Question

Fill in the blanks by choosing the appropriate word(s) from those given in the brackets:

(first, zero, twice, lanthanoid, iron, copper, yellow, blue, benzophenone, transition)

The half-life of a ______ order reaction is independent of the initial concentration of reactants. For a first-order reaction, the time required for 75% completion is ______ the half life time.

Answer 1

The half-life of a first order reaction is independent of the initial concentration of reactants. For a first-order reaction, the time required for 75% completion is twice the half life time.

Explanation:

The half-life of a reaction is defined as the time required to reduce the concentration of a reactant to one half of its initial value.

k = `2.303/"t" log ("a"/("a" - "x"))`

If amount reacted X = `"a"/2` then t = `"t"_(1//2)` Thus,

`"t"_(1//2) = 2.303/"t" log ("a"/("a" - "a"//2))`

= `2.303/"k" log 2`

`"t"_(1//2) = 0.693/"k"` sec.

Thus, the half-life period of a first order reaction is independent of the initial concentration of the reactant.

⇒ we know that (according to statement):

at t(50%) ⇒ `"t"_(1//2) = 2.303/"k" log  "a"_0/("a"_0 - "a"_0/2)`

= `2.303/"k" log 2` ........(i)

and t_75% = `2.303/"k" log  "a"_0/("a"_0 - 3/4 "a"_0)`

= `2.303/"k" xx log 4`

∴ t_75% = `2.303/"k" 2 log 2` ........(ii)

Now from equations (i) and (ii), we get,

t_75% = `2 xx "t"_(1//2)`

⇒ Hence, for a first order reaction, the time required for 75% completion of a reaction is twice the half-life time.