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### Student Question

Secondary III • 2yr.

Good evening,

Can you show me how to solve a complete dilution problem? I have a lot of difficulty with that.

Science

## Explanations (1)

• Explanation from Alloprof

Explanation from Alloprof

This Explanation was submitted by a member of the Alloprof team.

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Team Alloprof • 2yr.

First, when you dilute a solution, you try to decrease the concentration of its solute by adding solvent. It goes without saying that the final concentration of a dilute solution is less than the initial concentration of this solution.

The following formula is used when performing dilution calculations:

$$C_{1} \bullet V_{1} = C_{2} \bullet V_{2}$$

Legend:

• C1: initial concentration of the solution

• V1: initial volume of the solution

• C2: final concentration of the solution

• V2: final volume of solution

Several units can be used to describe the concentration and volume of a solution in the dilution formula. As long as the units are the same on both sides of the formula, the formula works.

Most dilution problems give three of the four variables in the problem statement. The expression must then be handled algebraically in order to isolate the missing term:

$$C_{1} = \frac{C_{2}\bullet V_{2}}{V_{1}}$$

$$V_{1} = \frac{C_{2}\bullet V_{2}}{C_{1}}$$

$$C_{2} = \frac{C_{1}\bullet V_{1}}{V_{2}}$$

$$V_{2} = \frac{C_{1}\bullet V_{1}}{C_{2}}$$

Certain problems require finding a volume of solution to add. In this case, the following formula must be remembered:

$$V_{final} = V_{initial} + V_{to add}$$

It is then necessary quite simply to modify the expression of the equation in order to find the volume to add:

$$V_{to add} =V_{final} - V_{initial}$$

Thank you for your question !