Solutions and Units of Concentration May 21, 2015 REVIEW: Units of Concentration A solution is a homogeneous mixture of one substance dissolved in another substance Concentration is a ratio of the amount of solute to the amount of solvent Molality (m) moles of solute m = kg of solvent Concentration unit based on number of moles of solute per kilogram of solvent. Because both moles and mass do not change with temperature, molality (unlike molarity) is not temperature dependent Concentration of Solutions Molarity (M) moles of solute M = liters of solution Molality (m) moles of solute m = mass of solvent (kg) 12.3 Concentration: Molality Example Calculate the molality of the following solution: 1) What is the molality when 0.75 mole is dissolved in 2.50 L of solvent? m = moles of solute = .75 moles = 0.3m kg solvent 2.50 kg Concentration: Molality Example Calculate the molality of the following solution: 2) Suppose you had 58 grams of NaCl and you dissolved it in exactly 2.00 kg of pure water (the solvent). What would be the molality of the solution? MM NaCl = 58 g/Mole 58 g / 58 g/M = 1 Mole m = moles of solute = 1.0 mole = 0.5 m kg solvent 2.00kg Concentration: Molality Example Calculate the molality of the following solution: 3) What is the molality when 0.5 mol is dissolved in 5.50 L of solvent? (1 L = 1 kg) m = moles of solute = .5 moles = 0.091 m kg solvent 5.50 kg Mole Fraction (X) moles of A XA = total moles in solution Mole fraction is the number of moles of one component divided by the moles of all the components of the solution – Mole fraction is literally a fraction using moles of one component as the numerator and moles of all the components as the denominator Mole Fraction A B A B A A A B A B A B A A Mole Fraction (χ) moles of A A = χ A sum of moles of all components A + B moles of B B = χ B sum of moles of all components A + B Since A + B make up the entire mixture, their mole 1.00 fractions will add up to one. χχA +=B Concentration: Mole Fraction Calculate the mole fraction of the following: 1) A scuba tank is charged with a mixture 3 of 1.0 x 10 mol of oxygen (O2) and 4.5 x 103 mol of helium (He). Determine the mole fraction of each gas in the mixture. 3 XHe = moles of He = 4.5 x 10 mol = 0.82 3 Total moles 5.5 x 10 mol XO2 = 1.00 – 0.82 = 0.18 Mass Percentage mass of A in solution Mass % = 100 total mass of solution × Vol % = Volume of A in solution × 100 total volume of solution Concentration: Mass Percent Example 1: Find the percent by mass in which 41.0 g of NaCl is dissolved in 331 grams of water. 41 g x 100 = 11.0% 372 g Concentration: Volume Percent Example 2: What is the percent by volume concentration of a solution in which 75.0 ml of ethanol is diluted to a volume of 250.0 ml? 75.0 ml x 100 = 30.0% 250.0 ml Parts Per Million (ppm) grams of solute x 106 ppm = grams of solution mg of solute 6 ppm = liters of solution x 10 Parts Per Million is a measure of the concentration of a solution For very dilute solutions, weight/weight (w/w) and weight/volume (w/v)concentrations are sometimes expressed in parts per million Parts per million is abbreviated as ppm Used in environmental issues Concentration: ppm Example Problem 1 You add 11 mg of sulfuric acid to 2,000 grams of water. What is the resulting concentration of sulfuric acid, in ppm? 1000 mg = 1 g Mg to g: 11mg /1000 = 0.011 g gsolution: 0.011 g + 2000g = 2000.011 (.011g / 2000.011 g) x 106 = 5.5 ppm .