Concentration of Solution

Everyone talks about the concentration of solutions. They may also talk about the concentration of coffee or tea. Everyone has a particular view of what is meant by the concentration of a solution. You must have noticed that whenever you make coffee, if you add a lot of powder, you will end up with a concentrated drink, whereas if you add little, it will result in a dilute solution. Therefore, it is essential that you understand what the concentration of the solution is. In this chapter, we will learn about what is meant by the concentration of a solution; we will also see how to find the concentration of a solution and the different methods of expressing the concentration of the solution.

What is Concentration of a Solution?

In an aqueous solution, two parts exist, namely solute and solvent. They are the two basic solution concentration terms that you need to know. We always need to keep an account of the amount of solute in the solution. In chemistry, we define the concentration of solution as the amount of solute in a solvent. When a solution has more solute in it, we call it a concentrated solution. Whereas when the solution has more solvent in it, we call it a dilute solution.

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Now that you understand the concept of what is the concentration of solution let's move on to the different methods of expressing concentration.

Methods of Expressing the concentration of Solution

There are various methods of expressing the concentration of a solution. You will usually see Chemists working with the number of moles. Pharmacists will use percentage concentrations instead of the number of moles. Hence it is important to understand all the methods of expressing the concentration of solutions.

The concentration of the solution formula is given as follows.

Concentration of solution = \[\frac{\text{Weight of the solute in gram}}{\text{volume in Litres}}\]

We will also see other methods on how to calculate the concentration of a solution based on the different methods of expressing concentrations.

• Concentration in Parts per Million

It is expressed in terms of weight. The formula for parts per million is given as follows:

ppm(A)= \[\frac{\textrm{Mass of A}}{\textrm{Total mass of the solution}}\]x10\[^{6}\]

• Mass Percentage (w/w)

It is expressed in terms of mass percentage of solute to the solution. The formula for mass percentage is given as follows.

Mass percentage of A =  \[\frac{\text{Mass of component A}}{\text{Total mass of the soution}}\]x100

e.g. CH₃COOH 33% w/w, and H₂SO₄ 98.0% w/w.

• Volume Percentage (V/V)

It is expressed in terms of the volume percentage of solute to the solvent. The formula for volume percentage is given as follows.

Volume percentage of A = \[\frac{\text{Volume of component A}}{\text{Total volume of the solution}}\]x100

• Mass by Volume Percentage (w/V)

Percentage weight in volume expresses the number of grams of solute in 100 ml of product.

e.g. BaCl₂ solution 10% w/v, and H₂O₂ solution 5-7% w/v.

• Molarity (M)

It is the number of moles of solute contained in 1000 ml of solution. It is a commonly used method for expressing concentrations.

Molarity = \[\frac{\text{Mass of solute}}{\text{volume of solution in litres}}\]

• Molality (m)

The molality is expressed as the number of moles of a solute contained in 1000 gm of a solvent. The formula for molality is given as follows.

Molality (m) = \[\frac{\text{Mass of solute}}{\text{Mass of solvent in Kg}}\]

• Normality (N)

We can define it as the number of equivalents of the solute present in the solution, and it is also called equivalent concentration. The formula for normality is given as follows.

Normality (N) = \[\frac{\text{Weight of solute in grams}}{\text{Equivalent mass} \times \text{Volume in litre}}\]

• Mole Fraction:

The mole fraction (X) of a component in a solution is defined as the ratio of the number of moles of that component to the total number of moles of all components in the solution. The mole fraction of A is expressed as X_A with the help of the following equation in a solution consisting of A, B, C, … we can calculate X_A.

X\[_{A}\] = \[\frac{\text{moles of A}}{\text{mole of A + mole of B + momle of C +.... }}\]

Similarly, we can calculate the mole fraction of B, XB with the help of the following formula.

X\[_{B}\] = \[\frac{\text{moles of B}}{\text{mole of A + mole of B + momle of C +.... }}\]

Now that you know how to find the concentration of a solution using various concentrations of solution formulas, we will try to solve some concentrations of solution questions.

Solved Problems

Question 1) 2 ml of water is added to 4 g of a powdered drug. The final volume is 3ml. Find the mass by volume percentage of the solution?

Answer 1) Given, Mass of solute = 4g

Volume of solution = 3ml

Mass by volume percentage = \[\frac{\text{Mass of solute}}{\text{Volume of solution}}\]x100 = \[\frac{4g}{3ml}\] = 133%

Therefore, the mass by volume percentage is 133 %.

Question 2) Many people use a solution of Na₃PO₄ to clean walls before putting up wallpaper. The recommended concentration is 1.7 % (m/v). Find the mass of Na3PO4 needed to make 2.0 L of the solution?

Answer 2) Given, 

Mass/Volume percentage = 1.7 %

Volume of Solution = 2000 ml

Mass by volume percentage = \[\frac{\text{Mass of solute}}{\text{Volume of solution}}\] × 100 

1.7 % = \[\frac{\text{Mass of solute}}{2000ml}\] ×100

Mass of solute = 34 g

Therefore, the mass required is 34 g.

In chemistry, we are often required to calculate the concentration of the solution. The above-mentioned methods of expressing the concentration of a solution are important. The solved examples are helpful for a better understanding of the concept of concentration of a solution.