The reaction :
`X rarr ` Product
follows first order kinetics . In 40 minutes the concentration of X changes from 0.1 to 0.025 M. Then the rate of reaction when concentration of X is 0.01 M is

Options

A. `1.73xx10^(-4) "M min"^(-1)`
B. `3.47xx10^(-5) "M min"^(-1)`
C. `3.47 xx 10^(-4) "M min"^(-1)`
D. `1.73 xx10^(-5) " M min"^(-1)`

Answer

C

Explanation

For a first order reaction
`k = (2.303)/(t) "log" ([A]_(0))/([A])`
`=(3.303)/(40) "log"(0.1)/(0.025)`
or `=(2.303)/(40) "log"4 `
`=(2.303)/(40)xx0.6020`
`=0.0347 min^(-1)`
Now at 0.01 M concentration
Rate = k[A] =`0.0347 xx0.01`
`3.47xx10^(-4) "mol L"^(-1) "min"^(-1)`