12.4 NOTES Solution Concentration

II. Solution Concentration A. Expressing concentration Many different ways of giving the concentration of a solution: concentration is a measure of solute in a given amount of solvent qualitative - concentrated (large amounts of solute) vs. dilute (small amounts of solute); quantitative – numbers B. Molarity – the most common unit in the lab 1. Determining molarity M = moles solute L of solution

Examples: a. 47.5 grams of NaOH are dissolved in enough water to make 1500 mL of solution. M? 47.5g ( 1 mol NaOH) = 1.19 mol = 0.79 M 40.0 g 1.5 L  

b. 1.78 g CaBr2 are dissolved in 200. mL of solution. Molarity? 1.78g (1 mol CaBr2) = 0.00890 mol = 0.0445 M 200. g 0.200 L

2. Preparing molar solutions to make solution, dissolve solute in volume smaller than desired final volume (b/c solute particles will also take up space) and then add solvent to raise the volume to the desired value; If M = moles solute , then M x L = moles solute, or MV = mol (V is in L) L solution

Examples: a. How many grams of CaBr2 are needed to prepare 2 Examples: a. How many grams of CaBr2 are needed to prepare 2.5 L of a 1.0 M solution? 2.5 L x 1.0 M = 2.5 mol (199.9 g CaBr2) = 500 g 1 mol

b. What mass of NaOH is present in 500. mL of a 0.75 M solution? 0.500 L x 0.75 M = 0.38 mol (40.0 g NaOH) = 15. g 1 mol

c. How many grams of HCl are dissolved in 350. 0 mL of a 2 c. How many grams of HCl are dissolved in 350.0 mL of a 2.0 M solution? 0.3500 L x 2.0 M = 0.70 mol (36.5 g HCl) = 26 g 1 mol

3. Diluting solutions When diluting a solution, the number of moles of solute has not been changed. Therefore, we can use the relationship M1V1 = M2V2. Since volume appears on both sides of the equation, V does not have to be in liters.

Examples: a. What volume of 6. 0 M HCl is needed to make 1 Examples: a. What volume of 6.0 M HCl is needed to make 1.5 liters of 1.0 M solution? (6.0)(V) = (1.5)(1.0) V = 0.25 L  

b. If you dilute 25. 0 mL of 12. 0 M HCl to 500 b. If you dilute 25.0 mL of 12.0 M HCl to 500. mL of solution, what is the new molarity? (25.0)(12.0) = (500.)(M) 0.60 = M

C. Molality The molarity of a solution changes with temperature as the solution expands or contracts. Molality, which is a ratio of moles of solute to grams of solvent, does NOT change with temperature.   Molality (m) = moles of solute kilogram of solvent

Examples: a. What is the molality if 35 Examples: a. What is the molality if 35.6 grams of NaOH is dissolved in 200.0 grams of water? 35.6 g (1 mol NaOH) = 0.890 mol = 4.45 m 40.0 g 0.2000 kg

b. What is molality of a solution if 2 b. What is molality of a solution if 2.3 grams of KNO3 is dissolved in 50.0 grams of water? 2.3 g (1 mol KNO3) = 0.023 mol = 0.46 m 101.1 g 0.050 kg  

D. Mole Fraction Mole fraction is denoted by an X. Xa = moles of a = na Total moles na + nb

Examples: a. What is the mole fraction of CH3OH if 20 Examples: a. What is the mole fraction of CH3OH if 20.0 grams are mixed into 100. grams of water? CH3OH = 20.0/32.0 = 0.625 mol Xmethanol = 0.625 = .101 H2O = 100./18.0 = 5.56 mol 6.19 6.19 mol

b. What is the mole fraction of HCl in an aqueous solution that is 15 b. What is the mole fraction of HCl in an aqueous solution that is 15.0% HCl by mass? 15% by mass = 15% HCl and 85% H2O so… 15.0g HCl/36.5 g HCl/mol = 0.411 mol XHCl = 0.411 = 0.0801 85.0 g H2O/18.0 gH2O/mol = 4.72 mol 5.13 5.13 mol