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In this article, we shall study numerical problems to calculate molality of a solution. Example – 01: 7.45 g of potassium chloride (KCl) was dissolved in 100 g of water. Calculate the molality of the solution. Given: mass of solute (KCl) = 7.45 g, mass of solvent (water) = 100 g = 0.1 kg To Find: Molarity of solution =? Solution: Molecular mass of KCl = 39 g x 1 + 35.5 g x 1 = 74.5 g mol-1 Number of moles of solute (KCl) = given mass/ molecular mass Number of moles of solute (KCl) = 7.45 g/ 74.5 g mol-1 = 0.1 mol Molality = Number of moles of solute/Mass of solvent in kg Molality = 0.1 mol /0.1 kg = 1 mol kg-1 Ans: The molality of solution is 1 mol kg-1 or 1 m. Example – 02: 11.11 g of urea (NH2CONH2) was dissolved in 100 g of water. Calculate the molarity and molality of the solution. Given N = 14, H = 1, C = 12, O = 16. Given: mass of solute (urea) = 11.11 g, mass of solvent (water) = 100 g = 0.1 kg To Find: Molarity of solution =? Solution: Molecular mass of urea (NH2CONH2) = 14 g x 2 + 1 g x 4 + 12 g x 1 + 16 g x 1 Molecular mass of urea (NH2CONH2) = 60 g mol-1 Number of moles of solute (urea) = given mass/ molecular mass Number of moles of solute (urea) = 11.11 g/ 60 g mol-1 = 0.1852 mol Volume of water = mass of water/ density = 100 g/1 g mL-1 = 100 mL = 0.1 L Molarity = Number of moles of solute/Volume of solution in L Molarity = 0.1852 mol /0.1 L = 1.852 mol L-1 or 1.852 mol dm-3 Molality = Number of moles of solute/Mass of solvent in kg Molality = 0.1852 mol /0.1 kg = 1.852 mol kg-1 Ans: The molarity of solution is 1.852 mol L-1 and the molality is 1.852 mol kg-1 Example – 03: 34.2 g of sugar was dissolved in water to produce 214.2 g of sugar syrup. Calculate molality and mole fraction of sugar in the syrup. Given C = 12, H = 1 and O = 16. Given: Mass of solute (sugar) = 34.2 g, Mass of solution (sugar syrup) = 214.2 g To Find: Molality and mole fraction =? Solution: Mass of Solution = Mass of solute + mass of solvent Mass of solvent = mass of solution – mass of solute = 214.2 g – 34.2 g = 180 g = 0.180 kg Molar mass of sugar (C12H22O11) = 12 g x 12 + 1 g x 22 + 16 g x 11 = 342 g mol-1 Number of moles of solute (sugar) = nB = Given mass/ molecular mass = 34.2 g/342 g mol-1 = 0.1 mol Molality = Number of moles of solute/Mass of solvent in kg Molality = 0.1 mol /0.180 kg = 0.5556 mol kg-1 Molar mass of water (H2O) = 1 g x 2 + 16 g x 1 = 18 g mol-1 Number of moles of solvent (water) = nA = Given mass/ molecular mass = 180 g/18 g mol-1 = 10 mol Total number of moles = nA + nB = 0.1 + 10 = 10.1 mol Mole fraction of solute (sugarl) = xB = nB/(nA + nB) = 0.1/10.1 = 0.0099 Mole fraction of sugar = 0.0099 Ans: Molality of solution = 0.5556 mol kg-1 and mole fraction of sugar = 0.0099 Example – 04: 10.0 g KCl is dissolved in 1000 g of water. If the density of the solution is 0.997 g cm-3, calculate a) molarity and b) molality of the solution. Atomic masses K = 39 g mol-1, Cl = 35.5 g mol-1. Given: the mass of solute (KCl) = 10 g, the mass of solvent (water) = 1000 g = 1 kg, density of solution = 0.997 g cm-3, To Find: molarity =? molality = ? Solution: Molecular mass of KCl = 39 g x 1 + 35.5 g x 1 = 74.5 g mol-1 Number of moles of solute (KCl) = given mass/ molecular mass Number of moles of solute (KCl) = 10 g/ 74.5 g mol-1 = 0.1342 mol Molality = Number of moles of solute/Mass of solvent in kg Molality = 0.1342 mol /1 kg = 0.1342 mol kg-1 Mass of solution = 10 g + 1000 g = 1010 g Volume of solution = mass of solution/density = 1010/0.997 g cm-3 Volume of solution = 1013 cm3 = 1013 mL = 1.013 L Molarity = Number of moles of solute/Volume of solution in L Molarity = 0.1342 mol /1.013 L = 0.1325 mol L-1 Ans: The molarity of the solution is 0.1325 mol L-1 or 0.1325 M, the molality of the solution is 0.1342 mol kg-1 or 0.1342 m. Example – 05: Calculate molarity and molality of the sulphuric acid solution of density 1.198 g cm-3 containing 27 % by mass of sulphuric acid. Given: density of the solution = 1.198 g cm-3, % mass of sulphuric acid = 27%, To Find: Molarity =? and molality =? Solution: Consider 100 g of solution Mass of H2SO4 = 27 g and mass of H2O = 100 – 27 g = 73 g = 0.073 kg Molecular mass H2SO4 = 1 g x 2 + 32 g x 1 + 16g x 4 = 98 g mol-1 Number of moles of H2SO4 = nB = 27 g/ 98 g = 0.2755 mol Density of solution = 1.198 g cm-3 Volume of solution = Mass of solution / density = 100 g /1.198 g cm-3 = 83.47 cm3 = 83.47 mL = 0.08347 L Molarity of solution = Number of moles of the solute/volume of solution in L = 0.2755/0.08347 = 3.301 M Molality = Number of moles of solute/mass of sovent in kg Molality = 0.2755 mol /0.073 kg = 3.774 mol L-1 Ans: The molarity of solution is 3.374 mol L-1 or 3.374 M, the molality of solution is 3.774 mol L-1 or 3.774 m Example – 06: Calculate the mole fraction, molality and molarity of HNO3 in a solution containing 12.2 % HNO3. Given density of HNO3 as 1.038 g cm-3, H = 1, N = 14, O = 16. Given: density of the solution = 1.038 g cm-3, % mass of HNO3 = 12.2 %, To Find: mole fraction =? molarity =? and molality =? Solution: Consider 100 g of solution Mass of HNO3 = 12.2 g and mass of H2O = 100 – 12.2 g = 87.8 g = 0.0878 kg Molecular mass of water (H2O) = 1 g x 2 + 16 g x 1 = 18 g mol-1 Molecular mass HNO3 = 1 g x 1 + 14 g x 1 + 16g x 3 = 63 g mol-1 Number of moles of water = nA = 87.8 g/ 18 g = 4.8778 mol Number of moles of HNO3 = nB = 12.2 g/ 63 g = 0.1937 mol Total number of moles = nA + nB + nC = 4.8778 + 0.1937 = 5.0715 Mole fraction of HNO3 = xB = nB/(nA +nB) = 0.1937/5.0715 = 0.0382 Density of solution = 1.038 g cm-3 Volume of solution = Mass of solution / density = 100 g /1.038 g cm-3 = 96.34 cm3 = 96.34 mL = 0.09634 L Molarity of solution = Number of moles of the solute/volume of solution in L = 0.1937/0.09634 =2.011 M Molality = Number of moles of solute/mass of sovent in kg Molality = 0.1937 mol /0.0878 kg = 2.206 mol kg-1 Ans: The mole fraction of HNO3 is 0. 0382, the molarity of solution is 2.011 mol L-1 or 2.011 M, the molality of solution is 2.206 mol kg-1 or 2.206 m Example – 07: Calculate molarity and molality of 6.3 % solution of nitric acid having density 1.04 g cm-3. Given atomic masses H = 1, N = 14 and O = 16. Given: density of the solution = 1.04 g cm-3, % mass of HNO3 = 6.3 %, To Find: mole fraction =? molarity =? and molality =? Solution: Consider 100 g of solution Mass of HNO3 = 6.3 g and mass of H2O = 100 – 6.3 g = 93.7 g = 0.0937 kg Molecular mass of water (H2O) = 1 g x 2 + 16 g x 1 = 18 g mol-1 Molecular mass HNO3 = 1 g x 1 + 14 g x 1 + 16g x 3 = 63 g mol-1 Number of moles of water = nA = 93.4 g/ 18 g = 5.189 mol Number of moles of HNO3 = nB = 6.3 g/ 63 g = 0.1 mol Density of solution = 1.04 g cm-3 Volume of solution = Mass of solution / density = 100 g /1.04 g cm-3 = 96.15 cm3 = 96.15 mL = 0.09615 L Molarity of solution = Number of moles of the solute/volume of solution in L = 0.1/0.09615 =1.040 M Molality = Number of moles of solute/mass of sovent in kg Molality = 0.1 mol /0.0937 kg = 1.067 mol kg-1 Ans: The molarity of solution is 1.040 mol L-1 or 1.040 M The molality of solution is 1.067 mol kg-1 or 1.067 m Example – 08: An aqueous solution of NaOH is marked 10% (w/w). The density of the solution is 1.070 g cm-3. Calculate molarity, molality and mole fraction of NaOH in water. Given Na = 23, H =1 , O = 16 Given: density of the solution = 1.038 g cm-3, % mass of HNO3 = 12.2 %, To Find: mole fraction =? molarity =? and molality =? Solution: Consider 100 g of solution Mass of NaOH = 10 g and mass of H2O = 100 – 10 g = 90 g = 0.090 kg Molecular mass of water (H2O) = 1 g x 2 + 16 g x 1 = 18 g mol-1 Molecular mass NaOH = 23 g x 1 + 16 g x 1 + 1 g x 1 = 40 g mol-1 Number of moles of water = nA = 90 g/ 18 g = 5 mol Number of moles of NaOH = nB = 10 g/ 40 g = 0.25 mol Total number of moles = nA + nB = 5 + 0.25 = 5.25 mol Mole fraction of NaOH = xB = nB/(nA +nB) = 0.25/5.25 = 0.0476 Density of solution = 1.070 g cm-3 Volume of solution = Mass of solution / density = 100 g /1.070 g cm-3 = 93.46 cm3 = 93.46 mL = 0.09346 L Molarity of solution = Number of moles of the solute/volume of solution in L = 0.25/0.09346 =2.675 M Molality = Number of moles of solute/mass of sovent in kg Molality = 0.25 mol /0.090 kg = 2.778 mol kg-1 Ans: The molarity of solution is 2.675mol L-1 or 2.675 M, the molality of solution is 2.778 mol kg-1 or 2.778 m, the mole fraction of NaOH is 0. 0476 Example – 09: A solution of glucose in water is labelled as 10 % (w/w). Calculate a) molality and b) molarity of the solution. Given the density of the solution is 1.20 g mL-1 and molar mass of glucose is 180 g mol-1. Given: density of the solution = 1.20 g cm-3, % mass of glucose = 10 %, molar mass of glucose is 180 g mol-1. To Find: molarity =? and molality =? Solution: Consider 100 g of solution Mass of glucose = 10 g and mass of H2O = 100 – 10 g = 90 g = 0.090 kg Molecular mass of water (H2O) = 1 g x 2 + 16 g x 1 = 18 g mol-1 Molecular mass glucose = 180 g mol-1 Number of moles of water = nA = 90 g/ 18 g = 5 mol Number of moles of glucose = nB = 10 g/ 180 g = 0.0556 mol Density of solution = 1.20 g cm-3 Volume of solution = Mass of solution / density = 100 g /1.20 g cm-3 = 83.33 cm3 = 83.33 mL = 0.08333 L Molarity of solution = Number of moles of the solute/volume of solution in L = 0.0556/0.08333 =0.6672 M Molality = Number of moles of solute/mass of sovent in kg Molality = 0.0556 mol /0.090 kg = 0.6178 mol kg-1 Ans: The molarity of solution is 0.6672 mol L-1 or 0.6672 M, the molality of solution is 0.6178 mol kg-1 or 0.6178 m, Example – 10: Battery acid 4.22 M aqueous H2SO4 solution, and has density 1.21 g cm-3. What is the molality of H2SO4. Given H = 1, S = 32, O = 16 Given: density of the solution = 1.21 g cm-3, Molarity of solution = 4.22 M. To Find: molality =? Solution: Let us consider 1 L of solution Molecular mass H2SO4 = 1 g x 2 + 32 g x 1 + 16g x 4 = 98 g mol-1 Molarity of solution = Number of moles of the solute/volume of solution in L Number of moles of solute = Molarity of solution x volume of solution in L = 4.22 x 1 = 4.22 Density of solution = 1.21 g cm-3 = 1.21 g/mL = 1.21 x 103 g/L = 1.21 kg/L Mass of solution = Volume of solution x density = 1 L x 1.21 kg/L = 1.21 kg Mass of solute (H2SO4) = Number of moles x molecular mass = 4.22 x 98 Mass of solute (H2SO4) = 413.56 g = 0.41356 kg Mass of solvent = mass of solution – mass of solute = 1.21 – 0.41356 = 0.79644 kg Molality = Number of moles of solute/mass of sovent in kg Molality = 4.22 mol /0.79644 kg = 5.298 mol kg-1 Ans: Molality of solution is 5.298 mol kg-1 or 5.298 m Example – 11: The density of 5.35 M H2SO4 solution is 1.22 g cm-3. What is molality of a solution? Given: density of the solution = 1.22 g cm-3, Molarity of solution = 5.35 M. To Find: molality =? Solution: Let us consider 1 L of solution Molecular mass H2SO4 = 1 g x 2 + 32 g x 1 + 16g x 4 = 98 g mol-1 Molarity of solution = Number of moles of the solute/volume of solution in L Number of moles of solute = Molarity of solution x volume of solution in L = 5.35 x 1 = 5.35 Density of solution = 1.22 g cm-3 = 1.22 g/mL = 1.22 x 103 g/L = 1.22 kg/L Mass of solution = Volume of solution x density = 1 L x 1.22 kg/L = 1.22 kg Mass of solute (H2SO4) = Number of moles x molecular mass = 5.35 x 98 Mass of solute (H2SO4) = 524.3 g = 0.5243 kg Mass of solvent = mass of solution – mass of solute = 1.22 – 0.5243 = 0.6957 kg Molality = Number of moles of solute/mass of sovent in kg Molality = 5.35 mol /0.6957 kg = 7.690 mol kg-1 Ans: Molality of solution is 7.690 mol kg-1 or 7.690 m Example – 12: Calculate the mole fraction of solute in its 2 molal aqueous solution. Given: molality = 2 molal To Find: Mole fraction =? Solution: Molecular mass of water (H2O) = 1 g x 2 + 16 g x 1 = 18 g mol-1 Molality of solution = 2 molal = 2 mol mol kg-1 The number of moles of solute = 2 The mass of solvent (water) = 1 kg = 1000 g Number of moles of solvent (water) = 1000/16 = 55.55 Mole fraction of solute = 2/(2 + 55.55) = 2/57.55 = 0.03475 Ans: Mole fraction of solute is 0.0345 Previous Topic: Numerical Problems on Molarity Next Topic: Short Cut Methods to Calculate Concentration of Solution Science > Chemistry > Solutions and Their Colligative Properties > Numerical Problems on Molality |