In a first order reaction `A to B`, if k is rate constant and initial concentration o f the reactant A is 0.5 M then the half-life is

Options

A. `(log 2)/( k)`
B. `(log 2)/( k sqrt(0.5) )`
C. `("In 2")/( k)`
D. `(0.693)/( 0.5k)`

Answer

C

Explanation

For a first order reaction
`k= (2.303)/( t) log_(10) "" ((a)/( a-x))`
When `t= t_(1//2)`
or `t_(1//2) = (2.303)/( k) log_(10) "" 2 = ("In 2")/(k)`
`k = (2.303)/( t_(1//2)) log_(10) ((a)/( a-x))`