Ch. 14: Solutions
Sec. 14.2: Solution Concentration
Objectives
• Describe the concentration of solutions
using different units.
• Determine the concentrations of solutions.
• Calculate the molarity of a solution.
Solution Concentration
• The concentration of a solution is a measure of
how much solute is dissolved in a specific
amount of solvent or solution.
dilute
concentrated
Expressing Concentration
• Qualitative Descriptions
– concentrated: a large amount of solute
– dilute: a small amount of solute
• Quantitative Descriptions
–
–
–
–
Percent by either mass or volume
Molarity
Molality
Mole Fraction
Percent by Mass
% by mass = mass of solute x 100
mass of solution
Note: mass of solution = mass solute + mass solvent
• In order to maintain a sodium chloride (NaCl)
concentration similar to ocean water, an
aquarium must contain 3.6 g NaCl per 100 g of
water. What is the % by mass of NaCl in the
solution?
• The % by mass of a NaOCl solution is 3.62%. If
you have 1500 g of solution, how much NaOCl
do you have?
Percent by Volume
% by volume = volume of solute x 100
volume of solution
Note: vol. of solution = vol. solute + vol. solvent
• What is the percent by volume of ethanol
in a solution that contains 35 mL of ethanol
dissolved in 115 mL of water?
• If you have 15 mL of 70% isopropyl
alcohol solution, how many mLs of alcohol
are in the solution?
Molarity
• Molarity (M) or molar concentration is
the number of moles of solute dissolved
per liter of solution.
M is read as molar. For example, 0.5 M
HCl is a 0.5 molar solution of HCl. It
contains 0.5 moles of HCl in every liter of
solution.
Molarity
To calculate molarity:
Molarity Practice Problems
• A 100.5 mL intravenous (IV) solution contains
5.10 g of glucose (C6H12O6). What is the
molarity of this solution? The molar mass of
glucose is 180 g/mol.
• Calculate the molarity of 1.60 L of a solution
containing 1.55 g of dissolved KBr.
• What is the molarity of an aqueous solution
containing 40.0 g of glucose in 1.5 L of solution?
Preparing Molar Solutions
Preparing Molar Solutions
• So, for 1 L of a 1M solution, you would need 1
mole of the salt, or 58.5 g NaCl.
• What if you needed 1 L of a 0.3 M solution?
M = moles solute
or 0.3 M = x moles
liters solution
1L
x = 0.3 mol or 17.6 g
• What if you only needed 150 mL of the 0.3 M
solution?
M = moles solute
or 0.3 M = x moles
liters solution
0.150 L
x = 0.045 mol or 2.63 g
Preparing Molar Solutions
• 1.0 L of a 0.10 M solution of CaCl2 is
needed. How many grams of CaCl2 must
be added to water to prepare this solution?
• How many grams of NaOH are needed to
make 250 mL of a 3.0 M NaOH solution?
• 500 mL of a 2 M NaOH solution contains
how many grams of NaOH?
Diluting Solutions
• Concentrated solutions called stock
solutions are sold for laboratory use.
• Stock solutions are then diluted to prepare
less concentrated solutions.
• When you add solvent to small amounts of
concentrated solutions, you increase the
number of solvent particles and, thus,
decrease the solution’s concentration.
Diluting Solutions
• Recall: M = moles solute/liters solution
• moles solute = M x liters solution
• The # of moles of solute does not change
during dilution - the # of solvent particles
changes.
• That means,
moles of solute in stock = moles of solute in diluted solution
Mstock x volume stock = Mdil x volume of dilute
or
M1V1 = M2V2
(12.0 M) V1 = (1.50 M)(5.00 L)
V1 = 0.625 L = 625 mL
Diluting Sol’ns Practice Problems
• What volume, in milliliters of 2.00 M of calcium
chloride (CaCl2) stock solution would you use to
make a 0.50 L of 0.300 M calcium chloride
solution?
• If you dilute 20.0 mL of a 3.5 M solution to make
100 mL of solution, what is the molarity of the
dilute solution?
• What volume of a 3.00 M KI stock solution
would you use to make 0.300 L of a 1.25 M KI
solution?
Molality
• If there is a temperature change, the volume of a
solution will change.
• If volume changes, the molarity will change.
• Therefore, there is a need for an alternative way
to express concentration.
• Since masses do NOT change with temperature,
concentration can be expressed in terms of moles
of solute in a mass of solvent.
Molality
• The molality of a solution, denoted m, is
defined as the number of moles of solute
dissolved in one kilogram of solvent:
• “1 m” is read as a 1 molal solution.
Molality
• In the lab, a student adds 4.5 g of sodium
chloride (NaCl) to 100 g of water. Calculate the
molality of the solution.
• A solution has naphthalene (C10H8) dissolved in
500 g of toluene. The solution has a molality of
0.468 m. How many grams of naphthalene are in
the solution?
• What is the molality of a solution containing 10.0
g of Na2SO4 dissolved in 1000 g of water?
Mole Fraction
• Mole fraction is the ratio of the number of
moles of solute (or solvent) in a solution to the
total number of moles of solute and solvent.
• If X represents mole fraction and A represents
the solute & B represents the solvent,
XA = nA
XB = nB
n A + nB
n A+ nB
Note: XA + XB = 1
(The sum of all the fractional components
equals “the whole.”)
Mole Fraction
• What is the mole fraction of HCl in a 100 g
of an aqueous solution if it contains 37.5 g
HCl? What is the mole fraction of water?
• What is the mole fraction of NaOH in an
aqueous solution that contains 22.8 %
NaOH by mass?
• Calculate the mole fraction of NaCl in a
solution in which 15.7 g NaCl is dissolved
in 100.0 g H2O.