Differentiate between concentration by mass and density Although they can be expressed in the same units, concentration by mass and density represent different concepts: c m V s D = = mass of solute volume of solution d m m V s d D = + = + mass of solute mass of solvent volume of solution Density can be calculated for a pure substance and for a solution. Concentration can only be measured in solutions (two or more substances). 36 3 g of glucose (C6H12O6) is dissolved in 20 mL of alcohol (d = 0.8 g/L). The solution occupies a volume of 21 mL. Calculate the density of the solution and the concentration of glucose in % by mass, g/L and M. Conclusions 1 SOLVED PROBLEM 11 We mix 35 mL of ethanol (C2H5OH, ethyl alcohol) with 15 mL of water. We obtain a solution with a density of 0.89 g/cm3. We know that dethanol = 0.79 g/cm3 and dwater = 1 g/cm3. Calculate the concentration of the solution, expressing it as: a) The percentage by mass of ethanol. b) The percentage by volume of ethanol. c) Grams of ethanol per litre. d) Moles of ethanol per litre. Organise the data in the diagram below: Solution dsolution = 0.89 g/cm3 Solute: water 15 mL, dwater = 1 g/cm3 Solvent: ethanol 35 mL, dethanol = 0.79 g/cm3 The concentration of a solution usually refers to the solute. In this case it is water, so here it refers to the solvent, which is the most important component. a) With the data for density, calculate the mass of each component: mwater 15 1 g 1 g mL mL = ⋅ =15 malcohol mL 10.79 g mL 27.65 g = ⋅ = 35 1 % m m m alcohol alcohol soluti n = ⋅ o 100 % malcohol 27.65 g 27.65 g 15 g 100 64.83 % = + ⋅ = b) The volume that results from mixing the two substances may not match the sum of the volumes. The mass of the mixture does match the sum of the masses. With that data and the density of the solution, calculate the volume: d m v V m d V = → = = + soluti n soluti n soluti n soluti g o o o on ( . ) . 15 27 65 0 89 g cm 47.92 mL 35 mL 3 alcohol alcohol soluti n alcohol = = = ⋅ % % V V V V o 100 47.92 mL ⋅ = 100 73.04 % c) The concentration of ethanol is: C m V ethanol ethanol soluti n 27.65 g 47.92 10 L 577 g/L = = ⋅ = − o 3 d) To calculate the molarity, the amount of ethanol must be calculated. M (C2H5OH) = 12 × 2 + 1.008 × 6 + 16 = 46.05 g/mol 27.65 1 mol of ethanol 46.05 0.6 mol g of ethanol g of ethanol ⋅ = M n V ethanol ethanol solution 0.6 mol 47.92 L = = ⋅ = 103 125 M 27
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