Half-life independent from initial concentration

[Jeffrey Hablewitz 2I]

I understand how the half-life equation is derived from the integrated rate law, but I was curious if there was a conceptual basis for the half-life being independent of initial concentration. I don't understand why the half-life of a first-order reaction wouldn't be dependent on initial concentration when the other half-life equations are.

[Sahiti Annadata 3D]

We can see that the length of half-life will be constant, independent of concentration for first-order reactions. It takes the same amount of time for the concentration to decrease from one point to another point, which is why half-life is independent of initial concentration for first-order.

[Arya Adibi 1K]

First order reactions have ln([A]) terms, which in which the [A]'s cancel out when calculating half life. I am not sure about the conceptual reason, but this is the algebraic explanation.

[Pratika Nagpal]

is there any mathematical way of understanding why half like of a first order reaction is independent of the concentration - other than considering the ln2/k formula

[Evelyn Silva 3J]

Could this maybe have to do with the fact that the exponent is 1?

[Eve Gross-Sable 1B]

I had the same question, but it just has to do with the concentrations cancelling. They don't end up appearing in the equation visibly, but the concentration is accounted for in k! So you just don't have to factor the initial concentration in again in first order but it is still technically accounted for I believe.

[AndrewNguyen_2H]

If you take a look at the half-life reactions for first order the concentration of A is missing from the equation so it is independent.

[Neha Jonnalagadda 2D]

I think it because the exponent is 1.

[Trisha Badjatia 2L]

Hi! I believe the half-life of a first-order reaction doesn't depend on initial concentration because the rate of the reaction depends on the concentration at that given moment. Thus, the half-life of a first-order reaction is constant. When the concentration is smaller, the rate of the reaction is slower, meaning it halves in the same amount of time as when the concentration is larger. We can prove this algebraically, and when we find the equation for the half-life of a first-order reaction, we substitute the concentration at the half-life with one-half of the initial concentration, which cancels with the concentration term on the other side. Hope that helps!!