In a first-order reaction `A rarr B`, if `K` is the rate constant and initial concentration of the reactant is `0.5 M`, then half-life is

Options

A. `(log 2)/(k sqrt(0.5))`
B. `(In2)/(k)`
C. `(0.693)/(0.5k)`
D. `(log2)/(k)`

Answer

B

Explanation

For a first order reaction `
`k=(1)/(t)In([R]_(0))/([R])`
At `t=t_(1//2)`
`[R]=([R]_(0))/(2)`
So, the above equation becomes
`k=(1)/(t_(1//2))In([R]_(0))/(R]_(0)//2)`
or `t_(1//2)=(In2)/(k)`