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Chemistry Question on Chemical Kinetics

For a first order reaction, (A)→(A)\to product. Concentration of AA, changes from 0.1 M0.1\, M to 0.025 M0.025 \,M in 4040 minutes the rate of reaction of when concentration of AA is 0.01 M0.01 \,M is :

A

3.47×10−4M/min−13.47\times10^{-4} M /min^{-1}

B

3.47×10−5M/min−13.47\times10^{-5} M /min^{-1}

C

1.73×10−4M/min−11.73\times10^{-4} M /min^{-1}

D

1.73×10−5M/min1.73\times10^{-5} M /min

Answer

3.47×10−4M/min−13.47\times10^{-4} M /min^{-1}

Explanation

Solution

For first order reaction,
k=2.303tlogaa−x=2.30340log0.10.025=3.46×10−2k=\frac{2.303}{t} log\frac{a}{a-x}=\frac{2.303}{40}log\frac{0.1}{0.025}=3.46\times10^{-2}
Rate= [k]A=3.46×10−2×0.01=3.46×10−4[k]A=3.46\times10^{-2}\times0.01=3.46\times10^{-4}