How to Dilute a Solution: The C1V1 = C2V2 Formula Guide

In biological and chemical laboratories, concentrated stock solutions are stored in high molarities (e.g., 10x PBS buffer or 12 M HCl) to save shelf space and maintain shelf life. Preparing working solutions requires diluting this stock with solvent.

This guide explains the conservation of mass dilution equation, explains how to calculate solvent volume to add, and connects to the CalculatorAll Dilution Calculator.

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The Dilution Equation (C₁V₁ = C₂V₂)

C₁ × V₁ = C₂ × V₂

Where:

• C₁: Initial concentration of concentrated stock solution.
• V₁: Volume of stock solution needed.
• C₂: Desired final concentration of working solution.
• V₂: Total final desired volume.
• Volume of Solvent to Add (V_solvent): V_solvent = V₂ - V₁

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Worked Example: Making 500 mL of 1.0 M Acid from 10.0 M Stock

Suppose you need to make 500 mL (V₂) of 1.0 M (C₂) hydrochloric acid from a concentrated 10.0 M (C₁) stock solution:

1. Rearrange Formula to Solve for V₁: V₁ = (C₂ × V₂) / C₁ = (1.0 M × 500 mL) / 10.0 M = 50.0 mL.
2. Calculate Solvent (Water) to Add: V_solvent = V₂ - V₁ = 500 mL - 50 mL = 450.0 mL.
3. Dilution Factor (DF): DF = C₁ / C₂ = 10.0 / 1.0 = 10x fold dilution.

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Critical Safety Rule: Always Add Acid to Water

Diluting concentrated strong acids (like sulfuric or hydrochloric acid) releases substantial exothermic heat:

"Do as you oughta, add acid to water."

• Correct Protocol: Measure 400 mL of water into a beaker first. Slowly pour in the 50 mL of acid while stirring. Allow heat to dissipate, then top up to the exact 500 mL mark.
• Dangerous Protocol: Never pour water into concentrated acid—the intense localized heat causes instant boiling, steam pockets, and violent acid splatter.