Answer to Question #206829 in General Chemistry for Styx

Question

The half-life for a first-order reaction is 32s. What was the original concentration if, after 2.0 minutes, the reactant concentration is 0.062

Answer 1

Half life = 32 s

use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k

= 0.693/(half life)

= 0.693/(32)

= 2.166×10^-2 s-1

we have:

[A] = 0.062 M

t = 2.0 minutes = 2×60 = 120 s

k = 2.166×10^-2 s-1

use integrated rate law for 1st order reaction

ln[A] = ln[A]o - k×t

ln(0.062) = ln[A]o - 2.166×10^-2×120

ln[A]o = -2.780621 + 2.166×10^-2×120

ln[A]o = -0.181871

[A]o = 0.834 M

Answer: 0.834 M