Question

The rate constant for this first‑order reaction is 0.470 s − 1 0.470 s−1 at 400 ∘ C. 400 ∘C. A ⟶ products A⟶products How long, in seconds, would it take for the concentration of A A to decrease from 0.920 M 0.920 M to 0.380 M?

Answer 1

Answer : The time taken by the reaction is, 1.88 s

Explanation :

Expression for rate law for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

k = rate constant  = $0.470s^{-1}$

t = time passed by the sample  = ?

a = initial amount of the reactant  = 0.920 M

a - x = amount left after process = 0.380 M

Now put all the given values in above equation, we get

$t=\frac{2.303}{0.470}\log\frac{0.920}{0.380}$

$t=1.88s$

Therefore, the time taken by the reaction is, 1.88 s