(b) Show that the half life period for a zero order reaction is directly proportional to initial concentration.

Explanation

we know that the rate constant of zero order reaction is
`K-([R]_(0)-[R])/(t)`
Where K = rate constant, `[R]_(0)=` initial concentration
`"[R] = concentration at any time"`
`"t = time"`
`"When "t=t_(1//2)" then "[R]=([R]_(0))/(2)`
Substitute these values in equation (1) we get
`K=([R]_(0)-([R]_(0))/(2))/(t_(1//2))`
`K=(2[R]_(0)-[R]_(0))/(2t_(1//2))`
`K=([R]_(0))/(2t_(1//2))`
`t_(1//2)=([R]_(0))/(2K) or t_(1//2) alpha [R]_(0)`
Thus half life of the zero order reaction is dependent on initial concentration.