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) =
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Mixing a Solution
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Dilution
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Using Molarities in 
Stoichiometric Calculations
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Solutions 
Titration 
The analytical 
technique in 
which one can 
calculate the 
concentration of a 
solute in a 
solution.
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Titration
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Ways of 
Expressing 
Concentrations 
of Solutions
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Mass Percentage 
Mass % of A = mass of A in solution 
total mass of solution × 100
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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
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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.
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Conversion of concetration 
units
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Changing Molarity to Molality 
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If we know the 
density of the 
solution, we can 
calculate the 
molality from the 
molarity, and vice 
versa.

Concentrations of solutions