Question

Half life of a substance in a first order reaction is 15 minutes .Calculate the Rate Constant?
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Answer 1

Topic

Chemical Kinetics

To Find

Rate Constant of given reaction.

Given

Half life of a substance in a first order reaction is 15 minutes.

Formula

Half life of a reaction in a first order reaction is given by,

$\boxed{\sf{t_{1/2} = \dfrac{ln(2)}{Rate\:\: Constant}}}$

where

$\sf {t_{1/2} = Half \: \: Life}$

Solution

It is given that,

Half Life = 15 minutes

Half Life = 15 × 60 seconds

Half Life = 900 seconds

Now, applying the formula :-

$\sf{900\:seconds = \dfrac{ln(2)}{Rate\:\: Constant}}$

$\sf{Rate\:\: Constant = \dfrac{ln(2)}{900\:\:seconds}}$

Now, ln2 = 0.693

$\sf{Rate\:\: Constant = \dfrac{0.693}{900\:\:seconds}}$

$\sf{Rate\:\: Constant = 0.00077\:second^{-1}}$

$\sf{Rate\:\: Constant = 7.7 \times 10^{-4}\:second^{-1}}$

Answer,

So, Rate constant is

$\sf{7.7 \times 10^{-4}\:second^{-1}}$

Learn More

First Order Reaction

A reaction in which rate of reaction depends linearly on only one reactant.

Half Life

Time in which a substance reduces to its half of initial.

Answer 2

$\sf{Answer}$

Step-by-step-explanation:-

Given :-

In a first order reaction

time

t½ = 15 minutes

To find :-

Rate constant

Formula implemented

t½ = $\sf\dfrac{0.693}{k}$

k = $\sf\dfrac{0.693}{t½}$

Solution:-

Just substuite the values

k = $\sf\dfrac{0.693}{t½}$

k = $\sf\dfrac{0.693}{15s}$

Convert 15 minutes to seconds

1minute = 60seconds

15 minutes = 15 × 60s

k = $\sf\dfrac{0.693}{15×60}$

k = $\sf\dfrac{693×10^-3}{9×10²}$

k = $\sf\dfrac{693×10^(-3-2)}{9}$

k =$\sf\dfrac{693×10^-5}{9}$

k = $\sf{77×10^-5}$

k = $\sf{77×10^-5}$ $\sf{second ^-1}$

So,

Rate constant = k = $\sf{77×10^-5}$ $\sf{second ^-1}$