Zumdahl s chapter 11
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Solutions. Zumdahl’s Chapter 11. Chapter Contents. Solution Composition Concentrations H solution Hess’s Law undersea Solubilities Henry’s Law: Gases and Raoult’s Law Temperature Effects. Colligative Properties T BP Elevation T FP Depression Osmotic Pressure van’t Hoff Factor

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Zumdahl’s Chapter 11

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Zumdahl s chapter 11


Zumdahl’s Chapter 11

Chapter contents

Chapter Contents

  • Solution Composition

    • Concentrations

  • Hsolution

    • Hess’s Law undersea

  • Solubilities

    • Henry’s Law: Gases

      • and Raoult’s Law

    • Temperature Effects

  • Colligative Properties

    • TBP Elevation

    • TFP Depression

    • Osmotic Pressure

  • van’t Hoff Factor

  • Colloids and Emulsions

Solution composition

Solution Composition

  • Molarity (M) = moles solute / liter sol’n.

    • If volumes don’t add, masses and moles do!

  • Molality (m) = moles solute / kg solvent

    • Not useful in titration unless density known.

    • Useful in colligative effects.

  • Mole fraction (XA)= moles A / total moles

  • Normality (N) – equivalents per liter of solution

Various methods for describing solution composition

Various Methods for Describing Solution Composition

  • A solution is prepared by mixing 1.00 g of ethanol with 100.0 g of water to give a final volume of 101 ml. Calculate the molarity, mass percent, mole fraction, & molality of ethanol in this solution.

Calculating various methods of solution composition from the molarity

Calculating various methods of solution composition from the molarity

  • The electrolyte in automobile lead storage batteries is a 3.75 M sulfuric acid solution that has a density of 1.230 g/ml. Calculate the mass percent, molality, & normality of the sulfuric acid.

Conceptual mixing enthalpies

  • Expand both solvent and solute

    at the expense of H1 and H2

    in lost intermolecular


Conceptual Mixing Enthalpies

  • Merge the

    expanded liquids

    together recovering

    H3 from the

    new interactions.

But even if it

requires heat,

mixing may

well happen

since entropy

favors it!

3. If the exothermic

mixing exceeds

the endothermic

expansion, there

will be a net exo-

thermic heat of

solution. If not it is an

endothermic process.



  • “Like dissolves like”

    • Polar substances dissolve polar substances

    • Nonpolar dissolves nonpolar.

    • The process of a nonpolar substance (ex. Oil) being dissolves in a polar substance (ex. Water) is very endothermic it doesn’t happen.

Differentiating solvent properties

Differentiating Solvent Properties

  • Decide whether liquid hexane (C6H14) or liquid methanol (CH3OH) is the more appropriate solvent for the substances grease (C20H42) and potassium iodide.

Factors affecting gas solubilities

Factors Affecting - Gas Solubilities

  • No doubt about it: pressure influences solubility. And directly.

    • CO2 in soft drinks splatter you with dissolution as you release the pressure above the liquid.

  • Henry’s Law codifies the relationship:

  • C =kH•P (kH is Henry’s constant)

    • It applies only at low concentrations; so

    • It applies not at all to strongly soluble gases!

  • Calculations using henry s law

    Calculations Using Henry’s Law

    • A certain soft drink is bottled so that a bottle at 250C contains CO2 gas at a pressure of 5.0 atm over the liquid. Assuming that the partial pressure of CO2 in the atmosphere is 4.0 x 10-4 atm, calculate the equilibrium concentrations of CO2 in the soda both before & after opening. The Henry’s law constant for CO2 in aqueous solution is 3.1 x 10-2 mol/L * atm at 250C.

    Raoult s and henry s laws









    Psolution = Psolvent° solvent

    Raoult’s and Henry’s Laws

    • Raoult’s Law – shows the relationship between the vapor pressure of a solvent to the mole fraction of the solvent

    • The solute particles interfere with the solvent particles leaving the solution

    Calculating vapor pressure

    Calculating Vapor Pressure

    • Calculate the expected vapor pressure at 250C for a solution prepared by dissolving 158.0 g common table sugar (sucrose, molar mass = 342.3 g/mol) in 643.5 cm3 of water. At 250C, the density of water is 0.9971 g/cm3 and the vapor pressure is 23.76 torr.

    Calculating vapor pressure of a solution containing ionic solute

    Calculating Vapor Pressure of a solution containing ionic solute

    • Predict the vapor pressure of a solution prepared by mixing 35.0 g of solid sodium sulfate (molar mass = 142.05 g/mol) with 175 g of water at 250C. The vapor pressure of pure water at 250C is 23.76 torr.

    Vapor pressure of nonideal solutions

    Vapor Pressure of Nonideal Solutions

    • For liquid-liquid solutions where both components are volatile, a modified form of Raoult’s Law is used

    Calculating vapor pressure of a solution containing two liquids

    Calculating Vapor Pressure of a Solution Containing Two Liquids

    • A solution is prepared by mixing 5.81 g acetone (C3H6O molar mass = 58.1 g/mol) and 11.9 g chloroform (HCCl3 molar mass = 119.4 g/mol). At 350C, this solution has a total vapor pressure of 260. torr. Is this an ideal solution? The vapor pressure of pure acetone and pure chloroform at 350C are 345 & 293 torr, respectively.

    Solubility and temperature

    Solubility and Temperature

    • Sometimes the intermolecular interactions are so much weaker than intramolecular forces holding the molecules together that 2 substances won’t mix even though entropy favors it.

      • Since T favors entropy for most solids & liquids, some of the immiscible solutions mix at higher T.

    • Solidsolubilities normally rise with T.

      • Exceptions are known … like alkali sulfates.

    Gases flee hot solutions

    Gases Flee Hot Solutions

    • You boiled lab water to drive out its dissolved gases, especially CO2.

      • That’s why boiled water tastes “flat.”

        • Genghis Khan invented tea (cha) to flavor the water his warriors refused to boil for their health as they conquered Asia and Eastern Europe.

    • Increased T expands Vgas, making it more favored by entropy vs. dissolved gas.

      • This time, no exceptions!

    Changed phase changes



    Changed Phase Changes

    • The Phase Diagram

      • Mixing in a solute lowers solvent Pvapor

        • So TBP must rise.

      • Since the solvent’s solid suffers no Pvapor change, TFP must fall.

    • Liquid span must increase in solution.

    Boiling point elevation freezing point depression

    Boiling point elevation & Freezing point depression

    • Both colligative properties arise from the same source: Raoult’s Law.

      • Freezing Point Depression:

        • TFP = Kf msolute

          • TFP – freezing point depression

          • Kf - freezing point depression constant

          • msolute - molality of the solute

        • Boiling Point Elevation:

        • TBP = Kb msolute

    Calculating the molar mass by boiling point elevation

    Calculating the Molar Mass by Boiling-Point Elevation

    • A solution is prepared by dissolving 18.00 g of glucose in 150.0 g of water. The resulting solution was found to have a boiling point of 100.340C. Calculate the molar mass of glucose.

    Calculating the molar mass by freezing point depression

    Calculating the Molar Mass by Freezing-Point Depression

    • A chemist is trying to identify a human hormone, which controls metabolism, by determining its molar mass. A sample weighing 0.546 g was dissolved in 15.0 g of benzene, & the freezing-point depression was determined to be 0.2400C. Calculate the molar mass of the hormone. Kf for benzene is 5.120C

    Practical phase changes

    Practical Phase Changes

    • Antifreeze / Summer Coolant are the same

      • Ethylene glycol (1,2-Ethanediol) is soluble in the radiator water, non-corrosive, nonscaling, and raises the boiling point in summer heat while lower-ing freezing point in winter.

    • “Road salt” is MgCl2 now since NaCl corrodes cars.

    Col liga tive utility

    Colligative Utility

    • Ligare means “to bind.” These features are bound up with just numbers of moles.

      • NOT the identity of the molecules!

  • Indeed, Kf and Kb are seen not to depend on solute properties but on solvent ones.

    • So they’re used to count solute moles to convert weights to molar weights!

      • Not sensitive enough for proteins, MW~10 kg

  • Osmotic pressure

    Osmotic Pressure

    • To count protein moles, we need Osmotic Pressure that is very sensitive to [solute].

      • Solvent will diffuse across a membrane to dilute a concentrated solute solution.

      • If the solute is too large (protein) to diffuse back, the volume must increase.

      • Rising solution creates (osmotic) pressure to an equilibrium against further diffusion.

      • Thermodynamic derivation of the balance between  & diffusion on the equilibrium gives: V = nRT (!) or

      •  = MRT

    Determining molar mass from osmotic pressure

    Determining Molar Mass from Osmotic Pressure

    • To determine the molar mass of a certain protein, 1.00 x 10-3 g of it was dissolved in enough water to make 1.00 ml of solution. The osmotic pressure of this solution was found to be 1.12 torr at 250 C. Calculate the molar mass of the protein.

    Isotonic solutions

    Isotonic Solutions

    • What concentration of sodium chloride in water is needed to produce an aqueous solution isotonic with blood ( = 7.70 atm at 250 C)?

    Moles of what

    Moles of What?

    • The identity of the solute doesn’t matter only the number of solute particles present.

    • Count moles of ions if solute dissociates.

    • van’t Hoff Factor, i, measures ionization.

      • i multiplies molality in any of the colligative expressions to show apparent moles present.

      • Using the van’t Hoff factor our equation for freezing or boiling point becomes

      • T = imK

    Weak electrolyte corrections

    Weak Electrolyte Corrections

    • So in 0.001m K3PO4 , i should be nearly 4, and colligative properties see 0.004m?

    • PO43– is a conjugate base of HPO42–

      • Ka3 = 4.810–13 so Kb1 = Kw/Ka3 = 0.021 for PO43– + H2O  HPO42– + OH–

      • Equilibrium lies to left, so start with [OH–] = [HPO42–] = 0.001–x and [PO43–] = x

      • (0.001–x)2 / x = 0.021 or x ~ 4.810–5 ~ 0

      • Counting K+, total moles ~ 0.003+2(0.001)

      • So i ~ 0.005/0.001 = 5 not 4. (4.95 with care)

    Osmotic pressure using the van t hoff factor

    Osmotic Pressure Using the van’t Hoff Factor

    The observed osmotic pressure for a 0.10 M solution of Fe(NH4)2(SO4)2 at 25.00C is 18.0 atm. Compare the expected & experimental values for i.

    Reverse osmosis

    Reverse Osmosis

    • If dilution across a semipermeable (keeps out solute) membrane builds pressure,

  • Pressure should be able to squeeze water back out of a solution! …if the membrane survives.

  • Desalination plants are critical in desert nations like the Gulf States & N. Africa.

    • Waste water is much more (salt) concentrated, an environmental hazard to local sea life unless ocean currents are swift enough to dilute it.

  • When is a solution not a solution

    When is a SolutionNot a Solution?

    • When it’s a problem?

  • Insoluble materials precipitate out of a solution at a rate that increases with their mass. So small particles stay suspended.

  • With particle sizes of 1 m to 1 nm such suspensions are called colloids.

    • Since visible ~ 0.5 m, the larger colloids scatter visible light efficiently! (Tyndall effect)

  • Taxonomy of suspensions

    Taxonomy of Suspensions

    Dispersed Material Phase

    Dispersing Medium Phase

    Aqueous colloids










    Aqueous Colloids

    • Particles might be charged and stabilized (kept from coagulating) by electrostatics.

      • Even neutral ones will favor adjacency of one charge which develops double layer (an oppositely charged ionic shell) to stabilize the colloid.

      • “Salting out” destroys the colloid by over-whelming the repulsions with ionic strength.

        • Small, highly charged ions work best, of course.

    Surface chemistry liquids

    Surface Chemistry (liquids)

    • Colloid study, a subset of surface science.

    • Colloid molecules must be insoluble in the dispersing medium.

      • Solubility governed by “like dissolves like.”

      • But surface tensions play a role as well since solutes display surface excess concentration.

        • Interfaces between phases are not simply at the bulk concentrations; influences segregation.

    Surface chemistry solids

    Surface Chemistry (solids)

    • Industrial catalysts for many processes are solids.

      • Atoms and molecules adhere, dissociate, migrate, reassociate, and desorb.

      • Efficiency scales with catalyst surface area.

      • Area measured by adsorbing monolayers of gas (N2 ) and observing discontinuities as monolayer is covered.

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