Question
The decomposition of dinitrogen pentoxide $$\left( {{N_2}{O_5}} \right)$$ follows first order rate law. What will be the rate constant from the given data?
$$\eqalign{
& {\text{At}}\,t = 800\,s{\text{,}}\left[ {{N_2}{O_5}} \right] = 1.45\,mol\,{L^{ - 1}} \cr
& {\text{At}}\,t = 1600\,s,\left[ {{N_2}{O_5}} \right] = 0.88\,mol\,{L^{ - 1}} \cr} $$
A.
$$3.12 \times {10^{ - 4}}\,{s^{ - 1}}$$
B.
$$6.24 \times {10^{ - 4}}\,{s^{ - 1}}$$
C.
$$2.84 \times {10^{ - 4}}\,{s^{ - 1}}$$
D.
$$8.14 \times {10^{ - 4}}\,{s^{ - 1}}$$
Answer :
$$6.24 \times {10^{ - 4}}\,{s^{ - 1}}$$
Solution :
$$\eqalign{
& k = \frac{{2.303}}{{\left( {{t_2} - {t_1}} \right)}}\log \frac{{\left[ {{A_1}} \right]}}{{\left[ {{A_2}} \right]}} \cr
& k = \frac{{2.303}}{{\left( {1600 - 800} \right)}}\log \frac{{1.45}}{{0.88}} \cr
& \,\,\,\, = \frac{{2.303}}{{800}} \times 0.2169 \cr
& \,\,\,\, = 6.24 \times {10^{ - 4}}{s^{ - 1}} \cr} $$