# Concentration of a Solution

A solution may have a small amount of solute dissolved in it while another solution may have a large amount of solute dissolved in it. We can express this as concentration of a solution. The solution having small amount of solute is said to have low concentration. It is known as dilute solution. The solution having a large amount of solute is said to be of high concentration. It is known as concentrated solution.

The concentration of a solution is the amount of solute present in a given quantity of the solution.

It can be expressed in a number of different ways. The most common way of expressing the concentration of a solution is the ‘percentage method’. The percentage method of expressing the concentration of a solution refers to the ‘percentage of solute’ present in the solution. The percentage of solute can be ‘by mass’ or ‘by volume’.

If the solution is of a solid solute dissolved in a liquid, then we consider the mass percentage of solute in calculating the concentration of solution. So, in the case of a solid solute dissolved in a liquid solvent: It is defined as the mass of solute in grams present in 100 grams of the solution. For example – A 10 percent solution of common salt means that 10 grams of common salt is present in 100 grams of solution. 100 grams of the common salt solution also includes 10 grams of common salt. This means that the 100 grams of common salt solution contains 100 – 10 = 90 grams of water in it. Thus, we can prepare a 10 percent solution of common salt by dissolving 10 grams of common salt in 90 grams of water (so that the total mass of the solution becomes 10 + 90 = 100 grams). Please note that the concentration of a solution refers to the mass of solute in 100 grams of the solution and not in 100 grams of the solvent.

We can calculate the concentration of a solution in terms of mass percentage of solute by using the following formula –

Concentration of Solution = (mass of solute/mass of solution) × 100

The mass of solution is equal to the mass of solute plus the mass of solvent. That is:

mass of solution = mass of solute + mass of solvent

In the above given example:

Mass of solute (salt) = 10 g

Mass of solvent (water) = 90 g

Mass of solution = mass of solute + mass of solvent = (10 + 90) g = 100 g

Concentration of solution = (10/100) × 100 = 10 % (by mass)

Thus, the concentration of this salt solution is 10 percent (or 10%) by mass. Please note that if the concentration is in terms of mass, then the words ‘by mass’ are usually not written with it. It is well understood that the concentration of common salt will be expressed by mass as salt solution is a solid dissolved in liquid.

The case of a liquid solute dissolved in a liquid solvent –

If the solution is of a liquid solute dissolved in a liquid solvent, then we usually consider the ‘volume percentage of solute’ in determining the concentration of solution. So, in the case of a liquid solute dissolved in a liquid solvent: The concentration of a solution is defined as the volume of solute in millilitres present in 100 millilitres of solution.

For example – A 20 percent solution of alcohol means that 20 millilitres of alcohol are present in 100 millilitres of solution. 100 millilitres volume of solution also includes 20 millilitres volume of alcohol. This means that the 100 millilitres of alcohol solution contains 100 – 20 = 80 millilitres of water in it.

We can calculate the concentration of a solution in terms of percentage of solute by using the formula:

Concentration of Solution = (Volume of Solute/Volume of Solution) × 100

In the above example:

Volume of solute (alcohol) = 20 mL

Volume of solvent (water) = 80 mL

So, volume of solution = volume of solute + volume of solvent = (20 + 80) mL = 100 mL

Concentration of solution = 20/100 × 100 = 20 % (by volume)

Thus, the concentration of this alcohol solution is 20 percent or that it is a 20% alcohol solution (by volume).

In the industries, when the concentration of a solution is expressed is ‘percent by mass’ or ‘percent by weight’, it is denoted by the symbol w/w (which means ‘weight by weight’). Please note that the terms mass and weight are used in the same sense here. And when the concentration of a solution is expressed as ‘percent by volume’, then it is denoted by the symbol v/v (which means ‘volume by volume’).

We can see the symbols w/w or v/v on the labels of bottles of many liquid medicines. For example – a particular bottle of digestion mixture ‘milk of magnesia’ has these words written on its bottle “contains approximately 8.0 % w/w of hydrated magnesium oxide”.

### Questions related to the topic “Concentration of a Solution” from NCET textbook – Page 18

Question 3:-

To make a saturated solution, 36 grams of sodium chloride is dissolved in 100 grams of water at 293 K. Find its concentration at this temperature.

Solution:-

Concentration of Solution = (mass of solute/mass of solution) × 100

Here, Mass of solute (sodium chloride) = 36 g

And, Mass of solvent (water) = 100 g

So, Mass of solution = mass of solute + mass of solvent

= 36 + 100 = 136 g

Now, putting these values of ‘mass of solute’ and ‘mass of solution’ in the above formula, we get:

Concentration of Solution = (36/136) × 100

= 26.47% (by mass)

Concentration of a solution is the amount of solute present in a given quantity of the solution. The most common method of expressing concentration is percentage method. In percentage method we express concentration as amount of solute present in 100 grams of solution or volume of solute present in 100 mL of solution. There are two different methods of expressing concentration- ‘by mass’ or ‘by volume’. When solid solutes are dissolved in liquid solvents then concentration is expressed ‘by mass’ and when liquid solutes are dissolved in liquid solvents then the concentration is expressed ‘by volume’.