Calculating the Concentration of a Solution
Concentration is a measure of how much solute is dissolved in a  solvent
Concentration can be expressed in many different ways - g/mL, mol/L, or as a percent
1. Calculating Concentration in mol/L (also called Molarity)
-the most common method of representing concentration
Units
c = mol/L, also written as M
n = mol
c = n
V=L
V
-depending on what is given in the question, this equation can be rearranged to find concentration,
moles or volume
Sample Problem: A solution contains 5.85 g sodium chloride dissolved in 5.00 x 10 3 mL of solution.
Calculate the concentration of the solution in mol/L.
2. Calculating Percent Concentrations
a. Volume Percent
- two liquids combined to form a solution
%v/v =
volume of solute x 100%
volume of solution
Units
%v/v = unitless; written as %
volume of solute and solution may be
in L or mL as long as they match
Sample Problem: Vinegar is a dilute solution of acetic acid. If 28.5 mL of acetic acid is added to
100.0 mL of water, what is the % volume concentration of the solution?
b. Mass Percent
-compares the mass of the solute to the mass of the solution
Units
%m/m = mass of solute x 100%
%m/m = unitless; written as %
mass of solution
mass of solute and solution may be in
g or kg as long as they match
Sample Problem: A solution contains 5.3 g potassium chloride in 255.5 g of water. Calculate the
mass percent of solute in this solution.
c. Mass-Volume Percent
-generally used if the solute is a solid and the solvent is a liquid
Units
%m/v = mass of solute x 100%
%m/v = unitless; written as %
volume of solution
mass of solute = g
volume of solution = mL
Sample Problem: Ordinary tea typically contains 3.3% m/v caffeine. What mass of caffeine will
there be in a 150 mL cup of tea?
3. Calculating Concentration in ppm and ppb
-useful for measuring concentrations of trace pollutants
-part per million: 1 part in 106
-part per billion: 1 part in 109
ppm =
mass of solute
mass of solution
x 106
ppb =
mass of solute
mass of solution
x 109
Units
ppm = ppm; ppb = ppb
mass of solute and solution may be in
g or kg as long as they match
Sample Problem: Because of bioamplification, seabirds have been found to have 25 ppb DDT in
their systems, even though the water only contained 3 ppb. What mass of DDT would be present in
a 4.0 kg seabird?
4. Calculating Ionic Concentrations
-once an ionic compound dissolves, the concentration of each individual ion can be
calculated
-expressed in mol/L, just like a regular concentration
Sample Problem: If there is 15.6 g of magnesium chloride in a 1.25 L solution, what is the
concentration of chloride ions?
Sample Problem: A 525 mL solution contains 6.78 g CaBr2 and is mixed with a 325 mL solution
containing 11.4 g KBr. What is the bromide ion concentration after mixing?