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Dilution of Solutions Calculations (M1V1=M2V2)

Key Concepts

  • The concentration of a solution is usually given in moles per litre (mol L-1 OR mol/L).
        This is also known as molarity.

  • Concentration, or Molarity, is given the symbol M.
        A short way to write that the concentration of a solution of hydrochloric acid is 0.01 mol/L is to write [HCl]=0.01M
        The square brackets around the substance indicate concentration.

  • The solute is the substance which dissolves.

  • The solvent is the liquid which does the dissolving.

  • A solution is prepared by dissolving a solute in a solvent.

  • When a solution is diluted, more solvent is added to it.
        Since M = n ÷ V, and n (the moles of solute) is the same for the original solution and the new diluted solution, it follows that M1V1 = M2V2
        where M1=original concentration of solution
                V1=original volume of solution
                M2=new concentration of solution after dilution
                V2=new volume of solution after dilution

  • To calculate the new concentration (M2) of a solution given its new volume (V2) and its original concentration (M1) and original volume (V1):
        M2 = (M1 x V1) ÷ V2

  • To calculate the new volume (V2) of a solution given its new concentration (M2) and its original concentration (M1) and original volume (V1):
        V2 = (M1 x V1) ÷ M2

Examples

1. M2=(M1V1) ÷ V2

Calculate the new concentration (molarity) if enough water is added to 100mL of 0.25M sodium chloride to make up 1.5L.

  • M2=(M1V1) ÷ V2

  • M1 = 0.25M

  • V1 = 100mL = 100 ÷ 1000 = 0.100L (volume must be in litres)

  • V2 = 1.5L

  • [NaCl(aq)]new = M2 = (0.25 x 0.100) ÷ 1.5 = 0.017M
        (or 0.0.017 mol/L or 0.0.17mol L-1)

2. V2=(M1V1) ÷ M2

Calculate the volume to which 500mL of 0.02M coppper sulfate solution must be diluted to make a new concentration of 0.001M.

  • V2=(M1V1) ÷ M2

  • M1 = 0.02M

  • V1 = 500mL = 500 ÷ 1000 = 500 x 10-3L = 0.500L (since there are 1000mL in 1L)

  • M2 = 0.001M

  • V(CuSO4)new = V2 = (0.02 x 0.500) ÷ 0.001 = 10.00L
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Practice

To calculate the new concentration of solution after dilution, enter the original concentration and volume of the solution, and the final volume after dilution, then click the Calculate button. The answer will appear in the bottom textboxes.
Enter original concentration: mol/L
Enter original volume: L
Enter final volume: L
Click Calculate:
Calculation :
New concentration = M
To start again, click Reset:
 

Related AUS-e-TUTE Topics

Interactive Periodic Table

Molecular Mass (Formula Weight)

Calculating Percentage (Percent) Composition

Definitions of a Mole

Mass-Mole Calculations

Molarity of Solutions

Limiting Reagents and Reactants in Excess

 

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