Solution Dilution Calculator
Free Solution dilution Calculator for mixtures & solutions. Enter variables to compute results with formulas and detailed steps.
Formula
C1 x V1 = C2 x V2
The dilution equation states that the product of concentration and volume is conserved. C1 and V1 are the initial concentration and volume, while C2 and V2 are the final concentration and volume after dilution.
Frequently Asked Questions
What is the dilution equation C1V1 = C2V2?
The dilution equation C1V1 = C2V2 is a fundamental chemistry formula that relates the concentration and volume of a stock solution (C1, V1) to the concentration and volume of the diluted solution (C2, V2). It works because the amount of solute (moles) remains constant during dilution — you are only adding more solvent. The equation assumes that the volumes are additive and the solution behaves ideally, which is a good approximation for most laboratory dilutions.
How do you perform a serial dilution?
A serial dilution involves making a series of successive dilutions from a single stock solution. Each dilution uses a fixed dilution factor, typically 1:2, 1:5, or 1:10. For a 1:10 serial dilution, take 1 mL of the previous solution and add 9 mL of solvent to make 10 mL total. After n dilutions of factor f, the final concentration is the original concentration divided by f raised to the power n. Serial dilutions are essential in microbiology for plate counts and in immunology for antibody titrations.
What are common mistakes in dilution calculations?
The most common mistake is confusing the volume of solvent to add with the final volume. If C1V1 = C2V2 gives V2 = 100 mL and V1 = 10 mL, you add 90 mL of solvent (not 100 mL). Another common error is using inconsistent units between concentration and volume values. Always ensure that C1 and C2 use the same concentration unit, and V1 and V2 use the same volume unit. Also be careful that C2 must always be less than C1 for a dilution.
What is a dilution factor?
The dilution factor is the ratio of the initial concentration to the final concentration (C1/C2), or equivalently the ratio of final volume to initial volume (V2/V1). A dilution factor of 10 means the solution was diluted 10-fold, so the final concentration is one-tenth of the original. This can be written as 1:10. If you take 1 mL of stock and add 9 mL of solvent, the dilution factor is 10. Dilution factors multiply in serial dilutions, so three 1:10 dilutions give a total dilution of 1:1000.
How does the dilution formula work?
The dilution formula is C1V1 = C2V2, where C is concentration and V is volume. If you have 100 mL of 2M HCl and need 0.5M, solve: 2 x 100 = 0.5 x V2, so V2 = 400 mL total volume. Add 300 mL of water to 100 mL of stock solution. Always add acid to water, never the reverse.
How accurate are the results from Solution Dilution Calculator?
All calculations use established mathematical formulas and are performed with high-precision arithmetic. Results are accurate to the precision shown. For critical decisions in finance, medicine, or engineering, always verify results with a qualified professional.