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Calculate the rate constant (with appropriate units) for a first order reaction which is 30.0% complete in 363 s.

What is the value of the half-life of the reaction? 

How long will it take for the reaction to go to 95.5% completion? 

Jan 1st, 2015

30 % of reaction completion, means Ao = 1M and A = 0.3

The formula for calculation of the first order reaction is:

A = Ao e-k t

Where, A is the final amount (0.3)
Ao is the initial amount (1)
t = time ( 363 s)
k = rate constant that you are looking for

First, translate seconds of a given time into hours: 1 hour x 363 seconds / 3600 seconds = 0.1008 hours

Second,

A/Ao = e-k t

0.3/1 = e –k 0.1008

ln 0.3 = - k 0.1008

  • 1.2 = - k 0.1008

    k = 11.88 M/hr

t1/2 = ln2 / k = 0.693 / 11.88 = 0.058 hr M-1

Now, for 95.5% of reaction completion:

A/Ao = e-k t

0.955/1 = e -0.058 t

ln (0.955) = - t 0.058

-0.046 = - t 0.058

t= 0.79 hours or 2857.9 seconds

Happy New Year!


Jan 1st, 2015

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