Dilution

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Core Concept

Dilution is the process of reducing the concentration of a solution by adding more solvent. Dilutions are common in laboratory settings to prepare solutions of precise concentrations.

Practice Tips

  • Use Proper Glassware: A volumetric flask provides the most accurate measurement for final volume ($V_2$​).

  • Read the Meniscus at Eye Level: To avoid measurement errors, ensure the meniscus is aligned with the calibration line on the volumetric flask.

  • Use a Pipette for Small Volumes: For small volumes of stock solution ($V_1$​), use a pipette for accuracy.

  • Mix Thoroughly: After adding the solvent, invert or shake the flask to ensure the solution is evenly mixed.

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Dilution Formula

The relationship between the concentrations and volumes of the original (concentrated) solution and the final (diluted) solution is given by:

$M_1 V_1 = M_2 V_2$

Where:

  • $M_1$​ = Initial (starting) molarity (concentration) of the solution

  • $V_1$​ = Initial volume of the solution

  • $M_2$​ = Final molarity (concentration) of the solution

  • $V_2$​ = Final volume of the solution after dilution

This formula allows you to calculate any one of the variables if the others are known.

Steps for Performing a Dilution

  1. Calculate the Volume of Stock Solution Needed:

    • Use the dilution formula $M_1 V_1 = M_2 V_2$​ to find $V_1$​, the volume of concentrated solution needed.

    • Rearrange to solve for $V_1$​: $V_1 = \frac{M_2 V_2}{M_1}$ ​​

  2. Measure the Volume of Concentrated Solution (Stock Solution):

    • Use a graduated cylinder or pipette to measure $V_1$​ accurately.

  3. Add the Stock Solution to a Volumetric Flask:

    • Pour the measured volume of concentrated solution into a volumetric flask of volume $V_2$​.

  4. Dilute to the Mark with Solvent:

    • Add distilled water (or another appropriate solvent) to the volumetric flask until the solution reaches the calibration mark at the $V_2$​ level.

    • The bottom of the meniscus should be level with the calibration line.

  5. Mix the Solution Thoroughly:

    • Cap the flask and invert it several times to ensure the solution is homogeneous.

Example Problem: Preparing a Diluted Solution

Problem: You have a 2.0 M stock solution of HCl. How would you prepare 500 mL of a 0.5 M HCl solution?

Solution:

  1. Identify Given Values:

    • $M_1$ = 2.0 M

    • $M_2$ = 0.5 M

    • $V_2$ = 500 mL = 0.500 L

  2. Calculate $V_1$​:

    $V_1 = \frac{M_2 V_2}{M_1} = \frac{(0.5 \, \text{M})(0.500 \, \text{L})}{2.0 \, \text{M}} = 0.125 \, \text{L} = 125 \, \text{mL}$

  3. Procedure:

    • Measure 125 mL of the 2.0 M HCl solution.

    • Transfer it to a 500 mL volumetric flask.

    • Add distilled water to reach the 500 mL mark.

    • Invert to mix thoroughly.

Answer: You need 125 mL of the 2.0 M HCl solution, diluted to 500 mL with water, to make a 0.5 M HCl solution.

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