Question
In a first order reaction, the concentration of reactant decreases from $$400\,mol\,{L^{ - 1}}$$ to $$25\,mol\,{L^{ - 1}}$$ in 200 seconds. The rate constant for the reaction is
A.
$$1.01386\,{s^{ - 1}}$$
B.
$$2 \times {10^{ - 4}}\,{s^{ - 1}}$$
C.
$$1.386 \times {10^{ - 2}}\,{s^{ - 1}}$$
D.
$$3.4 \times {10^{ - 4}}\,{s^{ - 1}}$$
Answer :
$$1.386 \times {10^{ - 2}}\,{s^{ - 1}}$$
Solution :
$$\eqalign{
& {\text{For first order reaction,}} \cr
& k = \frac{{2.303}}{t}\log \frac{a}{{\left( {a - x} \right)}} \cr
& \,\,\,\, = \frac{{2.303}}{{200}}\log \frac{{400}}{{25}} \cr
& \,\,\,\, = \frac{{2.303}}{{200}} \times 1.204 \cr
& \,\,\,\, = 0.01386\,{s^{ - 1}} \cr
& \,\,\,\, = 1.386 \times {10^{ - 2}}{s^{ - 1}} \cr} $$