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Concentration and Dilution

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    Learning Objectives:

    • Covert between different types of concentration units. Below are the ones that are most important in this course.
      • Concentration based on moles

        \[Molarity\: (M) = \dfrac{moles\: solute}{L\: solution}\nonumber\]

      • Concentration based on mass (expressed for aqueous solutions)

    \[mass\: \% =\dfrac{component\: mass}{total\: mass} \times 100 \%\nonumber\]

    \[parts\: per\: million\: (ppm) =\dfrac{component\: mass}{total\: mass}\times 10^6 = \dfrac{\mu g}{mL}=\dfrac{mg}{L}\nonumber\]

    \[parts\: per\: billion\: (ppb) =\dfrac{component\: mass}{total\: mass}\times 10^9 = \dfrac{ng}{mL}=\dfrac{\mu g}{L}\nonumber\]

    • Calculate the final concentration of a solution following dilution(s).


      Note: Any concentration and volume units can be used in the above equation, as long as it is consistent on both sides.

    • Determine the original amount of an analyte in a sample following quantitative sample preparation.
    1. Hydrogen peroxide (H2O2) is sold in an aqueous solution that is 30.0% by weight. The solution has a density of 1.11 g/mL. What is the concentration of H2O2 in molarity?






    1. The maximum level of copper in drinking water allowed by the EPA is 1.3 ppm. What is this concentration in molarity?





    1. Cobalt (II) chloride is commonly sold as a hexahydrate salt, CoCl2·6H2O. How many grams should be used to prepare 250 mL of 6.00 mM Co2+? What is the molarity of Cl- in the resulting solution?






    1. You wish to prepare 100.0 mL of a 3.00 ppm Li+ solution. How many μL of a 500 ppm stock solution should you use? (1000 μL = 1 mL)





    1. A sample of ocean water is analyzed for Sr2+ by combining 25.0 mL of the sample with 75.0 mL of water. The diluted solution was found to have 2.36 ppm Sr2+. What is was the concentration (in ppm) of Sr2+ in the original sample?






    1. You carried out the following procedure to prepare a vitamin tablet for analysis of iron. The final solution had an iron concentration of 44 μM. Find the mg iron in the original tablet. Iron has an atomic weight of 55.845 g/mol.
      1. The tablet was first dissolved in 6 M HCl, then diluted to volume in a 100-mL volumetric flask with distilled water.
      2. 2.00 mL of this solution was transferred to a new 100-mL volumetric flask and diluted to volume.
      3. Then 10.00 mL of this solution was diluted to volume in a 50-mL volumetric flask. This solution was analyzed for iron.






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