Question

You have three solutions, “A”, “B” and “C”. Each must be diluted by the following dilution factors: 4X, 10X and 50X respectively. What would be the final volume of a solution prepared by adding each of the ingredients to 100 mL of solvent?

Answer is supposed to be 158.73mL. I'm confused how to get there. Thank you.

This is all the information that is given unfortunately

Answer 1

The law of equivalence is applied here, taking into account the fact that the product of volume and molarity which gives the no.of moles of the substance is directly measured as concentration in terms of moles per liter.

V₁M₁ = V₂M₂ where V and M are volume in mL and molarity in moles/liter while the suffixes 1 and 2 are before and after dilution respectively.

For 4x dilution, V₂ = 100 + V₁ and M₂ = 0.25M₁. This gives the equation as V₁M₁ = (100+V₁)(0.25M₁), giving V₁M₁ = 25V₁ + 0.25V₁M₁. Since molarity before dilution is a general variable that is constant, the equation reduces to V₁ - 0.25V₁ = 25, giving V₁ = 33.3333mL. So, taking 33.3333mL of a stock solution and adding it to 100mL of solvent will give 133.3333mL of solution with a concentration one-fourth of the stock i.e. 4x diluted solution.

Similarly, for 10x dilution ,we get V₁M₁ = (100+V₁)(0.1M₁), giving V₁M₁ = 10V₁ + 0.1V₁M₁. This then gives V₁ - 0.1V₁ = 10 giving a volume of 11.1111mL of stock, making the diluted solution's final volume to be 111.1111mL.

Following the same method gives for a 50x dilution, a final solution volume of 102.0408mL.

Please note that for no dilution given will the requirement be 58.73mL. In fact, taking 58.73mL of a stock adding it to 100mL of solvent to give a 158.73mL solution will dilute the stock around 2.7 times.