Calculations Involving Colligative Properties

Review Molarity (M) = moles of solute liter of solution Dilutions: M 1 x V 1 = M 2 x V 2 Percent by volume (%(v/v)) = volume of solute x 100% volume of solution Percent by mass (%(m/m)) = mass of solute x 100% mass of solution Molarity (M) = moles of solute liter of solution Dilutions: M 1 x V 1 = M 2 x V 2 Percent by volume (%(v/v)) = volume of solute x 100% volume of solution Percent by mass (%(m/m)) = mass of solute x 100% mass of solution

Review Colligative Property: A property that depends only upon the solute concentration and not on the solute’s identity. Four Important Colligative Properties of Solutions. –Vapor-pressure lowering –Boiling-point elevation –Freezing-point depression –Vapor Pressure Molarity (M) = moles of solute liter of solution Molality (m) = moles of solute_ kilogram of solvent Molality is the number of moles of solute dissolved in 1 kilogram (1000 g) of solvent. Colligative Property: A property that depends only upon the solute concentration and not on the solute’s identity. Four Important Colligative Properties of Solutions. –Vapor-pressure lowering –Boiling-point elevation –Freezing-point depression –Vapor Pressure Molarity (M) = moles of solute liter of solution Molality (m) = moles of solute_ kilogram of solvent Molality is the number of moles of solute dissolved in 1 kilogram (1000 g) of solvent.

Mole Fraction (another way to express concentration) Mole Fraction: the ratio of the moles of the solute to the total number of moles of solvent and solute. X A = n A ___X B = n B ___ n A + n B Mole Fraction: the ratio of the moles of the solute to the total number of moles of solvent and solute. X A = n A ___X B = n B ___ n A + n B

Freezing-Point Depression & Boiling- Point Elevation

Freezing-Point Depression ∆T f = K f m i ∆T f = Freezing Point Depression –Difference between the freezing point of the solution and the freezing point of pure solvent K f = Molal Freezing Point Depression Constant –Equals to the change in freezing point for a 1-molal solution of a nonvolatile molecule solid –Values are listed in a table –Depends upon the solvent –Units (°C/m) m = Molal Concentration i = Number of Ions from each formula unit ∆T f = K f m i ∆T f = Freezing Point Depression –Difference between the freezing point of the solution and the freezing point of pure solvent K f = Molal Freezing Point Depression Constant –Equals to the change in freezing point for a 1-molal solution of a nonvolatile molecule solid –Values are listed in a table –Depends upon the solvent –Units (°C/m) m = Molal Concentration i = Number of Ions from each formula unit

Freezing Point Depression

Applications –salting icy roads –making ice cream –antifreeze cars (-64°C to 136°C) fish & insects

Boiling-Point Elevation ∆T b = K b m i ∆T b = Boiling-Point Elevation –Difference between the boiling point of the solution and the boiling point of pure solvent K b = Molal Boiling Point Elevation Constant –Equals to the change in boiling point for a 1-molal solution of a nonvolatile molecule solid –Values are listed in a table –Depends upon the solvent –Units (°C/m) m = Molal Concentration i = Number of Ions from each formula unit ∆T b = K b m i ∆T b = Boiling-Point Elevation –Difference between the boiling point of the solution and the boiling point of pure solvent K b = Molal Boiling Point Elevation Constant –Equals to the change in boiling point for a 1-molal solution of a nonvolatile molecule solid –Values are listed in a table –Depends upon the solvent –Units (°C/m) m = Molal Concentration i = Number of Ions from each formula unit

Solution Calculations What is the molarity of a 1.11 ppm solution of Zn 2+ ions? What is the molarity of a 1.11 ppm solution of Zn 2+ ions?

How Vapor Pressure Depression Occurs Solute particles take up space in a solution. Solute particles on surface decrease # of solvent particles on the surface. Less solvent particles can evaporate which lowers the vapor pressure of a liquid.

Vapor Pressures of Pure Water and a Water Solution The vapor pressure of water over pure water is greater than the vapor pressure of water over an aqueous solution containing a nonvolatile solute. Solute particles take up surface area and lower the vapor pressure

Raoult’s Law Vapor pressure of a solution varies directly as the mole fraction of solvent Vapor Pressure Solution = (mole fraction solvent )(Vapor Pressure solvent )

Solid Calculations Chemical analysis showed 1.23 mg Fe in a g sample of soil. What is the Fe concentration in ppm? Chemical analysis showed 1.23 mg Fe in a g sample of soil. What is the Fe concentration in ppm?

Unusual concentration units How many nano moles of Cu are present in 12.3 µL of 25 ppm CuSO 4 ?