Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

A first order reaction is 50% completed in $1.26\times 10^{14}s$ . How much time would it take for 100% completion?

Option 1)
$1.26\times 10^{15}s$

Option 2)
$2.25\times 10^{14}s$

Option 3)
$2.25\times 10^{28}s$

Option 4)
Infinite

Answers (1)

best_answer

As we learned in concept

First Order Reaction -

The rate of the reaction is proportional to the first power of the concentration of the reaction

- wherein

Formula:

R $\rightarrow$ P

a 0

a-x x

$rate[r]=K[R]^{1}$

$\frac{-d(a-x)}{dt}=K(a-x)$

$\frac{-dx}{dt}=K(a-x)$ [differentiate rate law]

$ln \:[\frac{a}{a-x}]=kt \:(Integrated rate law)$

Unit of $k=sec^{-1}$

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

First Order Reaction -

The rate of the reaction is proportional to the first power of the concentration of the reaction

- wherein

Formula:

R $\rightarrow$ P

a 0

a-x x

$rate[r]=K[R]^{1}$

$\frac{-d(a-x)}{dt}=K(a-x)$

$\frac{-dx}{dt}=K(a-x)$ [differentiate rate law]

$ln \:[\frac{a}{a-x}]=kt \:(Integrated rate law)$

Unit of $k=sec^{-1}$

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

In a first order reaction, $R\rightarrow P$

Rate = $k[R]$ , k= constant

$\ln \left ( \frac{a}{a-x} \right )= kt$

Given that at x= a/2, $t= 1.26*10^{14}$

but for 100% completion, x=a and that would render equation 1 as undefined.

So,first order reactions take infinite time to complete.

Option 1)

$1.26\times 10^{15}s$

Incorrect option

Option 2)

$2.25\times 10^{14}s$

Incorrect option

Option 3)

$2.25\times 10^{28}s$

Incorrect option

Option 4)

Infinite

Correct option

Posted by

Aadil

View full answer

Similar Questions

Trending Articles/News

anam-khan

BITSAT 2024 application correction facility begins tomorrow; editable fields

anam-khan

BITSAT 2024 registration window closes tomorrow; exam from May 20

anam-khan

BITSAT 2024 registration deadline extended till April 16; session 1 exam from May 19 to 24

Latest Question