Which or the following is correct for the first order reaction ?
`2N_(2)O_(5)(g)rarr4NO_(2)(g)+O_(2)(g)`
(i) The concentration of the reactant decreases exponentially with time.
(ii) The half life of the reaction decreases with increaseing temperature.
(iii) The half life of the reaction depends on the initial concentration of the reactant.
(iv) The reaction proceeds to `99.6%` completion in eigth half-life duration.

Options

A. (i), (ii), (iv)
B. (i), (iv)
C. only (iv)
D. inly (i)

Answer

A

Explanation

For first order of the reaction: `[R]=[R]_(0)e^(-E_(a)//RT)`
`t_(1//2)prop(1)/(k)`
`t_(1//2)=(0.693)/(k)`
Thus, half-life period is independent of initial concentration of the reacting species for a first order reaction.
`100%overset(t_(1//2))(rarr)50%overset(t_(1//2))(rarr)25%overset(t_(1//2))(rarr)12.5%overset(t_(1//2))(rarr)6.25%overset(t_(1//2))(rarr)3.125%overset(t_(1//2))(rarr)1.5625%overset(t_(1//2))(rarr)0.7813%overset(t_(1//2))(rarr)0.391%`
Thus, at the end eight half lives `99.6%` of reaction is over.