[CHM 330] Problem 9.10
Andrew J. Pounds
pounds_aj at mercer.edu
Tue Mar 29 12:11:38 EDT 2022
Some of you are struggling with problem 9.10 in the text (which is part
of the Mastering online homework). The key to unlocking these problems
is recognizing that you are dealing with EQUAL VOLUMES of EQUIMOLAR
SOLUTIONS. Parts B and D seem to be the hardest.
For part B you are told that the equation is first order with respect to
both A and B.
d[A]dt=k[A][B]\frac{d[A]}{dt}=k[A][B]but remember, these are equal
volumes and equal concentrations, so [A]=[B]
d[A]dt=k[A][B]=k[A][A]=k[A]2\frac{d[A]}{dt}=k[A][B]=k[A][A]=k[A]^2so you
can treat this essentially using second order kinetics and use the
second order integrated rate law to determine the concentrations as a
function of time.
In part D you are told that the equation is first order with respect to
A and half-order with respect to B. Again, employing the fact that
[A]=[B]..
d[A]dt=k[A][B]1/2=k[A][A]1/2=k[A]3/2\frac{d[A]}{dt}=k[A][B]^{1/2}=k[A][A]^{1/2}=k[A]^{3/2}Use
the same separation of variable techniques that we used before but apply
it to this particular problems...
∫[A]0[A]td[A][A]3/2=∫0tkdt\int_{[A]_0}^{[A]_t}\frac{d[A]}{[A]^{3/2}}=\int_0^tkdt
to come up with the integrated rate law that you can then use to solve
for the concenrations.
--
*/Andrew J. Pounds, Ph.D./*
/Professor of Chemistry and Computer Science/
/Director of the Computational Science Program/
/Mercer University, Macon, GA 31207 (478) 301-5627/
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