The time for half life period of a certain reaction $\mathrm{A} \rightarrow$ products is 1 hour. When the initial concentration of the reactant ' $A$ ', is $2.0 \mathrm{~mol} \mathrm{~L}^{-1}$, how much time does it take for its concentration to come from 0.50 to $0.25 \mathrm{~mol} \mathrm{~L}^{-1}$ if it is a zero order reaction?

JEE Main · 2010 · 11 Apr 2010 · Offline · Chemical Kinetics

The time for half life period of a certain reaction

A \to

products is 1 hour. When the initial concentration of the reactant '

A

', is

2.0 mol L^{- 1}

, how much time does it take for its concentration to come from 0.50 to

0.25 mol L^{- 1}

if it is a zero order reaction?

Answer: (C)

For a zero-order reaction the concentration falls at a steady rate, so the rate constant is

k = \frac{[ A ] _{0}}{2 t _{1/2}}

. With

[A]_{0} = 2.0

M and a half-life of

1

k = \frac{2.0}{2} = 1.0

mol L

^{- 1}

^{- 1}

. Since the rate does not depend on concentration, the time to go from

0.50

M to

0.25

M is simply the amount consumed divided by the rate,

t = \frac{0.50 - 0.25}{1.0} = 0.25

JEE Main · 2010 · 11 Apr 2010 · Offline · Single correct option