Solutions
Molarity, Molality, Dilutions,
Percent Solutions, & Mole
Fractions
Concentration
 Concentration is a value that represents the
amount of solute dissolved in a solvent.
Concentrated solutions have a large amount of solute
relative to the solvent
Dilute solutions have a small amount of solute relative
to the solvent
 Concentration can be measured in Molarity,
molality, %solution, ppm (parts per million)
How it is made…
2 Molar Solution of NaCl
requires 2 moles of NaCl to be dissolved to
make 1L of solution
2 moles of salt (or 117 grams) are dissolved in 1L of
water to make a 2M NaCl(aq) solution
Molarity
Molarity is the moles of solute per liter of
solution.
Note the volume is the total solution volume,
not the volume of solvent alone.
M = moles
Liters
= mass/molar mass
Liters
This is the most common way chemists
measure concentration
Practice Problem #1
 What is the molarity of HCl if 28g HCl is
dissolved in 500.mL of solution?
 mass=28.g
molar mass of HCl= 36.46g/mol
V= 500mL=0.500L (divide by 1000)
M= moles = (mass/molar mass)
Liter
Liter
=
(28/36.46)moles
0.500L
= 1.5 M
Practice Problem #2
 How many grams of sodium nitrate (NaNO3 ) are needed
to make 2 liters of a 0.100M solution?
M=0.100M
m=?
0.100M = (m/85)mols
2L
(0.100M)(2L)(85)= m
m=17g NaNO3
mm NaNO3 = 85g/mol
Solving using Dimensional Analysis
Molarity can be used as a conversion
factor.
2.0 L
0.100moles
1 Liter
85 grams = 17g
1 moles
Example 3
 What is the molarity of a solution with 10.0
grams of AgNO3 is dissolved in 500.mL of
solution.
Molarity = Mass / Molar Mass
Liters of Solution
Must convert to
Liters!!
500mL/ 1000
M = 10.0g / 169.88 g/mol
0.500 Liters
M = 0.118 Molar
= 0.500 Liters
Example 4
How many grams of KNO3 should be used to
prepare 2.00 Liters of a 0.500M solution?
Molarity = Mass / Molar Mass
Liters of Solution
0.500 = mass / 101.11
2.0
(0.500)(2.0) =
Mass
101.11
Mass = (0.500)(2.0)(101.11)
Mass = 101.11 grams
Example 5
To what volume should 5.0 grams of
KCl be diluted to in order to prepare a
0.25M solution?
Molarity = Mass / Molar Mass
Liters of Solution
0.25 = 5.0 / 74.55
Volume
V(0.25) = 5.0/74.55
V = 0.0671
0.25
V= 0.268 Liters =
268 mL
Molality (m)
 Molality is the concentration of a solution expressed
in moles of solute per kilogram of solvent.
 Molality (m) =
moles of solute (mol)
----------------------------------kilogram of solvent (kg)
Molality Sample Problem
 A solution was prepared by dissolving 17.1 g of
glucose, C6H12O6, in 275 g of water. What is the
molality (m) of this solution?
0.345 mol/kg or
0.345 m
More molality examples
Preparing Solutions from Other Solutions
 Many times solutions are prepared by diluting
concentrated solutions. These are called stock
solutions.
 Dilution = process of adding water to a stock
solution to achieve the molarity desired for a
particular solution.
 Adding water increases the volume of the solution
and this causes the concentration to decease.
 Dilution Equation:
M1V1 = M2V2
Dilutions and Molarity
Use this formula to make a more dilute
solution from a concentrated solution
Molarity1Volume1 = Molarity2Volume2
(Concentrated)
(Dilute)
(Moles before) =
(Moles after!)
M1V1 = M2V2
Sample Problem #1
How many milliliters of 1.0 Molar HCl are required
to make 100 mL of 0.025 M HCl?
M1V1 = M2V2
M1 = 1.0M V1 = ?
M2 = 0.025M V2 = 100mL
(1.0M)V1 = (0.025M)(100mL)
V1 = (0.025M)(100mL)
(1.0M)
= 2.5 mL of 1.0M HCl required, then dilute to 100mL
Sample Problem #2
 How much water should you add to the
volume of 1.0M HCl you calculated above to
make the solution?
We need 2.5 mL of concentrated 1.0M HCl.
Then we dilute to a final total volume of 100mL.
Therefore, 100mL – 2.5mL = 97.5 mL of water
should be added.
**Water added = V2 – V1
More dilution example problems
Percent Solutions
 Solutions can also be represented as percent of
solute in a specific mass or volume of solvent.
 For a solid dissolved in water, you use percent
by mass.
 % by mass =
mass solute
x 100
mass of solution
*Mass of solution = solute mass + solvent mass
For a liquid mixed with another
liquid
% by volume =
volume solute
x 100
Total volume of solution
Example 1
What percent solution do you have if you
dissolve 80 grams of NaCl in 1 liter of
water?
* 1 Liter = 1000mL = 1000grams for water
% mass =
= 7.4 %
80 grams NaCl
X 100
(80g + 1000g H2O)
Example #2
What percent solution will you have if you
mix 40mL of ethanol with 200 mL of
water?
%volume =
= 16.7%
40mLs
x 100
(200mLs + 40mLs)
What if the previous problem was
worded as follows?
What percent solution will you have if you
dilute 40mL of ethanol to a final volume
of 200mL?
% volume =
= 20%
40mL x 100
200mL*
*Denominator is
always total volume.
You must pay
attention the wording
in the problem!
More Percent Solution Problems
Mole Fraction (X)
Number of moles of a compound divided
by the total number of moles of all species
in the solution.
Adding all mole fractions should get you a
value of 1
Guess what the units are?
Example
What are the mole fractions of the
components of the solution formed when
92 g glycerol is mixed with 90 g water?
(molar mass of glycerol =92 g/mol)
Answer:

Example 2
What is the mole fraction of NaOH in an
aqueous solution that contains 22.8%
NaOH by mass? (molar mass of NaOH is
40 g/mol)
Answer:

More Mole Fraction Examples