werg!
 
  • #7
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 !
 

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

1. What is half life?

Half life is the amount of time it takes for half of a substance to decay or degrade into a different form. It is a measure of the stability of a substance and is often used in scientific fields such as nuclear physics and chemistry.

2. How is half life calculated?

The half life of a substance can be calculated using its decay constant and the following formula: t1/2 = ln(2)/λ, where λ is the decay constant. The decay constant is specific to each substance and can be determined through experiments.

3. What factors affect half life?

The half life of a substance can be affected by various factors such as temperature, pressure, and chemical environment. These factors can influence the stability of the substance and the rate at which it decays.

4. How does half life relate to radioactive decay?

Half life is commonly used in the study of radioactive decay. Radioactive elements have a specific half life, which means that after a certain amount of time, half of the atoms in the sample will have decayed into a different element.

5. Why is half life important in scientific research?

Half life is important in scientific research as it allows scientists to predict the rate of decay of a substance and understand its behavior. It is also used in various applications such as medical treatments, environmental studies, and dating techniques.

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