Question

The experimental data for decomposition of $N_2{O}_5$ $[2N_2{O}_5\to 4N{O}_2+O_2]$ in gas phase at $318K$ are given below:

t/s	$0$	$400$	$800$	$1200$	$1600$	$2000$	$2400$	$2800$	$3200$
${10}^2\times \left[N_2{O}_5\right]/mol{L}^{-1}$	$1.63$	$1.36$	$1.14$	$0.93$	$0.78$	$0.64$	$0.53$	$0.43$	$0.35$

(i) Plot $\left[N_2{O}_5\right]$ against t.
(ii) Find the half-life period for the reaction.
(iii) Draw a graph between $\log \left[N_2{O}_5\right]$ and t.
(iv) What is the rate law?
(v) Calculate the rate constant.
(vi) Calculate the half-life period from k and compare it with (ii)

Answer 1

(ii) Initial concentration of $N_2{O}_5=1.63\times {10}^2$ M
Half of initial concentration $=1.63\times {10}^{22}\times 0.5=0.815\times {10}^2$ M.

Time for half of initial concentration (i.e half life period) from plot is 1440 s

(iv) log $\left[N_2{O}_5\right]$ vs time is a straight line plot. This indicates first order reaction. The rate law expression is

$Rate=k\left[N_2{O}_5\right]$

(v) Slope $=\frac{-k}{2.303}=-2.10\times {10}^{-4}$

$k=4.84\times {10}^{-4}/s$

(vi) Half life period $t_{1/2}=\frac{0.693}{k}=\frac{0.693}{4.84\times {10}^{-4}}=1432s$