# Help Zone

### Student Question

Secondary III • 1yr.

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 • 1yr.

First off, diluting a solution is essentially decreasing 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 executing dilution calculations:

$$C_{1} • V_{1} = C_{2} • V_{2}$$

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 equation, the formula works.

Most dilution problems start off with 3 of the 4 variables in the equation. Algebraic manipulation subsequently allows to isolate the missing value:

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

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

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

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

Some problems require finding a volume of solution to add. In this case, you have to remember the following formula:

$$V_{final} = V_{initial} + V_{to_add}$$

Simply modifying the expression of the above equation allows to find the volume of solvent to add:

$$V_{to_add} = V_{final}− V_{initial}$$

There you go! Let us know if we can do anything else to help!