Question

The rate constant (k) of a first-order reaction is 4.5 × 10⁻² sec⁻¹. What will be the time required for the initial concentration of 0.4 M of the reactant to be reduced to 0.2 M?

Answer 1

For first order reaction k = `2.303/t log ([A_0])/([A_t])`    ...(1)

Where, k = rate constant = 4.5 × 10⁻² sec⁻¹

[A₀] = Initial concentration = 0.4 M of reactant

[A_t] = Final concentration = 0.2 M of reactant after time t sec

Putting values in equation (1),

t = `2.303/(4.5 xx 10^-2) log  0.4/0.2`

t = `2.303/(4.5 xx 10^-2) log 2`

t = `2.303/(4.5 xx 10^-2) xx 0.3010` .....(∵ log 2 = 0.3010)

t = 15.4 sec

∴ Time required = 15.4 sec.