For the first order reaction, `2N_(2)O_(5)(g) rarr 4NO_(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 99.61% completion in eight half -life duration

Answer

A, B, D

Explanation

For the first order reaction
`N = N_(0)e^(-k t)`, thus concentration of reactant decreases exponentially with time.
`t_(1//2) prop [N_(0)]^(0)` at constant temperature and thus half life is independent of initial concentration of reactant. Also `t_(1//2) = (0.693)/(k)`
The rate of reaction and rate constant increase with temperature and thus `t_(1//2)` decreases with temperature.
`t_(99.6%) = (2.303)/(k)log""(100)/(0.4) = (2.303)/(k)log250, " "t_(1//2) = (0.693)/(k)`
`t_(99.6) = t_(1//2) xx (2.303)/(0.693)log 250 = t_(1//2) xx 3.323 xx 2.40 = 8 xx t_(1//2)`