Question

When calculating the concentration of a diluted solution, a person can use the dilution equation: Mc Vc = Md Vd

Why does Mc Vc equal Md Vd ? What is this mathematical statement saying? Why would losing some concentrated solution from the pipet during the preparation stage ruin this equation? Explain in detail.

Answer 1

Ans.

            Mc = Molarity of concentrated solution

            Vc = Volume of concentrated solution

            Md = Molarity of diluted solution

            Vd = Volume of diluted solution

#A. “ Mc Vc = Md Vd” means that ‘the number of moles of solute (and similarly, mass and number of solute particles) remains equal between a concentrated solution and its diluted solution’.

# Consider the example-

            I. Concentration solution: 1.0 L of 10.0 M HCl

                        No. of moles of conc. solution = Molarity x Volume in liters

                                                            = 10.0 M x 1.0 L =10.0 moles

            II. Let mix the above concentrated solution (1.0 L) with 1.0 L of distilled water. It would serve as the diluted solution.

            Total volume of diluted solution = 1.0 L + 1.0 L = 2.0 L

Using C1V1 (concentrated solution) = C2V2 (diluted solution)

            Or, C2 = (10.0 M x 1.0 L) / 2.0 L = 5.0 M

Hence, [HCl] in the diluted solution = 5.0 M

# Now, No. of moles of diluted solution = Molarity x Volume in liters

                                                            = 15.0 M x 2.0 L =10.0 moles

# Conclusion:

Moles of solute in conc. solution = Moles of solute in diluted solution

Note that through dilution reduces the concentration of solute in the diluted solution, the number of moles of solute in both the solutions remains the same.

#B. If some volume of concentrated solution is lost during pipetting, then some moles of solutes being taken in the form of concentrated solution would also be lost. That is the actual number of moles taken in form of concentrated solution would be lesser than the expected moles. So, the resultant diluted solution would also have fewer moles of solute than the expected moles- and the loss is unaccounted.

Therefore, we can’t rely upon the expected molarity of diluted solution. So, the loss of some volume of the concentrated solution would ruin the preparation of the diluted solution.