Concentration of Solution

Concentration is defined as the amount of solute present in a given amount of solvent.  It can be expressed qualitatively and quantitatively.  The qualitative way of expressing the concentration is either diluted or concentrated.   A concentrated solution contains more solute in the solution while diluted solution contains less solute in the solution.  Very sweet sugar solution is an example of concentrated solution while sugar solution with little sweetness is an example of diluted solution.

There are many different ways in which we can express concentration quantitatively; some are these are the following: percent by mass, percent by volume, molarity, and molality.


Percent by Mass

Percent by mass (% by mass) is defined as the mass of the solute per mass of solution multiplied by 100.  In formula it can be written as

The formula above can be used when the given in the problem are the mass of the solute and the mass of the solution.   But if the given in the problem are the mass of solute and mass of solvent, you can use this formula:

Sample Problem 1.

A solution is made by dissolving of 13.5 g of glucose in 100 g of water.  What is the mass percentage of solute in this solution?

Solution:

Given:

13.5 g of glucose, mass of solute

100 g of water, mass of the solvent

Formula and calculation:

Sample Problem 2.

What is the percent by mass of the solution when 5.50 g of NaBr is dissolved in 78.2 g of solution?

Solution:

Given:

5.50 g of NaBr, mass of solute

78.2 g of solution, mass of solution

Formula and calculation:

Percent by Volume

Percent by volume is just the same with that of percent by mass, only that volume of the substance is being used. Percent by volume can also be calculated using the formula below:

   

Sample Problem 1.

What is the percent by volume of the solution when it contains 27 mL of alcohol in 100 mL of solution?

Solution:  

Given: 

27 mL alcohol, volume of solute

100 mL solution, volume of solution

Formula and calculation:

Degree Proof

Degree Proof is another measure of concentration related to percent by volume.  It is twice the percent by volume.  

This means that an 80 degree proof liquor contains 40 % of alcohol by volume.  The table below shows the alcohol content of some alcoholic drinks:

Molarity

Molarity (M) is also known as molar concentration, it refers to the number of moles of solute per liter of solution.

The unit of molarity is mole per liter (mol/L) or simply M.

Sample Problem 1.

What is the molarity of an 85 mL ethanol (C₂H₅OH) solution containing 1.77 g of ethanol?

Solution:

Given:

1.77 g of ethanol

85 mL of solution = 0.085 L solution

To calculate molarity the number of moles of solute must be calculated, and to calculate the number of moles the molar mass of ethanol should also be calculated first.  

Molar mass of ethanol

C = 2 x 12 =  24 g 

H = 6 x 1   =   6  g

O = 1 x 16 =  16 g

                      46 g/mol

Number of moles can be calculated by dividing the given mass to its  molar mass.

To calculate the molarity 

Molality

Molality (m) is also called molal concentration is the number of moles of solute per kilogram of solvent.  The unit of molality is mol/kg or m.

Sample Problem:

A solution is made by dissolving 4.35 g of glucose (C₆H₁₂O₆) in 25.0 kg of water.  Calculate the molality of glucose in the solution.  

Solution:

Given:

4.35 g glucose

25.0 g of water = 0.025 kg water

We need to calculate the molar mass of glucose (C₆H₁₂O₆), before we can calculate the number of moles.  

C = 6 x 12 = 72 g

H =12 x 1 =  12 g

O = 6 x 16 = 96 g

                    180 g

moles of solute can also be calculated using  factor label method as shown below:

   

For more Sample Problems click HERE