For the first order reaction
`2 N_(2)O_(5)(g) to 4 NO_(2) (g) + O_(2)(g)`

Options

A. the concentration of the reactant decreases exponentially with time
B. the half-life of the reaction decreases with increasing temperature
C. the half-life of the reaction depends on the initial concentration of the reactant
D. the reaction proceeds to `99.6%` completion in eight half-life duration

Answer

A, B, D

Explanation

`[A]=[A]_0e^(-kt)` Hence, (a) is correct
`t_(1//2)=(0.693)/k` As k increases with increasing tempeature, therefore, `t_(1//2)` of a first order reaction is independent of initial concentration.
Amount left after 8 half - lives `=([A]_0)/(2^8)`
`1/(256)"of"[A]_0=0.004"of"'[A]_0`
`:." Amount reacted"=0.996" of "[A]_0," i.e," 99.6%" of "[A]_0`. Hence, (d) is correct.