Question

The experimental data for decomposition of $N_2{O}_5[2N_2{O}_5⟶{4NO}_2+O_2]$ in gas phase at 318 K 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

Calculate the rate constant and the half-life period.

• A. $4.8\times {10}^{-4}{s}^{-1},1400s$
• B. $3.92\times {10}^{-4}{s}^{-1},1445s$
• C. $2.72\times {10}^{-4}{s}^{-1},1200s$
• D. $8.29\times {10}^{-4}{s}^{-1},1575s$

Answer 1

The correct option is A $4.8\times {10}^{-4}{s}^{-1},1400s$

$(0,1.63),(400,1.36)$

Slope $=\frac{1.63-1.36}{0-400}=-0.000675$

$(400,1.36);(800,1.14)$

Slope $=\frac{1.36-1.14}{400-800}=0.00055$

Slope is equal in almost every cases the graph will be linear so it's first order reaction in $N_2{O}_5$

$-\frac{dR}{dt}=k\left[N_2{O}_5\right]$

$k=\frac{1}{t}ln\frac{[N_2{O}_5{]}_0}{\left[N_2{O}_5\right]}$

$k=\frac{1}{400}ln\frac{1.63}{1.36}=4.527\times {10}^{-4}$

Half life $t_{1/2}=\frac{0.693}{4.527\times {10}^{-4}}=1430.8$