Dilution is the process of making a solution less concentrated by adding more solvent, usually water. It is one of the most common calculations in chemistry labs because many experiments need solutions at precise concentrations. Instead of making every solution from pure chemicals, chemists often start with a concentrated stock solution and dilute it to the needed strength.
Accurate dilution protects experimental results, saves materials, and improves lab safety.
Understanding Chemistry: Dilution Calculations
The dilution relationship comes from conservation of the solute. When water is added to a salt solution, acid solution, or food dye solution, the dissolved particles are spread through a larger space. The number of particles does not change, provided none are spilled, evaporated, or removed.
Their concentration changes because concentration compares an amount of solute with the total solution volume. This is why a small measured portion of a strong stock can make a much larger volume of a weaker working solution.
A dilution calculation only works when the units are handled carefully. Concentrations must use the same type of concentration on both sides, usually molarity. The two volumes must use the same volume unit.
They can both be in milliliters, or both in liters, because the matching units cancel in the calculation. A common mistake is using the desired final volume as the amount of water to add. Final volume means the total volume after mixing.
If a student needs one hundred milliliters of solution and uses twenty milliliters of stock, water is added until the total reaches one hundred milliliters. The water amount is therefore about eighty milliliters, not one hundred milliliters.
In a lab, the method matters as much as the arithmetic. A student first calculates the stock volume, then measures it with equipment suited to the needed precision. A volumetric pipette gives a more reliable small volume than a measuring cylinder.
The stock is transferred into a volumetric flask or another suitable container. Water is added partway, the mixture is swirled, and then water is added carefully to the calibration mark if a volumetric flask is used. Mixing is essential.
Without mixing, the bottom and top of the container can have different concentrations. Reading the bottom of the liquid meniscus at eye level helps prevent a volume error.
Serial dilution is useful when the required solution is far weaker than the available stock. Trying to measure an extremely tiny stock volume can produce a large percentage error. It is often better to make an intermediate solution, then dilute that solution again.
For example, repeated tenfold dilutions reduce concentration by a factor of ten each time. Students should record which tube was made from which previous tube, since a single label error can invalidate the whole series. This method appears in biology when estimating bacterial growth, in environmental testing of water samples, and in medicine when preparing standards for instruments.
Before accepting an answer, check whether it makes physical sense. A diluted solution must have a lower concentration than its starting stock, while its final volume must be greater than the sampled stock volume. The calculated stock volume should therefore be positive and smaller than the final volume for an ordinary dilution.
Significant figures matter because measuring tools have limits. A result calculated to many decimal places does not make the prepared solution exact. Students should keep extra digits during calculation, round at the end, label every solution with its concentration, and follow safety rules for concentrated acids, bases, and other hazardous stocks.
Key Facts
- Dilution equation: M1V1 = M2V2
- M1 and V1 describe the stock solution before dilution, while M2 and V2 describe the final diluted solution.
- Moles of solute stay constant during dilution: n1 = n2
- Molarity is concentration in moles per liter: M = n/V
- To find stock volume: V1 = M2V2/M1
- For serial dilutions, multiply the dilution factors: total dilution factor = DF1 × DF2 × DF3 ...
Vocabulary
- Dilution
- Dilution is the process of lowering a solution's concentration by adding solvent while keeping the amount of solute the same.
- Stock solution
- A stock solution is a concentrated solution used to prepare more dilute solutions.
- Molarity
- Molarity is the number of moles of solute per liter of solution.
- Volumetric flask
- A volumetric flask is a glass container designed to make a solution to one precise final volume.
- Serial dilution
- A serial dilution is a sequence of dilutions where each new diluted solution is used to make the next one.
Common Mistakes to Avoid
- Using the added water volume as V2, which is wrong because V2 is the final total solution volume after dilution.
- Forgetting to convert milliliters to liters when using molarity, which can give incorrect units even if the ratio in M1V1 = M2V2 still works when both volumes use the same unit.
- Mixing up M1 and M2, which leads to impossible answers such as needing more stock solution than the final solution volume for a dilution.
- Assuming moles decrease during dilution, which is wrong because adding solvent changes concentration but does not remove solute.
Practice Questions
- 1 A student needs 250.0 mL of 0.200 M NaCl from a 1.00 M NaCl stock solution. What volume of stock solution is needed?
- 2 You make a serial dilution by transferring 10.0 mL of solution into a flask and diluting to 100.0 mL, then repeating this step two more times. If the original concentration is 0.500 M, what is the final concentration?
- 3 Explain why the concentration decreases during dilution even though the number of moles of solute stays the same.