Combining assay batches
Mixing 20 mL at 100 mM with 30 mL at 20 mM gives 2600 umol in 50 mL, or 52 mM. Source A contributes 76.9% of the solute.
Chemistry and laboratory planning
Dilution Equilibrium Calculator
Calculate the homogeneous post-mixing concentration of two nonreacting solutions of the same solute from separate concentrations and volumes.
Chemistry / mixture balance
Balance two source solutions into one homogeneous endpoint
Here “equilibrium” means the uniform concentration after complete physical mixing of two nonreacting portions of the same solute. It does not calculate a thermodynamic equilibrium constant, dissociation, partitioning, or reaction extent.
Final concentration-
Total solute-
Combined volume-
Solute from A-
Solute from B-
LIVE CURRENT-VALUE ANALYSIS
Two inflows and their mixed endpoint
Source widths follow current volumes, color intensity follows concentration, and the final vessel reports the weighted concentration and amount contributions.
| Balance item | Input or subtotal | Operation | Current result | Unit |
|---|
DETAILED CALCULATION PROCESS
Formula, units, current substitution, and reconciliation
1. Governing relation
nA = cA VA; nB = cB VB; cf = (nA + nB) / (VA + VB)
Compute each source amount independently, add amounts and nominal volumes, then divide. Keeping the source ledgers separate exposes which portion contributes the solute.
2. Symbols and default basis
| Symbol | Meaning | Unit | Default basis |
|---|---|---|---|
| cA | Concentration of source A | mM | 100 |
| VA | Volume of source A | mL | 20 |
| cB | Concentration of source B | mM | 20 |
| VB | Volume of source B | mL | 30 |
| nT | Total solute amount | umol | 2600 |
| cf | Uniform post-mixing concentration | mM | 52 |
3. Unit normalization
- mM multiplied by mL equals umol because 1 mmol/L x 1 mL = 1 umol.
- Both source concentrations stay in mM, so no concentration scaling is hidden.
- The calculation assumes VA + VB is the final mixture volume.
4. Current numerical substitution
5. Independent reconciliation
HOW TO USE THIS CALCULATOR
Combine two same-solute portions into one auditable endpoint
- Verify that A and B contain the same tracked solute and do not react.
- Record each concentration from its own preparation or assay record.
- Enter the delivered volumes, not nominal container capacities.
- Compare the amount-contribution percentages before accepting the mixed concentration.
- Export the source records and retain evidence that the mixture reached homogeneity.
CHEMISTRY FOUNDATIONS
Why the mixed concentration is volume weighted
- Concentration averages are volume weighted
- The final value is not generally (cA+cB)/2 unless the volumes are equal.
- Amount is the conserved bridge
- Each source enters as cV, allowing different concentrations and volumes to combine consistently.
- A zero-concentration source is diluent
- It adds volume without adding tracked solute and is a valid boundary.
- Homogeneity is an operational assumption
- The equation gives the eventual uniform value; incomplete mixing creates spatial concentration differences.
- This is not chemical equilibrium
- No equilibrium constant, activity coefficient, or reaction stoichiometry appears in the model.
DEEP ANALYSIS 1
Why source contribution differs from volume share
At the default, A is only 40% of volume but supplies about 76.9% of solute because it is five times as concentrated as B.
DEEP ANALYSIS 2
Nonadditive volumes and concentrated media
Some solvent systems contract or expand on mixing. If precision requires measured final volume, replace the additive-volume assumption with that measurement.
DEEP ANALYSIS 3
How to audit a surprising endpoint
The final concentration should lie between cA and cB for positive volumes. A value outside that interval signals a unit, identity, or arithmetic error.
RESULT INTERPRETATION
Separate each source contribution from the final endpoint
The endpoint concentration answers a material-balance question; it does not prove adequate mixing time.
The contribution percentages allocate solute amount, not physical volume or uncertainty.
REAL USE CASES
Concentrated-source mixing and the zero-solute boundary
Diluent as source B
Mixing 5 mL at 200 mM with 45 mL at 0 mM yields 20 mM. This reproduces an ordinary tenfold dilution through a two-source balance.
EVIDENCE AND DATA QUALITY
Preserve delivered volumes and source concentration records
Retain solution identities, concentration methods, delivered-volume records, vessel and mixing protocol, temperature where volume matters, timestamps, and the exported source-amount ledger.
LIMITS AND EXCLUSIONS
Where the nonreacting homogeneous-mix model stops
- Only for the same conserved solute in both source portions.
- Excludes chemical reaction, precipitation, volatilization, adsorption, and phase partitioning.
- Assumes nominal additive volumes unless a measured final volume is substituted externally.
- Does not determine mixing time or spatial homogeneity.
- Does not calculate thermodynamic or acid-base equilibrium.
TERMS USED HERE
Vocabulary for source portions, contributions, and homogeneity
- Source portion
- One measured solution entering the mixture.
- Weighted concentration
- Total amount divided by total volume.
- Amount balance
- Accounting identity comparing incoming and final solute amounts.
- Homogeneous endpoint
- Uniform concentration after adequate mixing.
- Contribution fraction
- Share of total solute supplied by one source.
- Volume additivity
- Assumption that final volume equals the sum of delivered volumes.
RELIABLE SOURCES
Amount-balance and concentration references
FREQUENTLY ASKED QUESTIONS
Why is the simple average wrong? and related questions
Why is the simple average wrong?
It gives both sources equal weight even when their volumes differ.
Can solution B be zero concentration?
Yes; it then acts as a diluent while retaining its entered volume.
Can both concentrations be zero?
Yes. The result is a valid zero-solute mixture with zero contribution percentages.
Does the page calculate equilibrium chemistry?
No. The title uses equilibrium only for the fully mixed physical endpoint.
What if the solutes are different?
Track each species separately or use a reaction model; combining them as one solute is invalid.
Should I use measured final volume?
If contraction or expansion is material, calculate with a verified final volume in a suitable method rather than assuming additivity.
IMPORTANT BOUNDARY
A physical mixing endpoint, not thermodynamic equilibrium
Use this as a nominal same-solute mass balance, not evidence of chemical equilibrium, compatibility, sterility, complete mixing, or regulatory release.