## Half Life and k

$\frac{d[R]}{dt}=-k; [R]=-kt + [R]_{0}; t_{\frac{1}{2}}=\frac{[R]_{0}}{2k}$

Simmi Diwanji 2B
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Joined: Fri Sep 28, 2018 12:20 am

### Half Life and k

Why is there always an inverse relationship between half life and the rate constant k?

Christina Chang 1C
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Joined: Thu May 10, 2018 3:00 am

### Re: Half Life and k

I think this is because the half-life equation is derived from the rate law and therefore if you solve for t1/2, k becomes inversely proportional to t1/2.

Ava Kjos 1D
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Joined: Fri Sep 28, 2018 12:19 am

### Re: Half Life and k

the equation of half life is always t(1/2)=ln2/kr.

The proof for this is given in 7B.2 in the 7th edition textbook.

Michael Novelo 4G
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### Re: Half Life and k

because half life will always taking the form of k1/2 = 1/k[A]o (for a zero order reaction) since k is always on the bottom/denominator for any order if it increases then the value of k1/2 (half life) decreases and vice versa

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### Re: Half Life and k

How exactly do we calculate half life?

ran2000
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### Re: Half Life and k

This is because k is associated with how fast a reaction runs. If the reaction runs faster then the amount of time needed for the substance to fall to half its original decreases. Hence, K is inversely proportional to Half life.

amogha_koka3I
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### Re: Half Life and k

Will we be required to know how to derive half-life equations for each order of reaction

BenJohnson1H
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### Re: Half Life and k

Would it be correct that you need to know either the t1/2 or the [R]o to solve anything in the half life equation?

Brayan Claros
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### Re: Half Life and k

half life turns into k1/2 = 1/k[A]o for a zero order reaction since k is usually a denominator for an order. then if the order increases then the value of k1/2 half life decreases. its the same the other way around

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### Re: Half Life and k

amogha_koka3I wrote:Will we be required to know how to derive half-life equations for each order of reaction

I believe this is on the syllabus, and was gone over in lecture so I feel that we are responsible for knowing how to do this.

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Joined: Fri Sep 28, 2018 12:16 am

### Re: Half Life and k

Half life and k are related differently upon what order the reaction proceeds in. The most common half life problems use first order reactions and this is simply .693/k=t1/2. Therefore you can see the inverse relationship that exists.

He whose name cannot be spoken
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Joined: Sat Apr 28, 2018 3:00 am

### Re: Half Life and k

Half life is defined as "the time it takes for the concentration of reactant to be half of the original", while k is "the rate at which the reactant is becoming product". The higher k is, the faster the reactant becomes product, the lower the half life will be.