CHE 180 Handout – Units Gymnastics
Units Gymnastics
Converting information about a solution into the requested units typically is not too difficult.
Sometimes, however, we are asked to convert from one unit to another. It may appear that we do
not have enough information to make the requested conversion, but there is always a way! We
may have to make an assumption. One common assumption is that the density of a dilute
solution is the same as water’s density which is about 1 g/mL.
Before we get to the conversions (units gymnastics), we should limber up by writing down the
definitions for all of the units we will be using: M, m, X, % by mass, ppm and ppb. Let’s also
review density!
1. What is the definition for Molarity?
4. What is the definition for percent by mass?
or
2. What is the definition for molality?
5. What is the definition for ppm?
(
) or
(
)
(
)
6. What is the definition for ppb?
3. What is the definition for mole fraction?
(
) or
or
7. What is the definition for density?
Now that we have warmed up, it is time to try the following problems.
Convert the solution
from the given units into the requested units using assumptions where appropriate.
8. What is the molality of a 36% by mass solution of HCl? Hint: it’s not 9.9 m!
have:
want:
100 g sol’n – 36 g HCl = 64 g H2O
9. What is the percent by mass HNO3 in commercial strength nitric acid that is 16 M with a
density of 1.42 g/mL?
have:
&
want:
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CHE 180 Handout – Units Gymnastics
10. A solution is 5,432 ppb of a solute. What is the concentration of the solute in ppm?
(
)
have:
want:
(
)
11. What is the Molarity of concentrated sulfuric acid that is 95.0% by mass acid with a 1.84
g/cm3 density?
have:
&
want:
12. What is the mole fraction of chloride ion in a 1.584 M solution of calcium chloride? Hint:
it’s not 0.0670 or 0.0554 or 0.0335 or 0.0277 or 0.0648 or 0.0539!
have:
want:
Assume!
13. What is the percent by mass sugar, C12H22O11, in a solution if the mole fraction of sugar is
0.0027?
have:
want:
14. The LD50 of cyanide is 100-300 ppm. What is the Molarity of a NaCN solution that is 200
ppm CN–?
have:
want:
Assume!
15. What is the ppb of vitamin C, C6H8O6, in a 2.18×10–9 m solution?
have:
want:
(
)
(
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)
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CHE 180 Handout – Units Gymnastics
16. Commercial grade muriatic acid is 12.0 M HCl with a density of 1.18 g/cm3. What is the
molality of this HCl solution? Hint: it’s not 10.2!
have:
&
want:
742 g H2O
17. What is the mole fraction of KBr in a solution that is 0.075% by mass KBr?
have:
want:
18. If the mole fraction of the glycerol, C3H5(OH)3, is 0.093, what is the ppm of glycerol?
(
)
have:
want:
(
(
)
(
(
)
(
)
(
)
(
)
(
)
)
)
19. What is the Molarity of a NaNO3 solution with a mole fraction of 9.22×10–4 for NaNO3?
Hint: it’s not 0.0512.
have:
want:
Assume!
18.1 g sol’n
20. What is the percent by mass of ethanol, CH3CH2OH, in a 1.1 m solution?
have:
want:
21. What is the mole fraction of NaI in a 0.15 m NaI solution?
have:
want:
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CHE 180 Handout – Units Gymnastics
22. The FDA allows the level of arsenic in apple juice to be no higher than 2.3×10–6 % by mass.
What is this in ppb?
have:
want:
(
(
)
)
23. In January 2014, 4-methylcyclohexane methanol, C8H16O, was spilled into the waterways in
West Virginia. By the time it reached the Louisville area, the concentration was 0.023 ppm
(below the allowed maximum level of 1 ppm). What is the mole fraction of C8H16O in this
solution?
have:
want:
24. What is the ppm of lead ion in a 2.54×10–5 M of lead(II) nitrate?
(
have:
)
(
want:
)
Assume!
(
)
(
)
(
)
25. What is the molality of a KNO3 solution with a mole fraction of 0.0194 KNO3?
have:
want:
26. What is the molality of lithium ion in sea water if the average lithium ion concentration is
0.18 ppm?
have:
want:
27. The average U.S. water supply has a silver ion concentration of 28 ppb? What is the percent
by mass of silver ion in this solution?
have:
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want:
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CHE 180 Handout – Units Gymnastics
28. A potassium dichromate solution is 0.325 m, what is the Molarity of it?
have:
want:
Assume!
29.
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