7B.7 from Textbook

[Mia Chem14B]

Why is the equation used to find the answer in this question:

t=(ln([A]0/[A]t))/k and not t=(ln([A]t/[A]0))/k?

I thought the final concentration was always on top in the equation, but the solutions manual say otherwise. Also, why is k not -k? I also thought in the textbook that k would be negative in these sorts of equations.

Thanks in advance! :)

[905994971]

In the manual they just simplified the equation to find t differently, that's why they ended up with -k and [A]0/[A]

If you do the problem using t = ln([A]/[A]0)/k you'll see that you get the same answer they have in the manual.

[Seena Amin-Sanayei 2D]

the original eq: Ln(At) = -kt + Ln(A0) can be rewritten as kt = Ln(A0/At) since the textbook uses a log rule that states LogA-LogB = Log (a/b) and then you can simplify from there. hope this helps!