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Solutions 
Molarity 
• Two solutions can contain the same 
compounds but be quite different because the 
proportions of those compounds are different. 
• Molarity is one way to measure the 
concentration of a solution. 
moles of solute 
volume of solution in liters 
Molarity (M) =
Solutions
Solutions
Solutions 
Mixing a Solution
Solutions 
Dilution
Solutions
Solutions
Solutions 
Using Molarities in 
Stoichiometric Calculations
Solutions
Solutions 
Titration 
The analytical 
technique in 
which one can 
calculate the 
concentration of a 
solute in a 
solution.
Solutions 
Titration
Solutions
Solutions
Solutions 
Ways of 
Expressing 
Concentrations 
of Solutions
Solutions 
Mass Percentage 
Mass % of A = mass of A in solution 
total mass of solution × 100
Solutions 
Parts per Million and 
Parts per Billion 
Parts per Million (ppm) 
ppm = mass of A in solution 
total mass of solution × 106 
Parts per Billion (ppb) 
ppb = mass of A in solution 
total mass of solution × 109
Solutions
Solutions 
Mole Fraction (X) 
moles of A 
total XA = moles in solution 
• In some applications, one needs the 
mole fraction of solvent, not solute— 
make sure you find the quantity you 
need!
Solutions 
Molarity (M) 
mol of solute 
M = L of solution 
• You will recall this concentration 
measure from Chapter 4. 
• Because volume is temperature 
dependent, molarity can change with 
temperature.
Solutions 
Molality (m) 
mol of solute 
m = kg of solvent 
Because both moles and mass do not 
change with temperature, molality 
(unlike molarity) is not temperature 
dependent.
Solutions
Solutions 
Conversion of concetration 
units
Solutions
Changing Molarity to Molality 
Solutions 
If we know the 
density of the 
solution, we can 
calculate the 
molality from the 
molarity, and vice 
versa.

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Concentrations of solutions