1. Concentration of Solutions :
Concentration: Amount of a substance per defined space.
Percent by mass: Is the ratio of the solute’s mass
to the solution’s mass expressed
as a percent.
Percent by mass =
(solute)
(solution or solvent)
X 100

2. Example # 1:
Calculate the percent by mass of solute in 55 g of solution with 15 g of potassium nitrate dissolved in water.
Data:
15 g
Solute’s mass =
% by mass =
X 100
Solution’s mass =
55 g
% by mass = ? =
X 100
= 27 % of KNO3

3. Example # 2:
Calculate the percent by mass of solute in a solution made by 25 g of sodium chloride & 50 g of water.
Data:
25 g
Solute’s mass =
50 g
Solvent’s mass =
50 g + 25 g = 75 g
Solution’s mass =
% by mass = ?
X 100
% by mass = =
X 100
= 33 % of NaCl

4. Solution Concentration:
Example: Calculate the percent by volume of alcohol in 95 mL of solution which contains 30 mL of alcohol.
% by volume =
X 100
Data:
Solute =
30 mL
% by volume =
X 100
95 mL
Solution = =
X 100
% by volume = ? =
32 % of alcohol

5. Mole Fraction:
Is the ratio between the # of moles of each component & the total # of moles in the solution.
ΧA =
ΧA = Mole fraction of A
nA = Moles of A
nB = Moles of B

6. x NaOH + x H2O = 1 20.0 g = 0.500 mol = 4.99 mol ÷ 40.0 g/mol
20.0 g
÷ 40.0 g/mol
= mol
NaOH=
90.0 g
÷ g/mol
= 4.99 mol
H2O= =
Χ NaOH = =
NaOH =
Χ H2O =
= H2O
x NaOH + x H2O = 1

7. Example # 2:
Calculate the mole fraction of a solution made by 37.5% HCl and 62.5% water.
HCl=
37.5 %
= 37.5 g
÷ g/mol
= 1.03 mol
H2O=
62.5 %
= 62.5 g
÷ g/mol
= 3.47 mol
Χ HCl = = =
0.229 HCl =
Χ H2O = =
0.771 H2O
x HCl + x H2O = 1
x H2O = 1 - x HCl = ;