Dilution Calculations (M1V1 = M2V2) Cheat Sheet

Key Facts

• The dilution equation is $M_1V_1 = M_2V_2$, where the amount of solute before and after dilution is the same.
• Use $M_1$ for the initial stock concentration and $M_2$ for the final diluted concentration.
• Use $V_1$ for the volume of stock solution needed and $V_2$ for the final total volume after adding solvent.
• Volumes in $M_1V_1 = M_2V_2$ can be in liters or milliliters, but $V_1$ and $V_2$ must use the same unit.
• To solve for stock volume, rearrange the equation as $V_1 = \frac{M_2V_2}{M_1}$.
• The amount of solvent to add is $V_{\text{solvent}} = V_2 - V_1$.
• A dilution factor can be written as $DF = \frac{V_{\text{final}}}{V_{\text{stock}}} = \frac{M_{\text{stock}}}{M_{\text{final}}}$.
• For many dilute aqueous solutions, concentration in parts per million is approximated by $1\,\text{ppm} = 1\,\frac{\text{mg}}{\text{L}}$.

Vocabulary

Dilution

A dilution is the process of lowering a solution's concentration by adding more solvent.

Stock Solution

A stock solution is a concentrated solution used to prepare a less concentrated solution.

Molarity

Molarity is concentration measured as moles of solute per liter of solution, written as $M = \frac{\text{mol}}{\text{L}}$.

Solute

The solute is the substance being dissolved in a solution.

Solvent

The solvent is the substance that dissolves the solute, such as water in many chemistry labs.

Dilution Factor

The dilution factor compares the final solution volume to the stock volume, written as $DF = \frac{V_{\text{final}}}{V_{\text{stock}}}$.