Concentration as a Mass/Volume Percent
The concentration of an unsaturated solution is usually expressed as the
mass of solute dissolved per volume of the solution. In other words, the
mass of a solute dissolved in a volume of solution. This is calculated as a
percentage, and is referred to as the MASS/VOLUME PERCENT or as
percent (m/v).
Ex: A hospital patient requires an intravenous drip to replace body fluids.
The intravenous fluid is a saline solution containing 0.9g or sodium chloride
dissolved in 100mL, or it is 0.9%(m/v). Note: number of grams of solute per
100mL of solution is numerically equal to the mass/volume percent.
Therefore:
MASS/VOLUME PERCENT=
Mass of Solute (in g)
X 100%
Mass of solution (in mL)
Sample Problem:
A Pharmacist adds 2.00 mL of distilled water to 4.00g of powdered drug.
The final volume of the solution is 3.00mL. What is the concentration of the
drug in g/100mL of solution? What is the percent(m/v) of the solution?
Given:
solute= drug
-mass of solute: 4.00g
solution = water
-volume of solution: 3.00mL
Method 1
Method 2
Let x= mass of solute( that will dissolved in 100mL)
Percent (m/v) = 4.00g x 100%
3.00mL
Place in a ratio expression with the 4.00g of solute
= 133%
in 3.00mL of solution
Therefore the concentration of
Xg
= 4.00g
the drug in g/100mL is the same
100mL
3.00mL
as the percent(m/v) which is
X g = 1.33g/mL
133%
100mL
*look at Note above*
x= 100mL x 1.33g/mL
x= 1.33g
Therefore the concentration of the drug is
133g/100mL of solution or 133% (m/V)
Practice problems: Page 305 # 1-4
Concentration as a Mass/Mass Percent
Instead of calculating the concentration of a solution that contains a solid
solute dissolved in a liquid solvent, the concentration can also be calculated
as the mass of the solute dissolved in the mass of the solution as a
percentage. This is referred to as MASS/MASS PERCENT, and can also be
called Percent (m/m) or the mass percent.
Therefore:
MASS/MASS PERCENT =
Mass of Solute (in g)
X 100%
Mass of Solution (in g)
Ex: 100g of seawater contains 0.129 g of magnesium ion (along with other
substances). The concentration of Mg2+ in seawater is 0.129% (m/m). Note:
number of grams of solute per 100g of solution is numerically equal to the
mass/mass percent
Sample Problem
Calcium Chloride, CaCl2, can be used instead of road salt to melt the ice on
roads during the winter. To determine how much calcium chloride had been
used on a nearby road, a student took a sample of the slush to analyze. The
sample had a mass of 23.47g. When the solution was evaporated, the residue
had a mass of 4.58g (assuming I was the only solute present). What was the
mass/mass percent of calcium chloride in slush? How many grams of calcium
chloride were present in 100g of solution?
Given:
solute= CaCl2
- mass of solution: 23.47g
solution= slush
- mass of calcium chloride dissolved in solution (solute) : 4.58g
Method 1
Method 2
Percent (m/m) = 4.38g x 100%
Let x= mass of solute dissolved in 100g
23.47g
Place in a ratio expression with the 4.00g of
= 19.5%
solute in 3.00mL of solution
Therefore the concentration of
Xg
= 4.58g
the drug in g/100mL is the same as
100g
23.47g
the percent(m/v) which is 19.5%
Xg = 0.195
*look at Note above*
100g
x= 0.195 x 100
x= 19.5g Therefore the concentration of the
drug is 19.5g/100g of solution or 19.5% (m/m)
Practice Problems: Page 308 #5-9
Concentration as a Volume/Volume Percent
It is easier to measure the volume of a mixture of two liquids in a solution
than by measuring their masses. Thus to find the concentration of a liquid in
a liquid solution a VOLUME/VOLUME PERCENT can be determined by
dividing the volume of the solute by the volume of the solution, expressed as
a percentage. The volume/volume percent can also be referred to as the
volume percent concentration, volume percent, percent (v/v), or as percent
by volume.
Therefore:
VOLUME/VOLUME PERCENT = Volume of Solute (in mL) X 100%
Volume of Solution (in mL)
Sample Problem:
Rubbing alcohol is commonly used as an antiseptic for small cuts. It is sold as
70% (v/v) solution of isopropyl alcohol in water. What volume of isopropyl
alcohol is used to make 500mL of rubbing alcohol?
Given:
- volume/volume percent: 70% (v/v)
Solute: isopropyl
Solution: rubbing alcohol
- final volume: 500mL
Method 1
Rearrange above equation to solve for volume
of solute.
Volume solute = volume/volume % x volume soln
100%
= 70% x 500mL
100%
= 350mL
Therefore the volume of the isopropyl alcohol
to make 500mL of 70% rubbing alcohol is
350mL
Practice Problems: Page 310 # 10-14
Method 2
Let x= volume of solute (in 500mL)
Place in a ratio expression with 70mL
of solute in 100mL of solution.
X mL
= 70mL
500mL
100mL
X = 70 mL x 500mL
100mL
X= 350mL
Therefore the volume of the
isopropyl alcohol to make 500mL of
70% rubbing alcohol is 350mL
Concentration in Parts per Million and Parts per Billion
In the human body or in the environment the concentrations of certain
substances are very small. Thus a measure of concentration is required to
take into account of such small concentrations. These concentrations can be
expressed in parts per million (ppm) and parts per billion (ppb). Both of
these are usually expressed as the mass/mass relationship, such the
concentration of the solute in the solution is the mass of the solute divided
by the mass of the solution.
Therefore:
ppm = Mass of Solute
OR Mass of Solute =
Xg
X 106
6
Mass of Solution
Mass of Solution
10 g of Solution
ppb = Mass of Solute
Mass of Solution
X 109
OR
Mass of Solute =
Xg
9
Mass of Solution
10 g of Solution
Sample Problem:
A fungus that grows on peanuts produces a deadly toxin. When ingested in
large amounts, this toxin destroys the liver and can cause cancer. Any
shipment of peanuts that contains more than 25 ppb of this dangerous
fungus is rejected. A company receives 20 t of peanuts to make peanut
butter. What is the maximum mass (in g) of fungus that is allowed?
Given:
solute: fungus
-allowed concentration of fungus: 25 ppb
solution: peanuts
-mass of shipment: 20 t
convert 20 t to grams: 20t x 1000kg/t x 1000g/kg = 20 x 106 g
Method 1
Method 2
Rearrange formula to solve for mass of
Let X= mass of solute (fungus) (in 20 x 106 g
solution- peanuts)
fungus
Set up a Ratio expression
Fungus= solute
peanuts= solution
X g solute
= 25 g of solute
6
Mass of fungus = ppb x mass of peanuts
20 x 10 g solution
1 x 10 9 g solution
9
X g fungus= 25 g of fungus x 20 x 106 g
10
1 x 10 9 g peanuts
= 22ppb x 20 x 106
X = 0.5 g
109
The maximum mass of fungus that is allowed is
0.5g
= 0.5 g
The maximum mass of fungus that is allowed is
0.5g
Practice Problems: Page 312 # 15-18
Molar Concentration
The most useful unit of concentration in chemistry is the molar
concentration. MOLAR CONCENTRATION is the number of moles of solute
dissolved in 1L of solution (Note: that the volume of the solution is in litres).
Molar concentration is also known is molarity.
Therefore:
Molar concentration (in mol/L) = Amount of Solute (in mol)
Volume of Solution (in L)
Short form: C = n/V
Why is molarity the most useful unit of concentration in chemistry?
Sample Problem:
A saline solution contains 0.90g of sodium chloride, NaCl, dissolved in 100mL
of solution. What is the molar concentration of the solution?
Given:
- mass of sodium chloride (solute): 0.90g
- volume of solution: 100mL
o conversion: Volume (in L)= 100mL x (1.000L/1000mL)= 0.100L
Since molarity is expressed in mol, must convert mass of NaCl to mol
Molar mass of NaCl = 22.99+35.45
= 58.44 g/mol
mol of NaCl= 0.90g
= 1.54x10-2 mol
58.44g/mol
Molarity = 1.54x10-2 mol
0.100L
= 1.54x10-1 mol/L
Therefore the molar concentration of the saline solution is 0.15 mol/L.
Practice Problems: Page 316 # 19-24