Question
For a first order reaction $$(A) →$$ products the concentration of A changes from $$0.1 M$$ to $$0.025 M$$ in 40 minutes. The rate of reaction when the concentration of $$A$$ is $$0.01 M$$ is :
A.
$$1.73 \times {10^{ - 5}}M/\min $$
B.
$$3.47 \times {10^{ - 4}}M/\min $$
C.
$$3.47 \times {10^{ - 5}}M/\min $$
D.
$$1.73 \times {10^{ - 4}}M/\min $$
Answer :
$$3.47 \times {10^{ - 4}}M/\min $$
Solution :
For a first order reaction
$$\eqalign{
& k = \frac{{2.0303}}{t}\log \frac{a}{{a - x}} \cr
& = \frac{{2.303}}{{40}}\log \frac{{0.1}}{{0.025}} \cr
& = \frac{{2.303}}{{40}}\log 4 \cr
& = \frac{{2.303 \times 0.6020}}{{40}} \cr
& = 3.47 \times {10^{ - 2}} \cr
& R = K{\left( A \right)^1} \cr
& = 3.47 \times {10^{ - 2}} \times 0.01 \cr
& = 3.47 \times {10^{ - 4}} \cr} $$