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Other Ways of Expressing the Concentration of Solutions
percent concentration,
ppm, ppb
Percentage Concentration
Can be expressed as:
1. % mass/volume, or % m/v;
2. % mass/mass, or % m/m;
3. % volume/volume, or % v/v.
1. % mass/volume, or % m/v
% m/v = mass of solute (g)100 mL solution1
—or— mass of solute (g) * 100% vol of solution (mL)
1solution = solute + solvent
sample problem 1
What is the % concentration when 4.52 g KNO3 is dissolved in 250 mL of solution?
Answer:
(4.52 g/250 mL) * 100% = 1.81%
—or—4.52 g = ? g .
250 mL 100 mL
? = 1.81 g/100 mL or 1.81 %
sample problem 2
Na3PO4 is sold in hardware stores under the (incorrect) name “Trisodium phosphate”, or TSP.
A 1.7% (m/v) solution of TSP is recommended for cleaning walls before painting or putting up wallpaper.
What mass of TSP is needed to make 2.0 L of solution?
Answer: 1.7% (m/v) means
1.7 g per 100 mL or
? g per 2000 mL
cross-multiplying gives
? = (1.7 g * 2000 mL)/100 mL
= 34 gUse 34 g TSP to make 2.0 L of cleaning sol’n.
NB. Solutions of TSP are VERY BASIC.
Wear Gloves!!
2. % mass/mass, or % m/m
% m/m = mass of solute (g)100 g solution1
—or— mass of solute (g) * 100% mass of solution (g)
1solution = solute + solvent
sample problem 3
CaCl2 is often used as an ice-melter.
If 45.3 g of slush (snow, ice, CaCl2) was evaporated to yield 6.37 g CaCl2, calculate the % m/m CaCl2 in the slush.
Here, the slush represents the
solution.
Answer:
% CaCl2 = (6.37 g CaCl2/45.2 g slush)*100%
CaCl2 = 14.1 % (m/m)
3. % volume/volume, or % v/v
% v/v = volume of solute (mL)100 mL solution1
—or— volume of solute (mL) * 100%
volume of solution (mL)
1solution = solute + solvent
sample problem 4
Rubbing alcohol is a 70% (v/v) solution of isopropyl alcohol in water.
What volume of isopropyl alcohol is required to prepare 350 mL of rubbing alcohol?
Answer:
70 mL isopropyl alcohol = ? mL
100 mL rubbing alcohol 350 mL
? = (70 mL * 350 mL)/100 mL
= 245 mL isopropyl alcohol in 350 mL
Practical Application
The concentration of alcohol (ethanol) in alcoholic beverages is stated as % (v/v).
Regular beer is 5.0% (v/v) ethanol;
“lite” beer is 4.0% (v/v).Express the % ethanol in “lite” beer as % (m/v).
What information do you need?
Density of ethanol = 0.80 g/mL.
Answer:4.0% (v/v) =
4.0 mL ethanol/100 mL
We need to convert 4.0 mL ethanol mass.4.0 mL*(0.80 g·mL-1) = 3.2 g ethanol/100 mL
% ethanol (m/v) in “lite” beer = 3.2%
If you were the brewer, would you label % ethanol in “lite” beer as m/v or v/v?
ppm concentration*ppm =mass of solute * 106
mass of solution
or
mass of solute = . ? g .
mass of solution 106 g solution
(*parts per million—106)
ppb concentration*
ppb = mass of solute * 109
mass of solution
or
mass of solute = . ? g . mass of solution 109 g solution
(*parts per billion—109)
sample problem 5
Symptoms of mercury poisoning become apparent after the ingestion of more than 20 mg of Hg. For a 70 kg person, convert this to
a) % m/m
b) ppm
c) ppb
Answer:a) % m/m = (20 x 10-3 g/70 x 103 g) * 100%
= 2.9 x 10-5 is percent Hg in body
b) ppm = (20 x 10-3 g/70 x 103 g) * 106
= 0.29 ppm Hg
c) ppb = (20 x 10-3 g/70 x 103 g) * 109
= 2.9 x 102 ppb Hg
HW
P 371 to 377, do several problems from each set.