Solution Dilution Calculator

C1V1 = C2V2 Chemistry Tool

Calculate the required volume or concentration for diluting solutions using the classic C1V1 = C2V2 formula. Enter any three values to solve for the fourth.

Example Calculations

Click an example to load it into the calculator.

Lab: Diluting a Stock Solution

Laboratory

Prepare 100 mL of 0.1 M NaCl from a 1 M stock.

Calculate For: Initial Volume (V1)

C1: 1 M

V1: undefined undefined

C2: 0.1 M

V2: 100 mL

Pharma: IV Solution Preparation

Pharmaceutical

Make 250 mL of 0.9% saline from a 10% stock.

Calculate For: Initial Volume (V1)

C1: 10 %

V1: undefined undefined

C2: 0.9 %

V2: 250 mL

Environmental: PPM Dilution

Environmental

Prepare 1 L of 50 ppm solution from a 500 ppm stock.

Calculate For: Initial Volume (V1)

C1: 500 ppm

V1: undefined undefined

C2: 50 ppm

V2: 1 L

Education: Find Final Concentration

Education

What is the final concentration if you dilute 5 mL of 2 M HCl to 50 mL?

Calculate For: Final Concentration (C2)

C1: 2 M

V1: 5 mL

C2: undefined undefined

V2: 50 mL

Other Titles
Understanding Solution Dilution: A Comprehensive Guide
Master the art of solution preparation and dilution with this in-depth guide, covering theory, practice, and real-world applications.

What is Solution Dilution?

  • Definition and Importance
  • The C1V1 = C2V2 Formula
  • Common Scenarios
Solution dilution is the process of reducing the concentration of a solute in a solution, usually by adding more solvent. This is a fundamental technique in chemistry, biology, and medicine.
The C1V1 = C2V2 Equation
The dilution equation, C1V1 = C2V2, relates the concentrations and volumes before and after dilution. It allows you to calculate any one variable if the other three are known.
Where is Dilution Used?
Dilution is used in laboratories, hospitals, environmental testing, and classrooms. It is essential for preparing reagents, medications, and test samples.

Dilution in Practice:

  • Making saline for IVs in hospitals
  • Preparing standard solutions for titration
  • Diluting environmental samples for analysis

Step-by-Step Guide to Using the Solution Dilution Calculator

  • Choosing the Variable to Calculate
  • Entering Values and Units
  • Interpreting Results
The calculator allows you to solve for any one of the four variables in the dilution equation. Select which variable you want to calculate, then enter the other three values and their units.
Selecting the Unknown
Use the 'Calculate For' dropdown to choose which variable to solve for: C1, V1, C2, or V2. The input fields will adjust accordingly.
Inputting Values and Units
Enter the known values and select the appropriate units for concentration and volume. The calculator will automatically handle unit conversions where possible.
Understanding the Output
The result section displays the calculated value, the formula used, and a step-by-step breakdown of the calculation.

Calculator Usage Examples:

  • Calculate V1: How much stock do you need to make 100 mL of 0.1 M solution from 1 M stock?
  • Calculate C2: What is the final concentration if you dilute 5 mL of 2 M HCl to 50 mL?

Real-World Applications of Solution Dilution

  • Laboratory Science
  • Medical and Pharmaceutical
  • Environmental Testing
Dilution calculations are essential in many fields. In labs, they are used to prepare reagents and standards. In medicine, they ensure correct drug dosages. In environmental science, they help analyze pollutant concentrations.
Lab Applications
Standard solutions, titrations, and sample preparations all require accurate dilutions.
Medical Uses
IV fluids, injectable drugs, and diagnostic reagents are all prepared using dilution principles.
Environmental Science
Water and soil samples are often diluted to bring analyte concentrations within measurable ranges.

Application Examples:

  • Preparing a buffer for a biology experiment
  • Making a saline solution for medical use
  • Diluting a water sample for heavy metal analysis

Common Misconceptions and Correct Methods

  • Unit Confusion
  • Volume Additivity
  • Over-Dilution
Mistakes in dilution calculations often arise from unit mismatches, assuming volumes are always additive, or over-diluting beyond measurable limits.
Unit Consistency
Always ensure that concentration and volume units match or are properly converted before calculation.
Volume Additivity
Remember that adding solute to solvent may not always result in perfectly additive volumes, especially at high concentrations.
Avoiding Over-Dilution
Diluting too far can make solutions too weak to measure accurately. Always check the detection limits of your method.

Misconception Examples:

  • Mixing mL and L without conversion
  • Assuming 10 mL + 90 mL always equals 100 mL
  • Diluting a sample below the detection limit

Mathematical Derivation and Examples

  • Deriving the Formula
  • Worked Examples
  • Tips for Accuracy
The C1V1 = C2V2 formula is derived from the conservation of mass: the amount of solute before and after dilution remains constant.
Derivation
C1 × V1 = C2 × V2, where C = concentration and V = volume. Rearranging allows you to solve for any variable.
Worked Example
To make 100 mL of 0.1 M NaCl from 1 M stock: V1 = (C2 × V2) / C1 = (0.1 × 100) / 1 = 10 mL.
Tips for Accurate Calculations
Double-check units, use calibrated equipment, and record all values for reproducibility.

Derivation and Example Calculations:

  • V1 = (C2 × V2) / C1
  • C2 = (C1 × V1) / V2