Question

the rate of first order reaction is 1.5*10-2 mol/l/min at 0.5 M concentration of the reactant. the half life of the reaction is?

Answer 1

Solution is in the attachment:

Answer 2

The half life of the first order reaction is 23.1 minutes.

Explanation:

We are given:

Rate of the first order reaction = $1.5\times 10^{-2}mol/L.min$

Concentration of reactant = 0.5 M

Rate law for first order reaction is written as:

$\text{Rate}=k\text{[reactant]}$

Putting values in above equation, we get:

$1.5\times 10^{-2}=k\times 0.5\\\\k=\frac{1.5\times 10^{-2}}{0.5}=3\times 10^{-2}min^{-1}$

The equation used to calculate rate constant from given half life for first order kinetics:

$t_{1/2}=\frac{0.693}{k}$

We are given:

$k=3\times 10^{-2}min^{-1}$

Putting values in above equation, we get:

$t_{1/2}=\frac{0.693}{3\times 10^{-2}}=23.1min$

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