For a reversible reaction carried out in a closed vessel at constant temperature

MATHEMATICS · Subjective · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

For a reversible reaction carried out in a closed vessel at constant temperature, the forward reaction rate is given by

r_f(t) = 1.2e^{-0.040t}\,\text{mol}\,\text{L}^{-1}\,\text{s}^{-1}

, and the reverse reaction rate is

r_r(t) = 1.2\bigl(1-e^{-0.040t}\bigr)\,\text{mol}\,\text{L}^{-1}\,\text{s}^{-1}

, where

t

is time in seconds. Calculate, to the nearest

0.1\,\text{s}

, the time at which the rates of the forward and reverse reactions are equal.