Solutions: Dilutions.
A. Dilutions: Introduction
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1
B. The dilution equation
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2
C. The logic of the dilution equation
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3
D. Should you “memorize” the dilution equation?  Attention X11 students... 4
E. Practical notes
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5
F. Dilutions involving other concentration units
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5
G. Problems
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6
H. Dilution factor
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7
I. Multiple dilutions; serial dilutions
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7
J. Answers
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8
This handout was originally written for another purpose. It was intended as a
selfpaced review for students to use on their own, with staff available for help.
It was part of a set of several such handouts. Some of the other handouts are
mentioned here; if you are interested in one of them, let me know.
This handout follows Molarity. One problem uses material from Percentage. However, for the
most part, Dilutions and Percentage are independent; they can be done in parallel, or in either
order.
A.
Dilutions: Introduction
In the previous work we discussed preparing solutions from the pure components (for example,
solid NaCl solute and the solvent, water). However, sometimes you prepare one solution from
another. In particular, it is common to take a concentrated solution and prepare a dilute
solution, by adding more solvent. (The terms concentrated and dilute are qualitative terms that
refer to a  relatively  high or low concentration, respectively, of solute in the solution.)
Preparing solutions by dilution is convenient. One can make a single concentrated stock
solution of a solute, and then quickly prepare a variety of more dilute solutions by dilution.
(Why is it easier? Measuring volumes is quicker than weighing.) Further, dilution of a
concentrated solution is a practical way to make solutions that are so dilute you would have
trouble weighing the solute.
There is a simple equation for calculating dilutions. It is also easy to present the logic of the
equation.
We mainly discuss dilution problems using molarity as the concentration unit.
Within the problem sets, some problems are marked with an *. This indicates
that the problem introduces something new. If you are skipping around in the
problems, you may well want to stop for a bit at a problem marked with an *.
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Solutions: Dilutions.
Page
2
I did not intend significant figures (SF) to be an issue when I wrote the original
version of this. However, some who use this now may care about SF. The
answers do now show the correct number of SF. Exception: In some simple
problems, with simple integer data, I have treated the data as “exact”.
B.
The dilution equation
V
c
M
c
= V
d
M
d
.
In this equation, V = volume and M = molarity. The subscripts c and d refer to the concentrated
and dilute solutions, respectively.
Example
Need: 100 mL of 1.0 M NaCl. Have: a 5.0 M NaCl stock solution.
To make the desired solution, we will take some volume (V
c
) of the concentrated solution, and
then add water (solvent) until the total volume is the desired 100 mL. The question is, how
much of the concentrated solution do we need, or what is V
c
?
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 Spring '08
 Andersen
 Organic chemistry, .........

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