Get 2 FREE Instant-Explanations on Filo with code FILOAPP

For a first order reaction Percentage of B in the product is

Question

For a first order reaction
Percentage of $B$ in the product is $30$ %. Calculate the value of $k_{1}$ and $k_{2} . (t_{1/2})_{o v er a ll} = 100 h r$ .

Views: 1,767 students

Found 8 tutors discussing this question

Theodore Discussed

For a first order reaction
Percentage of

B

in the product is

30

%. Calculate the value of

k_{1}

and

k_{2} . (t_{1/2})_{o v er a ll} = 100 h r

11 mins ago

Discuss this question LIVE

11 mins ago

Text solutionVerified

[B] = 2 [A_{0}] e^{- k_{1} t}

[C] = 3 [A_{0}] e^{- k_{2} t}

[A] = [A_{0}] e^{- (k_{1} + k_{2}) t}

% of

[B] = \frac{2 [ A _{0} ] e ^{- k_{1} t} \times 100}{2 [ A _{0} ] e ^{- k_{1} t} + 3 [ A _{0} ] e ^{- k_{2} t}}

\frac{30}{100} = \frac{2 e ^{- k_{1} t}}{2 e ^{- k_{1} t} + 3 e ^{- k_{2} t}}

\frac{3}{10} = \frac{1}{1 + \frac{3}{2} e ^{(k_{2} - k_{1}) t}}

3 + \frac{9}{2} e^{- (k_{2} - k_{1}) t} = 10

e^{- (k_{2} - k_{1}) t} . \frac{14}{9}

k_{1} - k_{2} = l n \frac{14}{9}

t = 100 h r

k_{1} - k_{2} = 0.4418 \times 1 0^{- 2}

\frac{l n ^{2}}{k _{1} + k _{2}} = 100 h r

k_{1} + k_{2} = 0.693 \times 1 0^{- 2}

by solving

k_{1} = 0.5674 k_{2} = 0.1256

Was this solution helpful?

150

Report

One destination to cover all your homework and assignment needs

Learn Practice Revision Succeed

Instant 1:1 help, 24x7

60, 000+ Expert tutors

Textbook solutions

Big idea maths, McGraw-Hill Education etc

Essay review

Get expert feedback on your essay

Schedule classes

High dosage tutoring from Dedicated 3 experts

Trusted by 4 million+ students

Stuck on the question or explanation?

Connect with our chemistry tutors online and get step by step solution of this question.

231 students are taking LIVE classes

Question Text	For a first order reaction Percentage of $B$ in the product is $30$ %. Calculate the value of $k_{1}$ and $k_{2} . (t_{1/2})_{o v er a ll} = 100 h r$ .
Answer Type	Text solution:1
Upvotes	150