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.

Key Concept: 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.