Question

In a reaction $A⟶B+C$, The following data were obtained:
t in seconds 0 900 1800
conc. of A 50.8 19.7 7.62
Prove that it is a first order reaction.

Answer 1

For a 1st order reaction

$k=\frac{2.303}{t}log\frac{\left[A_0\right]}{\left[A\right]}$

Taking the 1st 2

$k=\frac{2.303}{900}log\frac{\left[50.8\right]}{\left[19.7\right]}$

$k=1.05\times {10}^{-3}{s}^{-1}$

Taking 1 and 3

$k=\frac{2.303}{1800}log\frac{\left[50.8\right]}{\left[7.62\right]}$

$k=1.05\times {10}^{-3}{s}^{-1}$

So it is a 1st Order Reaction