Molarity and Mole fraction

Mole Fraction The mole fraction of a component substance A (XA) in a solution is defined as the moles of component substance divided by the total moles of solution (moles of solute plus solvent). XA = (moles of substance A)/(total moles of solution) Example. Calculating the Mole Fractions of Components What are the mole fractions of glucose and water in a solution containing 5.67 g of glucose, C6H12O6, dissolved in 25.2 g of water? Solution Here, 5.67 g of glucose equals 0.0315 mol of glucose. The moles of water in the solution are (25.2 g H2O)(1 mol H2O/18.0 g H2O = 1.40 mol H2O and the total moles of solution are 1.40 mol + 0.0315 mol = 1.432 mol (retain an extra figure in the answer for further computation.) Finally, you get: Mole fraction glucose = 0.0315 mol/1.432 mol = 0.02199 = 0.0220 Mole fraction H2O = 1.40 mol/1.432 mol = 0.978 Check: note that the sum of the mole fractions is 1.000. Calculating Molality What is the molality of a solution that contains 5.67 g of glucose (180.2 g/mol) dissolved in 25.2 g of water? Glucose is C6H1206. Solution. molality = m = mols solute/kg solvent First, calculate mols solute (glucose): mols glucose = (5.67 g)(1 mol glucose/180.2 g) = 0.0315 mol Next, calculate kg solvent: kg solvent = (25.2 g water)(l kg water/1000 g water) = 25.2 x 10-3 kg molality = (0.0315 mol glucose)/( 25.2 x 10-3 kg water) = 1.25 m glucose Example. Converting Molality to Mole Fractions An aqueous solution is 0.120 m in glucose, C6H1206. What are the mole fractions of each component in the solution? Solution A 0.120 m glucose solution contains 0.120 mol of glucose in 1.00 kg of water. The moles of H2O in 1.00 kg of water are (1.00 x 103 g H2O)(1 mol H2O/18.0 g H2O) = 55.6 mol H2O So, mole fraction glucose = (0.120 mol)/(0.120 + 55.6) mol) = 0.00215 and mole fraction water = (55.6 mol)/(0.120 + 55.6) mol) = 0.998 Example. Converting Mole Fractions to Molality A solution is 0.150 mole fraction glucose, C6H1206 and 0.850 mole fraction water. What is the molality of glucose in the solution? Example. Converting Mole Fractions to Molality –Solution Assume exactly 1.000 mol of solution, so one mole of solution contains 0.150 mol of glucose and 0.850 mol of water. The mass of this amount of water is (0.850 mol H2O)(18.0 g H2O/mol H2O) = 15.3 g H2O (or, 0.0153 kg H2O) Therefore, the molality of glucose, C6H1206, in the solution is m = (0.150 mol C6H1206)/( 0.0153 kg H2O) = 9.80 C6H1206 /mol H2O = 9.80 m C6H1206 . Example. Converting Molality to Molarity An aqueous solution is 0.273 m KCl. What is the molar concentration of potassium chloride, KCl? The density of the solution is 1.011 x 103 g/L. Solution. Here, there is 0.273 mol KCl per kg of water. To calculate the molarity, you must first find the volume of solution for a given mass of solvent. Assume an amount of solution containing 1.000 kilogram of water (1.000 x 103 g H2O). The mass of potassium chloride in this quantity of solution is g KCl = (0.273 mol KCl)( 74.6 g KCl /1 mol KCl) = 20.4 g KCl Next, the total mass of the solution equals the mass of water plus the mass of potassium chloride, so g solution = 1.000 x 103 g + 20.4 g = 1.020 x 103 g The volume of solution equals its mass divided by the density of the solution: Volume of solution = (1.020 x 103 g)/(1.011 x 103 g/L = 1.009 L and the molarity (M) of the solution = (0.273 mol KCl)/(1.009 L solution) = 0.271 M KCl Note that the molarity and the molality of this solution are approximately equal. This is generally true when solutions are dilute and their density is about 1 g/mL. Example. Converting Molarity to Molality An aqueous solution is 0.907 M Pb(NO3)2. What is the molality of lead Pb(NO3)2, in this solution? The density of the solution is 1.252 g/mL. Solution. There is 0.907 mol Pb(NO3)2 per liter of solution. Begin by assuming 1 L (= 1.000 x 103 mL) of solution and calculate its mass. You can then calculate the mass of Pb(NO3)2 and then find the mass of water by difference, where mass of solution = density x volume: g solution = (1.252 g/mL)(1.000 x 103 mL) = 1.252 X 103 g The mass of Pb(NO3)2 is g Pb(NO3)2 = (0.907 mol Pb(NO3)2)(331.2 g Pb(NO3)2/mol) = 3.00 X 102 g Pb(NO3)2 The mass of the water in this solution is mass of H2O = mass of solution - mass of Pb(NO3)2 = 1.252 x 103 g - 3.00 x 102 g = 9.52 x 102 g (= 0.952 kg) molality of Pb(NO3)2 = (0.907 mol Pb(NO3)2/0.952 kg H2O) = 0.953 m Pb(NO3)2