**Ch. 14: Solutions** Sec. 14.2: Solution Concentration

**Objectives** • Describe the concentration of solutions using different units. • Determine the concentrations of solutions. • Calculate the molarity of a solution.

**Solution Concentration** • The concentration of a solution is a measure of how much solute is dissolved in a specific amount of solvent or solution. dilute concentrated

**Expressing Concentration** • Qualitative Descriptions • concentrated: a large amount of solute • dilute: a small amount of solute • Quantitative Descriptions • Percent by either mass or volume • Molarity • Molality • Mole Fraction

**Percent by Mass** % by mass = mass of solute x 100 mass of solution Note: mass of solution = mass solute + mass solvent • In order to maintain a sodium chloride (NaCl) concentration similar to ocean water, an aquarium must contain 3.6 g NaCl per 100 g of water. What is the % by mass of NaCl in the solution? • The % by mass of a NaOCl solution is 3.62%. If you have 1500 g of solution, how much NaOCl do you have?

**Percent by Volume** % by volume = volume of solute x 100 volume of solution Note: vol. of solution = vol. solute + vol. solvent • What is the percent by volume of ethanol in a solution that contains 35 mL of ethanol dissolved in 115 mL of water? • If you have 15 mL of 70% isopropyl alcohol solution, how many mLs of alcohol are in the solution?

**Molarity** • Molarity(M) or molar concentration is the number of moles of solute dissolved per liter of solution. M is read as molar. For example, 0.5 M HCl is a 0.5 molar solution of HCl. It contains 0.5 moles of HCl in every liter of solution.

**Molarity** To calculate molarity:

**Molarity Practice Problems** • A 100.5 mL intravenous (IV) solution contains 5.10 g of glucose (C6H12O6). What is the molarity of this solution? The molar mass of glucose is 180 g/mol. • Calculate the molarity of 1.60 L of a solution containing 1.55 g of dissolved KBr. • What is the molarity of an aqueous solution containing 40.0 g of glucose in 1.5 L of solution?

**Preparing Molar Solutions**

**Preparing Molar Solutions** • So, for 1 L of a 1M solution, you would need 1 mole of the salt, or 58.5 g NaCl. • What if you needed 1 L of a 0.3 M solution? M = moles solute or 0.3 M = x moles liters solution 1 L x = 0.3 mol or 17.6 g • What if you only needed 150 mL of the 0.3 M solution? M = moles solute or 0.3 M = x moles liters solution 0.150 L x = 0.045 mol or 2.63 g

**Preparing Molar Solutions** • 1.0 L of a 0.10 M solution of CaCl2 is needed. How many grams of CaCl2 must be added to water to prepare this solution? • How many grams of NaOH are needed to make 250 mL of a 3.0 M NaOH solution? • 500 mL of a 2 M NaOH solution contains how many grams of NaOH?

**Diluting Solutions** • Concentrated solutions called stock solutions are sold for laboratory use. • Stock solutions are then diluted to prepare less concentrated solutions. • When you add solvent to small amounts of concentrated solutions, you increase the number of solvent particles and, thus, decrease the solution’s concentration.

**Diluting Solutions** • Recall: M = moles solute/liters solution • moles solute = M x liters solution • The # of moles of solute does not change during dilution - the # of solvent particles changes. • That means, moles of solute in stock = moles of solute in diluted solution Mstock x volume stock = Mdil x volume of dilute or M1V1 = M2V2

**(12.0 M) V1 = (1.50 M)(5.00 L)** V1 = 0.625 L = 625 mL

**Diluting Sol’ns Practice Problems** • What volume, in milliliters of 2.00 M of calcium chloride (CaCl2) stock solution would you use to make a 0.50 L of 0.300 M calcium chloride solution? • If you dilute 20.0 mL of a 3.5 M solution to make 100 mL of solution, what is the molarity of the dilute solution? • What volume of a 3.00 M KI stock solution would you use to make 0.300 L of a 1.25 M KI solution?

**Molality** • If there is a temperature change, the volume of a solution will change. • If volume changes, the molarity will change. • Therefore, there is a need for an alternative way to express concentration. • Since masses do NOT change with temperature, concentration can be expressed in terms of moles of solute in a mass of solvent.

**Molality** • The molality of a solution, denoted m, is defined as the number of moles of solute dissolved in one kilogram of solvent: • “1 m” is read as a 1 molal solution.

**Molality** • In the lab, a student adds 4.5 g of sodium chloride (NaCl) to 100 g of water. Calculate the molality of the solution. • A solution has naphthalene (C10H8) dissolved in 500 g of toluene. The solution has a molality of 0.468 m. How many grams of naphthalene are in the solution? • What is the molality of a solution containing 10.0 g of Na2SO4 dissolved in 1000 g of water?

**Mole Fraction** • Mole fraction is the ratio of the number of moles of solute (or solvent) in a solution to the total number of moles of solute and solvent. • If X represents mole fraction and A represents the solute & B represents the solvent, XA = nA XB = nB nA+ nB nA+ nB Note: XA + XB = 1 (The sum of all the fractional components equals “the whole.”)

**Mole Fraction** • What is the mole fraction of HCl in a 100 g of an aqueous solution if it contains 37.5 g HCl? What is the mole fraction of water? • What is the mole fraction of NaOH in an aqueous solution that contains 22.8 % NaOH by mass? • Calculate the mole fraction of NaCl in a solution in which 15.7 g NaCl is dissolved in 100.0 g H2O.