ln [A]

[605941366]

Hi,
when we are doing first-order decomposition problems, why is ln[A] divided by ln[A] initial? On the equation sheet, we are given ln[A]=-kt+[A]inital. So to solve for something like final concentration we would have ln[A]/ln[A]inital but I don't understand the math going on here, why woudln't we subtract them, like why is it not ln[A]/ln[A]inital as -kt was added to a inital? Is it a calculus rule?

I understand that ln[A]/ln[A]inital is how the math must be done so please don't say thats just the way we do it.

[Marianna 1H]

Hello,
In first-order decomposition problems, we divide the final concentration's natural logarithm by the initial concentration's natural logarithm. This helps us compare how much the concentration changes relative to its starting value over time. It's a simple way to understand the reaction's progress and kinetics.

[Anahi Guzman 3L]

Hi so what if you subtract you would still get the same answer you would just have to take the ln of both the final and initial which is more work compared to ln( [A]/[A]initial)=−kt. Also subtracting logarithms is equivalent to dividing them which is one of the logarithms properties. I hope that helps.