Dilution Volume

The Dilution Volume calculator returns the volume of a substance based on is molarity, and the volume and molarity of the second substance in the mixture.

INSTRUCTIONS: Choose units and enter the following:

• (M₁) Molarity of Substance 1
• (V₁) Volume of Substance 1
• (M₂) Molarity of Substance 2

Diluted Volume of Substance 2 (V₂): The calculator returns the volume in liters.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Dilution formula, M₁V₁= M₂V₂, can be utilized for several outputs. Volumes of either substance involved can be calculated, as well as molarities. As long as three of the four variables are known, the equation can be rearranged and the fourth variable calculated. This equation is usually used to calculate how much of a substance is needed in order to achieve a certain dilution.

The inputs are:

• Molarity of Substance 1 (M₁)
• Volume of Substance 1 (V₁)
• Molarity of Substance 2 (M₂)
• Volume of Substance 2 (V₂)

The default units are moles per liter (mols/L) for molarity and liters (L) for volume. 

Example

Create 3 liters of a 3.5 M solution of HCl from a stock solution of 12.1 mols/L. 

A problem like this may look confusing at first, however, it is simpler than it appears. The unit "M" is the same as writing "mols/L", so all molarity units are the same in this problem. To start, we need to identify our variables:

M₁ = 3.5M

V₁ = 3L

M₂ = 12.1M

In order to make 3 liters of a 3.5M solution, we need to find out how much of the 12.1M stock solution we will use. In other words, we need to find V2 (seeing as it is the only unknown variable that we currently have in our dilution equation). So we'll set up our equation with what we have:

M₁V₁ = M₂V₂

(3.5M)(3L) = (12.1M)(V₂)

And use simple algebra to solve for V2, to get 0.867L of the stock solution HCl. Therefore, we know we need 0.867L of 12.1M HCl (or 867mL, depending on which units are preferred) to make our 3L of 3.5M HCl solution.

Supplemental Materials

Dilution Video and Lesson (study.com)

References

Whitten, et al. "Chemistry" 10th Edition. Pp. 17