Problem: A first-order reaction is 75.0% complete in 320. s.b. How long does it take for 90.0% completion?

FREE Expert Solution

The integrated rate law for a first-order reaction is as follows:

ln [A]t=-kt+ln [A]0

where:

[A]t = concentration at time t 
k = rate constant
t = time
[A]0 = initial concentration


 

Calculate rate constant, k:

let [A]0 = 100%

[A]t = 100% - 75% = 25% (left of the reactant)


ln [A]t=-kt+ln [A]0ln (25%)=-kt+ln (100%)3.2188=-k(320 s)+4.60513.2188-4.6051=-k(320 s)-1.3863-320=-k(320 s)-320 s

k = 4.3321x10-3 s-1


Solving for time t:

let [A]0 = 100%

[A]t = 100% - 90% = 10% (left of the reactant)

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Problem Details

A first-order reaction is 75.0% complete in 320. s.

b. How long does it take for 90.0% completion?

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Integrated Rate Law concept. You can view video lessons to learn Integrated Rate Law. Or if you need more Integrated Rate Law practice, you can also practice Integrated Rate Law practice problems.

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Our data indicates that this problem or a close variation was asked in Chemistry: An Atoms First Approach - Zumdahl 2nd Edition. You can also practice Chemistry: An Atoms First Approach - Zumdahl 2nd Edition practice problems.