For a zero order reaction , the correct expression for rate constant (k) at half-life time `(t_(1//2))` is `R_0` = initial concentration of reactant )

Options

A. `k="2.303"/t_(1//2) "log"([R_0])/([R_0]//2)`
B. `k="2.303"/t "log"([R_0])/([R_0])`
C. `k=([R_0]-1/2[R_0])/t(1//2)`
D. `k=(2.303)/((t_2-t_1))"log"[R_0]`

Answer

C

Explanation

Given ,
For a Zero-order reaction,
Rate constant = K
Half life time = `t_(1/2)`
Initial concentration of reactant = `R_0`
The equation for integrated rate is given by ,
`K=([R_0]-[R])/t`
Where ,
[R]- Concentration at time , t
But , `t=t_1/2`
Then `[R]=([R_0])/2`
`rArr K=([R_0]-[R_0/2])/t_(1/2)`
`therefore K=([R_0]-1/2[R_0])/t_(1/2)`