Question

For the first order reaction, half-life is equal to ____________.

विकल्प

• `(["R"_0])/(2"K")`

• `0.693/"K"`

• `(["R"_0])/"K"`

• `(2.303["R"_0])/"K"`

Answer 1

For the first order reaction, half-life is equal to `underline(0.693/"K")`.

Explanation:

Half-life period means the time when the concentration of reactant becomes half to the original concentration of the reactant.

for first order reaction rate constant can be calculated as follows:

t = `2.303/"K" log  (["A"_0])/(["A"])`

for the half-life period, t = t_1/2, [A] = `(["A"_0])/2`

on solving,

t_1/2 = `2.303/"K" log  (["A"_0])/((["A"_0])/2)`

t_1/2 = `2.303/"K" log 2`

= `(2.303 xx 0.3010)/"K"`

t_1/2 = `0.693/"K"`

where letters have their usual meanings.