Calculations Involving Colligative PropertiesCalculations Involving Colligative Properties

ReviewReview

Molarity (M) = moles of solute liter of solution

Dilutions:M1

x V1 = M2

x V2

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:M1

x V1 = M2

x V2

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

ReviewReview

• 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 (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.

XA= nA___ XB= nB___

nA + nB nA + nB

Mole Fraction: the ratio of the moles of the solute to the total number of moles of solvent and solute.

XA= nA___ XB= nB___

nA + nB nA + nB

Freezing-Point Depression & Boiling-Point Elevation

Freezing-Point Depression & Boiling-Point Elevation

Freezing-Point DepressionFreezing-Point Depression

∆Tf = Kf m i• ∆Tf = Freezing Point Depression

– Difference between the freezing point of the solution and the freezing point of pure solvent

• Kf = 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

∆Tf = Kf m i• ∆Tf = Freezing Point Depression

– Difference between the freezing point of the solution and the freezing point of pure solvent

• Kf = 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

•Applications–salting icy roads–making ice cream–antifreeze

• cars (-64°C to 136°C)• fish & insects

Boiling-Point ElevationBoiling-Point Elevation

∆Tb = Kbm i• ∆Tb = Boiling-Point Elevation

– Difference between the boiling point of the solution and the boiling point of pure solvent

• Kb = 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

∆Tb = Kbm i• ∆Tb = Boiling-Point Elevation

– Difference between the boiling point of the solution and the boiling point of pure solvent

• Kb = 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 CalculationsSolution Calculations

• What is the molarity of a 1.11 ppm solution of Zn2+ ions?

•

• What is the molarity of a 1.11 ppm solution of Zn2+ ions?

•

MXg

Znmole

mg

g

liter

Znmg 52

1070.139.65

1*

1000

1*

1

11.1

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 LawRaoult’s Law• Vapor pressure of a solution varies

directly as the mole fraction of solvent

Vapor Pressure Solution =

(mole fractionsolvent)(Vapor Pressuresolvent)

Solid CalculationsSolid Calculations

• Chemical analysis showed 1.23 mg Fe in a 15.67 g sample of soil.• What is the Fe concentration in ppm?

• Chemical analysis showed 1.23 mg Fe in a 15.67 g sample of soil.• What is the Fe concentration in ppm?

ppmmg

g

sampleg

Femg5.7810*

1000

1*

67.15

23.1 6

Unusual concentration unitsUnusual concentration units

• How many nano moles of Cu are present in 12.3 µL of 25 ppm CuSO4?

• How many nano moles of Cu are present in 12.3 µL of 25 ppm CuSO4?

molenmolem

molen

mg

molem

L

mg

L

LL 93.1

1

10*

65.159

1*

25*

10

1*3.12

6

6