Answer to Question #156118 in General Chemistry for Apple Bulok

Question

For the reaction of crystal violet with NaOH(aq), the measured rate of reaction is 1.27 x 10^-6 mol L^-1 s^-1 when the concentration of crystal violet cation is 4.13 x 10^-5 mol/L. Estimate how long it will take for the concentration of crystal violet to drop from 4.30 x 10^-5 mol/L to 3.96 x 10^-5 mol/L.

Answer 1

Knowing that the reaction is first-ordered:

v=k[A]

k=v/[A]=1.27×10^-6/4.13×10^-5=0.03(s^-1)

ln[A]₁=-kt+ln[A]₂

t=(ln[A]₂-ln[A]₁)/k

t=(ln3.96×10^-5-ln4.30×10^-5)/0.03= (10.14-10.05)/0.03=0.09/0.03=3(s)