Question

The half-life of a first-order reaction is 13 min. If the initial concentration of reactant is 0.13 M, it takes ________ min for it to decrease to 0.085 M. The half-life of a first-order reaction is 13 min. If the initial concentration of reactant is 0.13 M, it takes ________ min for it to decrease to 0.085 M. 10. 11 7.0 12 8.0

Answer 1

Answer:

Therefore it takes 8.0 mins for it to decrease to 0.085 M

Explanation:

First order reaction: The rate of reaction is proportional to the concentration of reactant of power one is called first order reaction.

A→ product

Let the concentration of A = [A]

$\textrm{rate of reaction}=-\frac{d[A]}{dt} =k[A]$

$k=\frac{2.303}{t} log\frac{[A_0]}{[A]}$

[A₀] = initial concentration

[A]= final concentration

t= time

k= rate constant

Half life: Half life is time to reduce the concentration of reactant of its half.

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

Here $t_{\frac{1}{2} }=0.13 min$

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

$\Rightarrow k=\frac{0.693}{13 }$

To find the time takes for it to decrease to 0.085 we use the below equation

$k=\frac{2.303}{t} log\frac{[A_0]}{[A]}$

$\Rightarrow t=\frac{2.303}{k} log\frac{[A_0]}{[A]}$

Here ,   $k=\frac{0.693}{13 }$,  [A₀] = 0.13 m and [ A] = 0.085 M

$t=\frac{2.303}{\frac{0.693}{13} } log(\frac{0.13}{0.085})$

$\Rightarrow t= 7.97\approx 8.0$

Therefore it takes 8.0 mins for it to decrease to 0.085 M

Answer 2

The time taken is 8 minutes.

The rate of decay of a radioactive substance is given by:

     $-\frac{dN}{dt}=$ λN

here N is the concentraion, λ is the decay constant. If inially the concentration is $N_{0}$  t time t = 0.

Then solving the above equation we get:

λ = $\frac{2.303}{t}log\frac{N_{0} }{N}$

Now the half-life is defined as the time after which half of the initial concentration is left. The relation between half-life and decay constant is:

λ = $\frac{0.693}{t_{\frac{1}{2} }}$  

Given that   $t_{\frac{1}{2} }$ = 13 min

λ = 0.693/13 = 0.0533

So, the time taken for a first-order reaction such that the concentration decreases from 0.13 M to 0.085M can be calculated by following equation:

λ = $\frac{2.303}{t}log\frac{N_{0} }{N}$

t =  $\frac{2.303}{0.0533}log\frac{0.13 }{0.085}$

t = 8 min

Learn more about radioactivity:

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