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

For zero-order reaction, integrated rate equation is given as :
`k=([R_(0)]" "[R])/t`
`K=` rate constant
where, `[R_(0)]=` initial concentration
and `[R]=` concentration at time (t)
When, `t=t_(1//2)`
`[R]=([R_(0)])/2`
Thus, `K=([R_(0)]-1/2 [R_(0)])/t_(1//2)`
Hence, option (c) is the correct answer.