The term concentration refers to the strength of a solution, and is determined by the amount of dissolved solute present in a given amount of solute. Concentration can be quantitatively represented in the ways listed below.
Percent (%) – parts solute per 100 parts solution
Parts per Million (ppm) – parts solute per 1,000,000 parts solution
Mole Fraction (X) – moles of solute per total moles of all solution components
Molarity (M) – moles of solute per liter (L) of solution
Molality (m) – moles of solute per kilogram (kg) of solvent
All percent concentration values simply variations of the formula for calculating percent.
Percent = Part x 100%
Whole
Mass percent concentration compares the mass of the solute (part) to the mass of the solution (whole).
Percent Mass = Mass of Solute (g) x 100
Mass of Solution (g)
Note: Both masses must have the same units.
Volume percent concentration compares the volume of the solute (part) over the volume of the entire solution (whole). This type of concentration is calculated when two liquids are mixed together to form a solution.
Percent by Volume = Volume of Solute (mL) x 100
Volume of Solution (mL)
Note: Both volumes must have the same units.
Mass-Volume percent concentration compares the mass of solute (part) dissolved over the volume of the solution (whole)
Percent by Mass-Volume = Mass of Solute (g) x 100
Volume of Solution (mL)
Note: Mass is usually in grams (g) and volume is usually in milliliters (mL)

Practice Problems – Percent Concentration
1. What is the percent concentration of the KOH solution made when 20.0 g of KOH is added to
80.0 g of distilled water?
2. What is the percent concentration of a salt solution made when 15.0 g of NaCl is added to
150. mL of distilled water?
3. What is the concentration of an ethanol solution if it was made by adding distilled water to 50.0 mL of pure ethanol up to a total volume of 300. mL?
4. What is the mass of KOH in 500. g of a
20.0% solution?
5. What is the mass of NaCl in 100. g of a
35.0% solution?
6. What is the mass (g) of distilled water needed to make a 25.0% solution containing 30.0g of
KOH?
7. What is the mass (g) of distilled water needed to make a 1.50% solution containing 1.00g of
NaCl?
8. What is the percent hydrogen peroxide if
25 mL of concentrated hydrogen peroxide is diluted with water to form 200. mL of solution?
9. What is the percent ammonia if 20.0 mL of concentrated ammonia is diluted with water to form a total of 2.00 L of solution?
10. A physiological saline solution is prepared by dissolving 9.00 g of NaCl in enough water to make 1000. mL of solution. What is the concentration of the saline solution?

If a solution is very dilute and contains a very small (trace) amount of solute , the concentration is expressed in parts per million. This essentially takes very small concentration values and multiplies them by one million to make them easier with which to work on a daily basis. Parts per million (ppm) are commonly used when measuring contaminants (pollution) in water and chemicals in swimming pools. ppm = Solute in grams x 1,000,000
Solution in grams
Practice Problems – Parts per Million
1. If 0.0000600 grams of PCB are dissolved in 100. g of water in the Hudson River, how many ppm of PCB are present?
2. If 0.000000120 grams of Nitrogen are present in 500. g of the well water used as a drinking water source by a community in
Vermont, how many ppm of Nitrogen are in the water?
3. If 0.000780 grams of Lead are dissolved in a 250. g of a water sample taken from an old house with lead pipes, what is the amount of Lead in ppm?
4. If a swimming pool contains
0.0000000670 grams of Chlorine in a 10.0 g sample of water, what is the amount of
Chlorine in ppm?
5. If 0.050 grams of Oxygen is dissolved in
10.00 L of distilled water, what is the concentration in ppm?
Note: Both masses must have the same units.
Note: 1.00 g of H
2
O = 1.00 mL dH
2
O

Concentration expressed as a mole fraction compares the number of moles of one of the components of the solution to the total number of moles.
X
A
= ___ n
A
_____
n
A
+ n
B
Solution AB = n
A
+ n
B n
A
= number of moles of A n
B
= number of moles of B
Practice Problems – Mole Fraction
1. A solution is prepared by mixing 3.0 moles of ethanol and 9.0 moles of distilled water. What is the mole fraction of the ethanol in the solution?
2. A solution is prepared by mixing 1.5 moles of ethanol with 3.0 mole of methanol.
What is the mole fraction of ethanol in the solution?
3. A solution is prepared by mixing 3.0 moles of acetone in 8 moles of petroleum ether. What is the mole fraction of petroleum ether in the solution?

Concentration in terms of Molarity (M) is determined by the number of moles of solute per liter of solution . Molar solutions are used when the amount of solute present is of primary interest.
M = Solute (mol)
Solution (L) or M = n solute
(mol)
V solution
(L)
Practice Problems - Molarity
1. What is the molarity of a solution that contains 3.00 mol of HCl in 6.00 L of solution?
2. What is the molarity of a 0.500 L NaCl solution that contains 0.200 mol of NaCl?
3. What is the molarity of 250. mL of a MgSO
4 solution that contains 1.50 mol of MgSO
4
?
4. What is the volume of a 4.00 M solution of NaCl that contains 8.00 mol of NaCl?
5. What is the volume of a 2.00 M solution of HCl that contains 0.500 mol of HCl?
6. What is the volume of a 0.500 M solution of
MgSO
4
that contains 2.00 mol of MgSO
4
?
7. How many moles of HCl are present in 2.00 L of a 0.500 M solution?
8. How many moles of NaCl are present in
250. mL of a 2.00 M solution?
9. How many moles of MgSO
4
are present in 1.50 L of a 1.50 M solution?
10. What is the molarity of a solution containing
223.5 g of KCl in 1.50 L of solution?
11. What is the molarity of a solution containing143 g of MgCl
2
in 2.0 L of solution?

12. What is the volume of a 2.00 M solution that contains 119 g of KBr?
13. What is the volume of a 1.50 M solution that contains 88.0 g of NaCl?
14. How many grams of KBr must be dissolved in distilled water to make 2.00 L of a 0.500 M solution?
15. How many grams of NaCl must be dissolved in distilled water to make 500. mL of a 1.00 M solution?
Concentration in Molality (m) is used when the amount of solute influences the properties of a solvent and as a result both the amount of solute and solvent must be known. m = Solute (mol)
Solvent (kg)
or m = n soluute
mass
(mol) solvent
(kg)
Practice Problems – Molality
1. What is the molality of a solution prepared by dissolving 34.2 g of sucrose in 200. grams of distilled water?
Note: Molar Mass of Sucrose = 342.0 g/mol
2. What is the molaity of a solution prepared by dissolving 51.0 g of NH
3
in
2.00 kg of distilled water?
3. What is the molality of a solution comprised of 10.0 g NaOH and 500. g of water?