Question

For a first-order reaction, A → B, the rate coefficient was found to be 3.4 × 10-4 s-1 at 23 °C. After 5.0 h, the concentration of A was found to be 0.00018 mol L-1. What was the original concentration of A?

Answer 1

Answer:

the original concentration of A = 0.0817092  M

Explanation:

A reaction is considered to be of first order it it strictly obeys the graphical equation method.

$k_1 = \dfrac{2.303}{t}log \dfrac{a}{a-x}$

where;

k = the specific rate coefficient  = 3.4 × 10⁻⁴ s⁻¹

t = time   = 5.0 h = 5.0 × 3600 = 18000 seconds

a = initial concentration = ???

a - x = remaining concentration of initial concentration at time t = 0.00018 mol L⁻¹

$3.4 \times 10^{-4}= \dfrac{2.303}{18000}log \dfrac{a}{0.00018}$

$3.4 \times 10^{-4}= 1.27944 \times 10^{-4} \times log \dfrac{a}{0.00018}$

$\dfrac{3.4 \times 10^{-4}}{1.27944 \times 10^{-4}}= log \dfrac{a}{0.00018}$

$2.657= log \dfrac{a}{0.00018}$

$10^{2.657}= \dfrac{a}{0.00018}$

$453.94 = \dfrac{a}{0.00018}$

$a =453.94 \times 0.00018$

a = 0.0817092  M

Thus , the original concentration of A = 0.0817092  M