The order of reaction is an experimentally determined quanity. It may be zero, poistive, negative, or fractional. The kinetic equation of `nth` order reaction is
`k xx t = (1)/((n-1))[(1)/((a-x)^(n-1)) - (1)/(a^(n-1))]` …(i)
Half life of `nth` order reaction depends on the initial concentration according to the following relation:
`t_(1//2) prop (1)/(a^(n-1))` ...(ii)
The unit of the rate constant varies with the order but general relation for the unit of `nth` order reaction is
Units of `k = [(1)/(Conc)]^(n-1) xx "Time"^(-1)` ...(iii)
The differential rate law for `nth` order reaction may be given as:
`(dX)/(dt) = k[A]^(n)` ...(iv)
where `A` denotes the reactant.
The rate constant for zero order reaction is
where `c_(0)` and `c_(t)` are concentration of reactants at respective times.

Options

A. `k = (c_(0))/(2t)`
B. `k = (c_(0)-c_(t))/(t)`
C. `k = ln.(c_(0)-c_(t))/(2t)`
D. `k = (c_(0))/(c_(t))`

Answer

B

Explanation

On uisng equation (i), for `n = 0`, we get
`t xx k = ((1)/(0-1))((1)/((a-x)^(0-1))-(1)/(a^(0-1)))`
`= -1[(a-x)-a]`
or `k = (a-(a-x))/(t) or (c_(0)-c_(t))/(t)`