[CHM 112] Rate law question

[Andrew J. Pounds]

On 6/30/20 6:33 PM,
> How do I determine if a reaction is second or first order by looking
> at the rate law?

So for a reaction with ONE COMPONENT, the order is the exponent to which
the concentration is raised.

$rate=k [A]$

would be a first order reaction and

$rate=k[A]^2$

would be a second order reaction.


> Also could you explain finding the k constant through half life? I was
> too busy writing to catch everything. 
>
> Get Outlook for iOS <https://aka.ms/o0ukef>

So when HALF of the compound is gone, the concentration is equal to
$[A]/2$,  Referring to page 142 from the lecture slides, we are
considering a first order reaction and are using the FIRST ORDER
INTEGRATED RATE LAW, e.g  ---

$[A] = [A_0] e^{-kt}$

so at the HALF LIFE (when half of the original compound is gone)

$\frac{[A_0]}{2} = [A_0] e^{-kt_{\frac{1}{2}}}$

this simplifies to

$\frac{1}{2} =  e^{-kt_{\frac{1}{2}}}$

I take the natural log of both sides to arrive at

$\ln{\frac{1}{2}} = -kt_{\frac{1}{2}}$

$-0.6931=-kt_{\frac{1}{2}}$

or...

$\frac{0.6931}{k}=t_{\frac{1}{2}}$

or

$\frac{0.6931}{t_{\frac{1}{2}}}=k$


For first order reactions if you are given the half life you can easily
find $k$

-- 
Andrew J. Pounds, Ph.D.  (pounds_aj at mercer.edu)
Professor of Chemistry and Computer Science
Director of the Computational Science Program
Mercer University,  Macon, GA 31207   (478) 301-5627

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