### Half Life and k

Posted:

**Sat Mar 09, 2019 10:50 am**Why is there always an inverse relationship between half life and the rate constant k?

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=147&t=43861

Page **1** of **1**

Posted: **Sat Mar 09, 2019 10:50 am**

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

Posted: **Sat Mar 09, 2019 11:34 am**

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.

Posted: **Sat Mar 09, 2019 12:36 pm**

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.

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

Posted: **Sat Mar 09, 2019 3:25 pm**

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

Posted: **Sat Mar 09, 2019 6:39 pm**

How exactly do we calculate half life?

Posted: **Sat Mar 09, 2019 7:08 pm**

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.

Posted: **Sat Mar 09, 2019 10:25 pm**

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

Posted: **Sun Mar 10, 2019 8:46 pm**

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?

Posted: **Sun Mar 10, 2019 10:17 pm**

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

Posted: **Sun Mar 10, 2019 10:41 pm**

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.

Posted: **Sat Mar 16, 2019 1:32 am**

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.

Posted: **Sat Mar 16, 2019 7:21 pm**

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.