Molar Dilution Calculator: Find the Volume to Add

A molar dilution calculator works out how much solvent to add, or what final concentration a dilution will produce, using the relationship between starting and final molarity. Enter the stock concentration, the target concentration, and either the starting or final volume; the calculator returns the missing volume and, when useful, the amount of solvent to add.

Formula

The standard dilution equation is C₁V₁ = C₂V₂. It expresses conservation of dissolved solute: adding solvent changes the solution’s volume and concentration, but does not change the amount of solute already present.

• C₁ is the starting (stock) concentration, in mol/L (also written M).
• V₁ is the volume of stock solution used, in mL or L.
• C₂ is the desired final concentration, in mol/L.
• V₂ is the total final solution volume, in the same volume unit as V₁.

Rearrange the equation to find whichever quantity is unknown. For example, V₁ = C₂V₂/C₁, and C₂ = C₁V₁/V₂. If the desired final volume is known and you want the solvent volume, subtract the stock volume: solvent to add = V₂ − V₁. The calculator’s first answer uses the example’s specified stock and final volumes; its second output checks the resulting concentration.

Worked Example

Using the calculator’s default values, the stock is 1 mol/L, the target is 0.1 mol/L, the stock volume is 100 mL, and the final volume is 1,000 mL.

1. Calculate the solvent volume: V₂ − V₁ = 1,000 mL − 100 mL = 900.00 mL.
2. Check the final concentration: C₁V₁/V₂ = (1 mol/L × 100 mL)/1,000 mL = 0.1000 mol/L.

The mL units cancel in the concentration calculation. The result is a tenfold dilution: the final solution has one-tenth the stock concentration.

What Molar Dilution Means

Molarity describes the amount of a substance, in moles, per litre of solution. A 1 mol/L solution contains one mole of the specified solute in each litre of final solution. Dilution lowers molarity by increasing the solution volume while keeping the solute amount constant.

This is why dilution calculations are useful when preparing a less concentrated working solution from a stronger stock. The equation applies to a straightforward dilution in which no solute is added or removed through a reaction, precipitation, evaporation, or transfer loss. It does not calculate how many grams of a solid are needed to make a solution from scratch; that requires the substance’s molar mass as well.

How to Use the Calculator

Choose values that describe the same dilution, and keep the volume units consistent. The example calculator takes stock concentration, target concentration, stock volume, and final volume, then reports solvent to add and the concentration implied by the volumes. To plan a different preparation, use the formula to solve for the unknown quantity.

• For a desired final concentration and final volume, calculate the stock volume with V₁ = C₂V₂/C₁.
• For a known stock volume and desired final volume, calculate the final concentration with C₂ = C₁V₁/V₂.
• For a known stock volume and target concentration, first find V₂ = C₁V₁/C₂; then subtract V₁ to get the approximate solvent volume.

For instance, if you calculate that 10 mL of stock is needed for a final volume of 100 mL, the practical instruction is to dilute the stock until the total solution volume is 100 mL. It is not always exactly equivalent to pouring 90 mL of solvent into 10 mL of stock, because volumes can change slightly on mixing.

Units, Measurement, and Rounding

Concentrations in mol/L and M are numerically equivalent. Volumes may be entered in mL or L as long as both volumes in the equation use the same unit. If one volume is in litres and another in millilitres, convert before calculating: 1 L = 1,000 mL. The same principle works with US customary volume units such as fluid ounces or quarts, but convert both volumes to one unit first; molarity itself is based on litres, not gallons or fluid ounces.

Keep extra digits during intermediate calculations and round only the final value to match the precision of your measurements and glassware. A calculator can display several decimal places without making the preparation equally precise. A measured 0.1 mL uncertainty, for example, can matter more than a result reported to four decimal places.

Common Errors and Limits

• Confusing final volume with solvent volume: “Make up to 100 mL” means the total solution ends at 100 mL, not that 100 mL of solvent is added.
• Mixing volume units: using 1 L as one value and 100 mL as another without conversion creates a factor-of-1,000 error.
• Reversing stock and target concentration: for ordinary dilution, the target concentration is lower than the stock concentration.
• Assuming all mixtures have perfectly additive volumes: the equation is a concentration balance, while actual final volume should be measured to the intended mark when accuracy matters.

A target concentration above the stock concentration cannot be obtained by dilution alone. Use a more concentrated stock or a different preparation method. Likewise, the formula assumes the stated stock concentration is accurate and that the solute remains dissolved and chemically unchanged. It does not account for temperature effects, chemical reactions, contamination, or non-ideal solution behavior.

Frequently Asked Questions

What is the formula for molar dilution?
The usual equation is C₁V₁ = C₂V₂. Use consistent volume units, then rearrange it for the value you need.

How do I calculate how much stock solution to use?
Multiply the target concentration by the desired final volume, then divide by the stock concentration: V₁ = C₂V₂/C₁.

Does final volume mean the amount of water to add?
No. Final volume is the total volume of stock plus solvent after mixing. The solvent amount is approximately the final volume minus the stock volume, but accurate preparations are brought to the final-volume mark.

Can I use mL in the dilution equation?
Yes. Both V₁ and V₂ can be in mL, provided they use the same unit. Convert one volume if the two are given in different units.

Can dilution make a solution more concentrated?
No. Adding solvent lowers concentration. To make a solution more concentrated, use a stronger stock, add more solute by a suitable preparation method, or remove solvent under an appropriate process.

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in c1 | Stock concentration | mol/L | 1 | 0
in c2 | Target concentration | mol/L | 0.1 | 0
in v1 | Stock volume | mL | 100 | 0
in vf | Final volume | mL | 1000 | 0
out vadd | Solvent to add | mL | vf - v1 | 2
out ccheck | Final concentration from volumes | mol/L | c1 * v1 / vf | 4