11.3 Concentration of Solution
If a teacher asks her students to prepare a cup of sugar solution, then depending on the taste, each student can dissolve different amounts of sugar in it. Although every student prepared a cup of sugar solution, all of these solutions will have different taste. There will be no consistency because they have different amounts of solute (sugar) present. To overcome this problem, we use different units to describe the concentration of the solution.
Molarity
One of the most used units of concentration in the chemistry laboratory is Molarity shown with M.
Molarity (M) =
You can go to this phet lab and see how a change in the amount of solute or volume of solution affect the concentration or molarity of solution.
https://phet.colorado.edu/sims/html/molarity/latest/molarity_en.html
Molality
We can also use other units such as molality, shown with m, to describe the concentration.
Molality (m) =
Mole Fraction
Another way to show concentration is by using mole fraction. Mole fraction can be calculated for any component in a solution.
Mole fraction of Solute X (solute) = 
Mole fraction of Solvent X (solvent) = 
Here Na = Moles of solute and Nb = Moles of solvent
Mass Percent and Volume Percent
Besides these units, we can also use units such as mass percent and volume percent to describe the concentration of a solution.
Weight percent or Mass percent m/m % =
You can measure the mass of solute and solvent using any units as long as they are consistent.
Volume percent v/v% = 
In calculating m/m % or v/v%, mass and volume of solute and solvent can be measured using any units as long as they are consistent.
Summary of Units of Concentration
| Equation | Comparison | Representation | |
| Molarity | (M) =  | Moles of solute to Volume of solvent | M |
| Molality | (m) =  | Moles of solute to Mass of solvent | m |
| Mole Fraction | X (a) = | Moles of component to moles of solution | X |
| Mass Percent Or Weight percent | m/m % =  | Mass of component to mass of solution | m/m % or w/w % |
| Volume Percent | v/v% =  | Volume of component to Volume of solution | v/v% |
Solved Example Problems:
Q. : A solution was prepared by dissolving 15.5 g of NaCl in 150.0 ml solution. Find molarity, molality, mole fraction of NaCl, and m/m% of solution given that the density of the solution was 1.05 g/ml.
We know Molarity (M) =
We are already given volume of solution = 150.0 ml = 0.1500 L
To find moles of solute, we need to know the molar mass of NaCl. From periodic table
Molar mass of NaCl = 1 (22.99) + 1 (35.45) = 58.44 g / mol
Moles of NaCl = = 0.265 mol
Molarity = = 1.77 M
To find molality we can use the formula Molality (m) =
We already have the number of moles of solute, but we also need to find the kg of solvent. We can use the density of the solution to find the mass of the solvent.
Density = ;
1.05 g/ml = ;
Mass = 1.05 g/ml x 150.0 ml = 157.5 g solution
More Example on Weight percent
Q.: A solution is prepared by adding 3.0 g of a substance A to 17 g of water. Calculate the mass percent of the solute.
Solution
Weight percent or Mass percent m/m % =
Given: Mass of solute = 3.0 g
Mass of Solvent = 17 g
m/m % = 100
=15%
Q. : How many grams of 5.0% by weight NaCl solutions will have 6.4 g NaCl in it?
Solution
Weight percent or Mass percent m/m % =
Given: m/m% = 5.0
Mass of solute = 6.4 g
If Mass of solvent = X
5.0 =
0.05 =
0.05 (6.4 + X) = 6.4
0.32 + 0.05 X = 6.4
0.05 X = 6.4 – 0.32 = 6.08
X = = 121.6 g
Mass of solution = 121.6 + 6.4 = 128 g
How to convert Weight percent to the mole fraction
Now if the weight percent of the solution is known, we can calculate the mole fraction of the solution or the solvent easily as explained in the example below.
Example
Q.: Calculate the mole fraction of HCl and H2O in a solution, which has 20% HCl by weight.
Given: Molar mass of HCl is 36.5 grams/mole, and the Molar mass of water is 18 grams/mole.
20% HCl by weight represents a solution, that contains 20 grams of HCl acid in every 100 g solution. Or we can say 20 grams solute is present in 80 grams of water.,
Moles of HCl = = .547 moles of HCl
Moles of water = = 4.44 moles of H2O.
Mole fraction of Solute (HCl) X (HCl) = ,
Mole fraction of HCl = =.109
Mole fraction of H2O = 
Mole fraction of H2O = 
0.890
Below is a summary of the steps needed to calculate the mole fraction.
Source: Commons.wikimedia.org/
Fig. 11.4
- Find the mass of Solute and solvent from weight percent or mass percent
- Find the molar mass of the solute and solvent
- Calculate the moles of solute and solvent using mass and molar mass
- Apply the mole fraction formula to obtain the mole fraction
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Learning Check:
- Find the molarity, molality, and mole fraction of NaOH in a solution prepared by dissolving 2.57 g of NaOH in 250. ml solution given that the density of the solution is 1.08 g/ml.
- Find molarity, molality, and mass/mass percent concentration of a solution prepared by dissolving 25.5 g of NaOH in 245 g of water. The density of the solution was found to be 1.10 g/ml.
Answer: 3) 0.257 M, 0.240 m, Mol fraction of NaOH = 0.00431
4) 2.59 M, 2.60 m, 9.43%