# Dilution Formula

Dilution is the process of reducing the concentration of a given solute in its solution. The chemist can do it simply by mixing with more solvent. For example, we can add water to the concentrated orange juice to dilute it until it reaches a concentration that will be pleasant to drink. Also, dilution refers to a drop in the pH of a chemical which may be a gas, vapor, or solution. In this topic, the student will learn and understand the Dilution Formula with examples. Let us learn this interesting concept!

## Dilution Formula

### Concept of Dilution:

Dilution is the process of decreasing the concentration of a solute in the solution by adding more solvent. To dilute a solution, we add more solvent without the addition of more solute. Then we mix the resulting solution thoroughly to ensure that all parts of the solution should be even.

For example, if 10 grams of salt are dissolved in 1 liter of water as a solvent, then it has a particular salt concentration. Then by adding 1 liter of water more to this solution, the salt concentration is reduced. But, the dilute solution still has 10 grams of salt.

Concentrating on the solutions involves removing the solvent gradually. Normally this is done by evaporating or boiling the solution with the assumption that the heat of boiling does not affect the solute. The dilution equation will be used in these circumstances as well.

### The Formula for Dilution:

In both the dilution and concentration processes, the amount of solute stays the same. As a result, this gives us a way to calculate what the new solution volume must be to get the desired concentration of the solute. From the definition of the molarity we know,

molarity = $$\frac {moles of solute} { liters of solution}$$

Then we may solve for the number of moles of solute as:

moles of solute = $$(molarity) \times (liters of solution)$$

We represent the molarity by M and volume of solution by V. Therefore, the equation becomes

moles of solute = M V

Since this quantity does not change before and after the change of concentration. Therefore the product MV must be the same before and after the concentration change. Using numbers to represent the initial and final conditions, we will get the dilution equation:

$$M_1 V_1 = M_2 V_2$$

Here, the volumes must be expressed in the same units. Also, this equation gives only the initial and final conditions, not the amount of the change. We may find the amount of change by subtraction.

Where,

 $$M_1$$ the molarity of the original solution $$V_1$$ the volume of the original solution $$M_2$$ the molarity of the diluted solution $$V_2$$ the volume of the diluted solution

## Solved Examples

Q.1:  One chemist needs 1.5 M hydrochloric acid for some reaction. The solution is available in 6 M of the HCl. What will be the volume of 6M HCl for dilution to get 5 L of 1.5 M HCl?

Solution: We have,

Initial concentration of HCl i.e. $$M_1$$ =  6 M

Final concentration of HCl i.e. $$M_2$$ = 1.5 M

Final volume of solution as needed, $$V_2$$ = 5 L

So, initial volume $$V_1$$ needs to be found, as:

$$M_1 V_1 = M_2 V_2$$

Substituting the values, we get

$$V_1$$ = $$\frac {1.5 \times 5.0} { 6 }$$

= 1.3 L

Thus volume of 6M HCl will be 1.3 L.

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