Calculadora de Dilución de Soluciones (C1V1 = C2V2)
Calcula diluciones con C₁V₁ = C₂V₂. Resuelve cualquier variable, mezcla stock + diluyente y obtén el factor de dilución al instante.
Ingresa cualquier 3 valores para resolver el 4to.
Tabla de Contenidos
¿Qué es una dilución de solución?
Una dilución es el proceso de reducir la concentración de una solución agregando más solvente (diluyente). En el trabajo de laboratorio, esto generalmente significa tomar un pequeño volumen de un stock concentrado y agregar tampón o agua.
Las diluciones son fundamentales en química, biología, medicina y muchas otras disciplinas científicas.
El principio clave detrás de la dilución es la conservación de masa: la cantidad de soluto permanece constante antes y después de la dilución.
Términos clave
- Solución stock: La solución concentrada con la que comienzas
- Diluyente: El solvente agregado para reducir la concentración (ej., agua, tampón, solución salina)
- Solución de trabajo: La solución diluida final a la concentración deseada
- Alícuota: Una porción medida tomada de un volumen mayor
La fórmula C₁V₁ = C₂V₂
La ecuación de dilución se deriva del principio de que la cantidad de soluto permanece constante durante la dilución.
C₁V₁ = C₂V₂
(Cantidad de soluto antes) = (Cantidad de soluto después)
Donde:
- C₁ (Concentración de stock): La concentración de tu solución inicial
- V₁ (Volumen de stock): El volumen de solución stock que usarás
- C₂ (Concentración final): La concentración objetivo después de la dilución
- V₂ (Volumen final): El volumen total de la solución diluida
Esta ecuación puede reorganizarse para resolver cualquiera de las cuatro variables cuando las otras tres son conocidas.
Solve for V₁:
V₁ = (C₂ × V₂) / C₁
Solve for V₂:
V₂ = (C₁ × V₁) / C₂
Solve for C₁:
C₁ = (C₂ × V₂) / V₁
Solve for C₂:
C₂ = (C₁ × V₁) / V₂
Cómo usar esta calculadora
Esta calculadora resuelve la ecuación C₁V₁ = C₂V₂ para cualquier variable.
Paso 1: Selecciona qué resolver
Haz clic en el botón de la variable que deseas calcular. Generalmente resolverás V₁ (cuánto stock usar).
Paso 2: Ingresa los tres valores conocidos
Completa los valores que conoces. Selecciona las unidades apropiadas en los menús desplegables.
Paso 3: Revisa los resultados
La calculadora calcula automáticamente la variable desconocida junto con el factor de dilución e instrucciones de mezcla.
Ejemplos
Example 1: Basic 10× dilution
Problem: Make 100 mL of 0.1 M NaCl from a 1.0 M stock solution.
Solution: Solve for V₁:
Procedure: Measure 10 mL of the 1.0 M stock, then add 90 mL of diluent (water) to reach 100 mL total volume.
Example 2: Converting between unit prefixes
Problem: Prepare 500 µL of a 50 µM working solution from a 10 mM stock.
Solution: The calculator handles unit conversion automatically. Setting C₁ = 10 mM, C₂ = 50 µM, V₂ = 500 µL:
Procedure: Pipette 2.5 µL of the 10 mM stock and add 497.5 µL of diluent.
Example 3: Mass/volume concentration
Problem: How much of a 10 mg/mL protein stock is needed to make 2 mL at 0.5 mg/mL?
Procedure: Add 100 µL of stock to 1900 µL of buffer.
Example 4: Calculating final concentration
Problem: You added 25 µL of a 4 M NaCl stock to reach a final volume of 1 mL. What is the final concentration?
Example 5: Working with percent solutions
Problem: Dilute a 20% (w/v) SDS stock to make 50 mL of 1% SDS.
Procedure: Add 2.5 mL of 20% SDS stock to 47.5 mL of water.
Entendiendo el factor de dilución
The dilution factor (DF) describes how much a solution has been diluted. It can be expressed in two equivalent ways:
DF = C₁/C₂ = V₂/V₁
A dilution factor of 10 (often written as "10×" or "1:10") means the final concentration is 10 times lower than the starting concentration. Equivalently, it means the final volume is 10 times the volume of stock used.
| Dilution Factor | Notation | Stock Fraction | Example |
|---|---|---|---|
| 2 | 2× or 1:2 | 50% | 1 mL stock + 1 mL diluent = 2 mL |
| 5 | 5× or 1:5 | 20% | 1 mL stock + 4 mL diluent = 5 mL |
| 10 | 10× or 1:10 | 10% | 1 mL stock + 9 mL diluent = 10 mL |
| 100 | 100× or 1:100 | 1% | 10 µL stock + 990 µL diluent = 1 mL |
| 1000 | 1000× or 1:1000 | 0.1% | 1 µL stock + 999 µL diluent = 1 mL |
The stock fraction is simply 1/DF, representing what proportion of the final volume comes from the stock solution. This is useful for understanding the composition of your diluted solution.
Diluciones en serie
A serial dilution is a series of sequential dilutions used to reduce concentration in a controlled, stepwise manner. This technique is essential when you need a range of concentrations (e.g., for standard curves) or when the required dilution factor is too large for a single step.
Why use serial dilutions?
- Accuracy: Large dilutions (e.g., 1:10,000) are error-prone in a single step due to pipetting very small volumes
- Standard curves: Create a series of known concentrations for calibration
- Titrations: Systematically test a range of concentrations
- Microbiology: Achieve countable colony numbers from concentrated samples
For a serial dilution with n steps, each using the same dilution factor (DF), the total dilution is:
Total dilution = DFn
Example: 10-fold serial dilution
Starting with a 1 M solution and performing three 10× dilutions:
- Tube 1: 1 M → 0.1 M (10× dilution)
- Tube 2: 0.1 M → 0.01 M (100× total)
- Tube 3: 0.01 M → 0.001 M (1000× total)
Unidades de concentración explicadas
This calculator supports two families of concentration units. Units within a family can be converted directly; converting between families requires knowing the molecular weight of the solute.
Molar concentration (amount per volume)
Molar units express concentration as moles of solute per liter of solution. This is preferred for most biochemical and molecular biology applications because it directly relates to the number of molecules.
| Unit | Full Name | Equivalent |
|---|---|---|
| M | Molar | 1 mol/L |
| mM | Millimolar | 10⁻³ M = 1 mmol/L |
| µM | Micromolar | 10⁻⁶ M = 1 µmol/L |
| nM | Nanomolar | 10⁻⁹ M = 1 nmol/L |
Mass/volume concentration
Mass/volume units express concentration as mass of solute per volume of solution. These are common for proteins, polymers, and situations where molecular weight is unknown or variable.
| Unit | Equivalent | Notes |
|---|---|---|
| g/L | 1 g per liter | Base unit |
| mg/mL | 1 g/L | Same as g/L |
| mg/L | 10⁻³ g/L | Also called ppm (parts per million) in water |
| µg/mL | 10⁻³ g/L | Same as mg/L |
| % (w/v) | 10 g/L | Grams per 100 mL |
Converting between molar and mass/volume
To convert between these families, you need the molecular weight (MW) of the solute:
Molarity (M) = Mass concentration (g/L) / MW (g/mol)
Mass concentration (g/L) = Molarity (M) × MW (g/mol)
Errores comunes a evitar
Mistake 1: Confusing V₂ with diluent volume
V₂ is the total final volume, not the volume of diluent added. The diluent volume is V₂ - V₁. If you want 100 mL final volume and use 10 mL stock, add 90 mL diluent (not 100 mL).
Mistake 2: Mixing incompatible concentration units
You cannot directly use C₁V₁ = C₂V₂ when C₁ is in molar units and C₂ is in mass/volume units (or vice versa). First convert both to the same unit family using the molecular weight.
Mistake 3: Ignoring significant figures
Your calculated result is only as accurate as your least precise input. If your stock concentration is known to ±5%, your final concentration will have at least that much uncertainty.
Mistake 4: Pipetting errors at extreme volumes
Very small volumes (<1 µL) and very large dilution factors (>100×) in a single step are prone to significant error. Consider serial dilutions for better accuracy when the calculated V₁ is extremely small.
Mistake 5: Assuming ideal mixing
C₁V₁ = C₂V₂ assumes volumes are additive (V_stock + V_diluent = V_final). This is approximately true for dilute aqueous solutions but may not hold for concentrated solutions or organic solvents where volume contraction or expansion can occur.
Preguntas Frecuentes
Significa que la cantidad de soluto antes de la dilución (C1 × V1) es igual a la cantidad de soluto después de la dilución (C2 × V2).
C1 y C2 deben usar unidades de la misma familia (todas molares o todas masa/volumen). V1 y V2 pueden usar cualquier unidad de volumen.
El factor de dilución (FD) = C1/C2 = V2/V1. Una dilución 10× significa que la concentración final es 10 veces menor que la concentración inicial.
Eso significa C2 > C1, lo cual no se puede lograr agregando diluyente. Necesitarías un stock más concentrado.
No. C1 y C2 deben estar en la misma familia de unidades.
Realiza múltiples diluciones en secuencia. Por ejemplo, dos diluciones 1:10 dan una dilución total de 1:100.