Half life and concentration

[Azlyn Hernandez 2E]

Conceptually, how does it make sense that the 1st order half life is not dependent on concentration?

[106052916]

First-order half-life is independent of concentration because in first order kinetics the rate of reaction is proportional to the concentration of the reactant.

[Maleeha Amir 2E]

Since in a first order reaction, the rate is directly proportional to the concentration, the rate decreases as the concentration does. The factor by which it decreases remains the same though regardless of what the concentration actually is. So, for the half-life, the concentration does not matter, only the value of k is needed.

[Deep Mehta]

This is because it is derived. If you were to fully derive, you would get ln(1[A]0 /2[A]0) which cancels out to ln(1/2). This then equals 0.693 = -kt(1/2) which then equals 0.693/k.