Molarity
There are several different ways to indicate the amount of solute dissolved in a given volume of solution. The most
common method used in chemistry is as the number of moles of solute dissolved in one litre of solution. This is
called molarity.
moles solute
Molarity
=
litre solution
Symbol for Molarity = M
As an example: The concentration of a solution might be
expressed as a "0.50 M NaOH".
You would read as "a 0.50 molar sodium hydroxide solution",
meaning that there are 0.50 moles of NaOH dissolved per
one litre of solution.
CAUTION
Be sure to note that molarity is
calculated as the total volume of the
entire solution, not just volume of
solvent! The solute contributes to
total volume.
Other important things to note:
 square brackets are often used to represent concentration.
So we could also write our example as: [NaOH] = 0.50 M.
 use the capital letter M for molarity, not a lower case m.
It will be important for you to be able to do calculations involving solution concentrations. Generally you will have
three types of problems:
1. calculate concentration
2. calculate the amount of solute (as the number of moles or mass) dissolved in a given volume of
solution, and
3. calculate the volume of a solution with a certain concentration that contains a certain amount of
solute.
EXAMPLES
1.
Antifreeze is a solution of ethylene glycol, C2H6O2 in water. If 4.50 L of antifreeze contains 27.5 g
of ethylene glycol, what is the concentration of the solution?
Solution:
1 mol
27.5 g
×
×
62.1 g
[C2H6O2 ] = 0.098 M
1
0.098 mol
=
4.5 L
L
2.
What mass of sodium carbonate, Na2CO3 is present in 50.00 mL of a 0.750 M solution?
Solution:
106.0 g
0.75 mol
×
×
mol
0.050 L
=
3.98 g
L
answer
3.
What volume of 1.50 mol/L HCl solution contains 10.0 g of hydrogen chloride?
Solution:
1
1 mol
×
1.50 mol
× 10.0 g =
0.183 L or 183 mL
36.5 g
answer
PRACTICE: Calculations – answers attached Due Date:
1.
A 0.750 L aqueous solution contains 90.0 g of ethanol, C2H5OH. Calculate the molar concentration of the solution in mol·L-1.
2.
What mass of NaCl are dissolved in 152 mL of a solution if the concentration of the solution is 0.364 M?
3.
What mass of dextrose, C6H12O6 is dissolved in 325 mL of 0.258 M solution?
4.
A mass of 98 g of sulfuric acid, H2SO4, is dissolved in water to prepare a 0.500 M solution. What is the volume of the solution?
5.
A solution of sodium carbonate, Na2CO3, contains 53.0 g of solute in 215 mL of solution. What is its molarity?
6.
What is the molarity of a solution of HNO3 that contains 12.6 g of solute in 5.00 L of solution?
7.
What mass of copper(II) nitrate, Cu(NO3)2, is present in 50.00 mL of a 4.55 × 10 -3 M aqueous solution?
Calculations Involving Solution Concentration
1.
Answers
A 0.750 L aqueous solution contains 90.0 g of ethanol, C2H5OH. Calculate the molar concentration of the solution in mol·L-1.
Solution:
mole
1. The question asks for concentration, which means finding molarity, or:
L
2. To convert mass of ethanol to moles, we need to find the molar mass of C 2H5OH using the periodic table. Molar
mass is 46.1 g·mol-1
3. Molarity also requires volume; the question tells us we have 0.750 L.
Put this information together to solve the problem, arranging the information to end up with the desired unit:
mol
1 mol
1
2.60 mol
 90 .0 g 


or 2.60 M
L
L
46 .1 g 0.750 L
Our final answer: [C2H5OH ] = 2.60M
2.
What mass of NaCl are dissolved in 152 mL of a solution if the concentration of the solution is 0.364 M?
Solution:
1. The question asks for mass, so we want to calculate grams
2.
We are given the concentration. I suggest you rewrite the concentration as
better see how the units will cancel out.
0.364 mol
L
shown to the right, to
3.
Because the question involves mass, we will need to know the molar mass of NaCl
Using a periodic table we find the molar mass of NaCl to be 58.5 g·mol -1
4. The question gives us the volume in mL. Our unit of concentration uses L, so we will convert 152 mL into 0.152 L.
Put this information together to solve the problem, arranging the information to end up with the desired unit:
58 .5 g 0.364 mol

 0.152 L  3.24 g
mol
L
Answer: 3.24 g of NaCl will be required.
g
3.
What mass of dextrose, C6H12O6 is dissolved in 325 mL of 0.258 M solution?
Solution:
1. The question asks for mass, so we want to calculate grams
2. We are given the concentration (0.258 M). I suggest you rewrite the
concentration as
0.258 mol
shown to the right, to better see how the units will cancel out.
3. Because the question involves mass, we will need to know the molar mass of
C6H12O6
L
Using a periodic table we find the molar mass of C6H12O6 to be 180.1 g·mol-1
4. The question gives us the volume in mL. Our unit of concentration uses L, so we will convert 325 mL into 0.325 L.
Put this information together to solve the problem, arranging the information to end up with the desired unit:
180 .1 g 0.258 mol

 0.325 L  15 .1 g
mol
L
Answer: 15.1 g of dextrose will be required.
A mass of 98 g of sulfuric acid, H2SO4, is dissolved in water to prepare a 0.500 M solution. What is the volume of the solution?
Solution:
1. The question asks for volume, so we want to calculate litres, L (or mL)
g
4.
2.
3.
The concentration of the solution is:
0.500 mol
L
Because the question involves mass, we will need to know the molar mass of H 2SO4
Using a periodic table we find the molar mass of H2SO4 to be 98.1 g·mol-1
Put this information together to solve the problem, arranging the information to end up with the desired unit:
1 L
1 mol

 98 .0 g  2.00 L
0.500 mol 98 .1 g
Answer: The volume of the solution will be 2.00 L.
L
5.
A solution of sodium carbonate, Na2CO3, contains 53.0 g of solute in 215 mL of solution. What is its molarity?
Solution:
mole
1. The question asks for molarity:
L
2. To convert mass of ethanol to moles, we need to find the molar mass of Na 2CO3 using the periodic table. The molar
mass of Na2CO3 is 106.0 g·mol-1
3. Molarity also requires volume; the question tells us we have 215 mL, or 0.215 L.
Put this information together to solve the problem, arranging the information to end up with the desired unit:
mol
1 mol
1
2.33 mol
 53 .0 g 


L
L
106 .0 g 0.215 l
Our final answer: [Na2CO3 ] = 2.33 M
6.
What is the molarity of a solution of HNO3 that contains 12.6 g of solute in 5.00 L of solution?
Solution:
mole
1. The question asks for molarity:
L
2. To convert mass of ethanol to moles, we need to find the molar mass of HNO 3 using the periodic table. Molar mass
is 64.0 g·mol-1
3. Molarity also requires volume, L; the question tells us we have 5.00 L.
Put this information together to solve the problem, arranging the information to end up with the desired unit:
mol
1 mol
1
0.0393 mol
 12 .6 g 


L
L
64 .0 g 5.00 L
Final answer: [HNO3] = 3.93 × 10-2 M
7.
What mass of copper(II) nitrate, Cu(NO3)2, is present in 50.00 mL of a 4.55 × 10 -3 M aqueous solution?
Solution:
1. The question asks for mass, so we need to calculate grams
2.
We are given the concentration:
4.55  10 3 mol
L
3.
Because the question involves mass, we will need to know the molar mass of Cu(NO 3)2
Using a periodic table we find the molar mass of Cu(NO 3)2 to be 187.6 g·mol-1
4. The question gives us the volume in mL. Our unit of concentration uses L, so we will convert 50.00 mL into
0.0.05000 L.
Put this information together to solve the problem, arranging the information to end up with the desired unit:
g
187 .6 g 4.55 10 3 mol

 0.500 L  4.27 10  2 g
mol
L
Final answer: 4.27  10-2 g of copper(II) nitrate are present.