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?

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:

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!

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