Dilution Calculator

The Art of Dilution: A Guide to the M₁V₁ = M₂V₂ Calculator

In chemistry and biology labs, it is rare to use chemical solutions at the high concentrations in which they are typically manufactured and sold. Instead, scientists prepare 'working solutions' of a desired lower concentration by diluting a more concentrated 'stock solution'. A dilution is the process of decreasing the concentration of a solute in a solution by adding more solvent (usually water). The process is a fundamental, everyday task in any laboratory setting, essential for preparing reagents, calibrating instruments, and conducting experiments. The key principle governing dilutions is the conservation of moles: the amount of solute in the solution remains the same; it is only the volume of the solvent that changes.

This principle is captured by a simple but powerful equation: M₁V₁ = M₂V₂. This calculator is designed to make using this formula effortless. It allows you to solve for any of the four variables, making it a versatile tool for any dilution scenario. Whether you need to figure out how much stock solution to use to make a specific new solution, or you want to determine the final concentration after a dilution, this tool provides an instant and accurate answer. It is indispensable for students, lab technicians, and researchers for ensuring the accuracy and reproducibility of their experimental work.

The Dilution Formula Explained: M₁V₁ = M₂V₂

The dilution formula is a statement of the conservation of moles. The number of moles of solute before dilution is equal to the number of moles of solute after dilution. Since the number of moles can be calculated as Molarity (M) × Volume (V), we get the equation:

M₁V₁ = M₂V₂

Where:

• M₁ is the Molarity (concentration) of the initial stock solution.
• V₁ is the Volume of the initial stock solution that you need to use.
• M₂ is the Molarity (concentration) of the final, diluted solution.
• V₂ is the final Volume of the diluted solution.

This calculator can algebraically rearrange the formula to solve for any of the four variables, provided the other three are known. It is crucial that the units for volume (e.g., mL or L) and concentration (e.g., M or mM) are consistent for both the initial and final states.

Practical Example: Preparing a Solution

Imagine you have a 2 M (M₁) stock solution of HCl, and you need to prepare 500 mL (V₂) of a 0.1 M (M₂) HCl solution for an experiment. The question is: how much of the stock solution (V₁) do you need?

1. Set up the equation: M₁V₁ = M₂V₂
2. Plug in the known values: (2 M) × V₁ = (0.1 M) × (500 mL)
3. Solve for V₁: V₁ = (0.1 M × 500 mL) / 2 M = 50 / 2 = 25 mL

Answer: You would need to take 25 mL of your 2 M stock solution and add enough water to bring the total volume up to 500 mL. You would not simply add 475 mL of water, as volumes are not always perfectly additive. The correct procedure is to add the 25 mL of stock to a 500 mL volumetric flask and then add solvent 'to the line'.