Molarity & Dilution

Solving for Concentration, Moles, or a Dilution Ratio

Molarity measures how many moles of a substance are dissolved in each liter of solution. Solve for molarity, moles, or volume from the other two, or switch to Dilution mode to find how much stock solution and diluent (like water) you need to reach a target, lower concentration.

The Formula

Molarity:

$$\vC{\text{Molarity}} = \frac{\vA{\text{Moles}}}{\vB{\text{Volume}}}$$

Dilution (the amount of solute stays the same before and after adding diluent):

$$\vA{C_1} \times \vB{V_1} = \vC{C_2} \times \vD{V_2}$$

Solved for the stock volume needed: $\vB{V_1} = \frac{\vC{C_2} \times \vD{V_2}}{\vA{C_1}}$

Worked Example

Molarity of a solution with 2 mol dissolved in 4 L:

1. Apply the formula: $\vC{\text{Molarity}} = \frac{\vA{2}}{\vB{4}} = \vC{0.5}$ mol/L.

Dilution — diluting a 5 mol/L stock solution down to 1 mol/L, making 0.5 L total:

1. Apply the formula: $\vB{V_1} = \frac{\vC{1} \times \vD{0.5}}{\vA{5}} = \vB{0.1}$ L of stock solution.
2. Find the diluent needed: $\vD{0.5} - \vB{0.1} = 0.4$ L of water.

Key Factors to Consider

• The dilution formula (C₁V₁ = C₂V₂) works because the total AMOUNT of solute never changes when you add more solvent — only its concentration does. Adding diluent spreads the same number of moles of solute across a larger volume, which is exactly why the product of concentration and volume stays constant before and after dilution.
• Molarity (mol/L) is one of several concentration units, and it’s specifically volume-based, not mass-based. Other common concentration measures — molality (mol/kg of solvent), mass percent, or parts per million — use different bases and aren’t directly interchangeable with molarity without additional information like the solution’s density.
• When preparing a diluted solution in practice, the diluent is added to reach a final total volume, not simply added on top of the stock volume. In real lab practice, the calculated stock volume is measured out first, then diluent is added until the combined solution reaches the target final volume (rather than adding the diluent volume separately) — this avoids small volume-of-mixing errors that can occur with some solutions.
• This calculator’s dilution mode assumes the solute itself doesn’t react with the diluent. For a simple dilution (adding water to a stock solution of the same substance), this assumption holds — but for solutions where mixing triggers a chemical reaction, this simple ratio no longer describes the resulting concentration.

Common Mistakes

• Mixing up volume units between fields. C₁V₁ = C₂V₂ only works when both volumes use the same unit (both liters, or both milliliters) — mixing mL with L silently throws off the result by a factor of 1,000.
• Assuming diluent volume equals final volume minus stock volume, then adding both separately. In practice, diluent is added to bring the mixture up to the target final volume, not measured out independently and poured in on top — the two approaches can differ slightly depending on the solution’s volume-of-mixing behavior.
• Trying to dilute up to a higher concentration. Adding solvent can only lower concentration, never raise it — reaching a higher concentration requires adding more solute or removing solvent, a different calculation entirely.
• Confusing molarity with other concentration units. Molality (mol/kg of solvent), mass percent, and parts per million all measure concentration differently and aren’t interchangeable with molarity without knowing the solution’s density.

Useful to Know

• Need a solute’s molar mass before you can convert grams to moles? Molar Mass Calculator adds up atomic weights from a chemical formula.
• Working with an acid or base’s concentration to find pH? pH Calculator calculates pH directly from concentration.
• Need to relate a gas’s pressure, volume, temperature, and moles instead of a solution’s? Ideal Gas Law Calculator covers the ideal gas law.