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Introductory Chemistry - 1st Canadian Edition: Colligative Properties of Ionic Solutes

Introductory Chemistry - 1st Canadian Edition
Colligative Properties of Ionic Solutes
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table of contents
  1. Cover
  2. Title Page
  3. Copyright
  4. Table Of Contents
  5. Acknowledgments
  6. Dedication
  7. About BCcampus Open Education
  8. Chapter 1. What is Chemistry
    1. Some Basic Definitions
    2. Chemistry as a Science
  9. Chapter 2. Measurements
    1. Expressing Numbers
    2. Significant Figures
    3. Converting Units
    4. Other Units: Temperature and Density
    5. Expressing Units
    6. End-of-Chapter Material
  10. Chapter 3. Atoms, Molecules, and Ions
    1. Acids
    2. Ions and Ionic Compounds
    3. Masses of Atoms and Molecules
    4. Molecules and Chemical Nomenclature
    5. Atomic Theory
    6. End-of-Chapter Material
  11. Chapter 4. Chemical Reactions and Equations
    1. The Chemical Equation
    2. Types of Chemical Reactions: Single- and Double-Displacement Reactions
    3. Ionic Equations: A Closer Look
    4. Composition, Decomposition, and Combustion Reactions
    5. Oxidation-Reduction Reactions
    6. Neutralization Reactions
    7. End-of-Chapter Material
  12. Chapter 5. Stoichiometry and the Mole
    1. Stoichiometry
    2. The Mole
    3. Mole-Mass and Mass-Mass Calculations
    4. Limiting Reagents
    5. The Mole in Chemical Reactions
    6. Yields
    7. End-of-Chapter Material
  13. Chapter 6. Gases
    1. Pressure
    2. Gas Laws
    3. Other Gas Laws
    4. The Ideal Gas Law and Some Applications
    5. Gas Mixtures
    6. Kinetic Molecular Theory of Gases
    7. Molecular Effusion and Diffusion
    8. Real Gases
    9. End-of-Chapter Material
  14. Chapter 7. Energy and Chemistry
    1. Formation Reactions
    2. Energy
    3. Stoichiometry Calculations Using Enthalpy
    4. Enthalpy and Chemical Reactions
    5. Work and Heat
    6. Hess’s Law
    7. End-of-Chapter Material
  15. Chapter 8. Electronic Structure
    1. Light
    2. Quantum Numbers for Electrons
    3. Organization of Electrons in Atoms
    4. Electronic Structure and the Periodic Table
    5. Periodic Trends
    6. End-of-Chapter Material
  16. Chapter 9. Chemical Bonds
    1. Lewis Electron Dot Diagrams
    2. Electron Transfer: Ionic Bonds
    3. Covalent Bonds
    4. Other Aspects of Covalent Bonds
    5. Violations of the Octet Rule
    6. Molecular Shapes and Polarity
    7. Valence Bond Theory and Hybrid Orbitals
    8. Molecular Orbitals
    9. End-of-Chapter Material
  17. Chapter 10. Solids and Liquids
    1. Properties of Liquids
    2. Solids
    3. Phase Transitions: Melting, Boiling, and Subliming
    4. Intermolecular Forces
    5. End-of-Chapter Material
  18. Chapter 11. Solutions
    1. Colligative Properties of Solutions
    2. Concentrations as Conversion Factors
    3. Quantitative Units of Concentration
    4. Colligative Properties of Ionic Solutes
    5. Some Definitions
    6. Dilutions and Concentrations
    7. End-of-Chapter Material
  19. Chapter 12. Acids and Bases
    1. Acid-Base Titrations
    2. Strong and Weak Acids and Bases and Their Salts
    3. Brønsted-Lowry Acids and Bases
    4. Arrhenius Acids and Bases
    5. Autoionization of Water
    6. Buffers
    7. The pH Scale
    8. End-of-Chapter Material
  20. Chapter 13. Chemical Equilibrium
    1. Chemical Equilibrium
    2. The Equilibrium Constant
    3. Shifting Equilibria: Le Chatelier’s Principle
    4. Calculating Equilibrium Constant Values
    5. Some Special Types of Equilibria
    6. End-of-Chapter Material
  21. Chapter 14. Oxidation and Reduction
    1. Oxidation-Reduction Reactions
    2. Balancing Redox Reactions
    3. Applications of Redox Reactions: Voltaic Cells
    4. Electrolysis
    5. End-of-Chapter Material
  22. Chapter 15. Nuclear Chemistry
    1. Units of Radioactivity
    2. Uses of Radioactive Isotopes
    3. Half-Life
    4. Radioactivity
    5. Nuclear Energy
    6. End-of-Chapter Material
  23. Chapter 16. Organic Chemistry
    1. Hydrocarbons
    2. Branched Hydrocarbons
    3. Alkyl Halides and Alcohols
    4. Other Oxygen-Containing Functional Groups
    5. Other Functional Groups
    6. Polymers
    7. End-of-Chapter Material
  24. Chapter 17. Kinetics
    1. Factors that Affect the Rate of Reactions
    2. Reaction Rates
    3. Rate Laws
    4. Concentration–Time Relationships: Integrated Rate Laws
    5. Activation Energy and the Arrhenius Equation
    6. Reaction Mechanisms
    7. Catalysis
    8. End-of-Chapter Material
  25. Chapter 18. Chemical Thermodynamics
    1. Spontaneous Change
    2. Entropy and the Second Law of Thermodynamics
    3. Measuring Entropy and Entropy Changes
    4. Gibbs Free Energy
    5. Spontaneity: Free Energy and Temperature
    6. Free Energy under Nonstandard Conditions
    7. End-of-Chapter Material
  26. Appendix A: Periodic Table of the Elements
  27. Appendix B: Selected Acid Dissociation Constants at 25°C
  28. Appendix C: Solubility Constants for Compounds at 25°C
  29. Appendix D: Standard Thermodynamic Quantities for Chemical Substances at 25°C
  30. Appendix E: Standard Reduction Potentials by Value
  31. Glossary
  32. About the Authors
  33. Versioning History

Colligative Properties of Ionic Solutes

Learning Objectives

  1. Determine the colligative properties of solutions of ionic solutes.

In the section “Colligative Properties of Solutions”, we considered the colligative properties of solutions with molecular solutes. What about solutions with ionic solutes? Do they exhibit colligative properties?

There is a complicating factor: ionic solutes separate into ions when they dissolve. This increases the total number of particles dissolved in solution and increases the impact on the resulting colligative property. Historically, this greater-than-expected impact on colligative properties was one main piece of evidence for ionic compounds separating into ions (increased electrical conductivity was another piece of evidence).

For example, when NaCl dissolves, it separates into two ions:

NaCl(s) → Na+(aq) + Cl−(aq)

This means that a 1 M solution of NaCl actually has a net particle concentration of 2 M. The observed colligative property will then be twice as large as expected for a 1 M solution.

It is easy to incorporate this concept into our equations to calculate the respective colligative property. We define the van’t Hoff factor (i) as the number of particles each solute formula unit breaks apart into when it dissolves. Previously, we have always tacitly assumed that the van’t Hoff factor is simply 1. But for some ionic compounds, i is not 1, as shown in Table 11.4 “Ideal van’t Hoff Factors for Ionic Compounds”.

Table 11.4 Ideal van’t Hoff Factors for Ionic Compounds
Compoundi
NaCl2
KBr2
LiNO32
CaCl23
Mg(C2H3O2)23
FeCl34
Al2(SO4)35

The ideal van’t Hoff factor is equal to the number of ions that form when an ionic compound dissolves.

Example 11.17

Predict the van’t Hoff factor for Sr(OH)2.

Solution
When Sr(OH)2 dissolves, it separates into one Sr2+ ion and two OH− ions:

Sr(OH)2 → Sr2+(aq) + 2OH−(aq)

Because it breaks up into three ions, its van’t Hoff factor is 3.

Test Yourself
What is the van’t Hoff factor for Fe(NO3)3?

Answer
4

It is the “ideal” van’t Hoff factor because this is what we expect from the ionic formula. However, this factor is usually correct only for dilute solutions (solutions less than 0.001 M). At concentrations greater than 0.001 M, there are enough interactions between ions of opposite charge that the net concentration of the ions is less than expected—sometimes significantly. The actual van’t Hoff factor is thus less than the ideal one. Here, we will use ideal van’t Hoff factors.

Revised equations to calculate the effect of ionization are then easily produced:

\begin{array}{rrl} \Delta T_{\text{b}}&=&imK_{\text{b}} \\ \Delta T_{\text{f}}&=&imK_{\text{g}} \\ \Pi&=&iMRT \end{array}

where all variables have been previously defined. To calculate vapour pressure depression according to Raoult’s law, the mole fraction of solvent particles must be recalculated to take into account the increased number of particles formed on ionization.

Example 11.18

Determine the freezing point of a 1.77 m solution of NaCl in H2O.

Solution
For NaCl, we need to remember to include the van’t Hoff factor, which is 2. Otherwise, the calculation of the freezing point is straightforward:

\Delta T_{\text{f}}=(2)(1.77 \cancel{m})\left(\dfrac{1.86^{\circ}\text{C}}{\cancel{m}}\right)=6.58^{\circ}\text{C}

This represents the change in the freezing point, which is decreasing. So we have to subtract this change from the normal freezing point of water, 0.00°C:

0.00^{\circ}\text{C}-6.58^{\circ}\text{C}=-6.58^{\circ}\text{C}

Test Yourself
Determine the boiling point of a 0.887 m solution of CaCl2 in H2O.

Answer
101.36°C

Food and Drink App: Salting Pasta Cooking Water

When cooking dried pasta, many recipes call for salting the water before cooking the pasta. Some argue — with colligative properties on their side — that adding salt to the water raises the boiling point, thus cooking the pasta faster. Is there any truth to this?

To judge the veracity of this claim, we can calculate how much salt should be added to the water to raise the boiling temperature by 1.0°C, with the presumption that dried pasta cooks noticeably faster at 101°C than at 100°C (although a 1° difference may make only a negligible change in cooking times). We can calculate the molality that the water should have:

\begin{array}{rrl} 1.0^{\circ}\text{C}&=&m\left(0.512^{\circ}\text{C}/m\right) \\ \\ m&=&1.95 \end{array}

We have ignored the van’t Hoff factor in our estimation because this obviously is not a dilute solution. Let us further assume that we are using 4 L of water (which is very close to 4 qt, which in turn equals 1 gal). Because 4 L of water is about 4 kg (it is actually slightly less at 100°C), we can determine how much salt (NaCl) to add:

4\cancel{\text{ kg }\ce{H2O}}\times \dfrac{1.95\text{ \cancel{mol NaCl}}}{1\cancel{\text{ kg }\ce{H2O}}}\times \dfrac{58.5\text{ g NaCl}}{1\text{ \cancel{mol NaCl}}}=456.3\text{ g NaCl}

This is just over 1 lb of salt and is equivalent to nearly 1 cup in the kitchen. In your experience, do you add almost a cup of salt to a pot of water to make pasta? Certainly not! A few pinches, perhaps one-fourth of a teaspoon, but not almost a cup! It is obvious that the little amount of salt that most people add to their pasta water is not going to significantly raise the boiling point of the water.

So why do people add some salt to boiling water? There are several possible reasons, the most obvious of which is taste: adding salt adds a little bit of salt flavour to the pasta. It cannot be much because most of the salt remains in the water, not in the cooked pasta. However, it may be enough to detect with our taste buds. The other obvious reason is habit; recipes tell us to add salt, so we do, even if there is little scientific or culinary reason to do so.

Key Takeaways

  • For ionic solutes, the calculation of colligative properties must include the fact that the solutes separate into multiple particles when they dissolve.
  • The equations for calculating colligative properties of solutions of ionic solvents include the van’t Hoff factor, i.

Exercises

Questions

  1. Explain why we need to consider a van’t Hoff factor for ionic solutes but not for molecular solutes.
  2. NaCl is often used in winter to melt ice on roads and sidewalks, but calcium chloride (CaCl2) is also used. Which would be better (on a mole-by-mole basis), and why?
  3. Calculate the boiling point of an aqueous solution of NaNO3 made by mixing 15.6 g of NaNO3 with 100.0 g of H2O. Assume an ideal van’t Hoff factor.
  4. Many labs use a cleaning solution of KOH dissolved in C2H5OH. If 34.7 g of KOH were dissolved in 88.0 g of C2H5OH, what is the boiling point of this solution? The normal boiling point of C2H5OH is 78.4°C and its Kb = 1.19°C/m. Assume an ideal van’t Hoff factor.
  5. What is the freezing point of a solution made by dissolving 345 g of CaCl2 in 1,550 g of H2O? Assume an ideal van’t Hoff factor.
  6. A classic homemade ice cream can be made by freezing the ice cream mixture using a solution of 250 g of NaCl dissolved in 1.25 kg of ice water. What is the temperature of this ice water? Assume an ideal van’t Hoff factor.
  7. Seawater can be approximated as a 3.5% NaCl solution by mass; that is, 3.5 g of NaCl are combined with 96.5 g H2O. What is the osmotic pressure of seawater? Assume an ideal van’t Hoff factor.
  8. The osmotic pressure of blood is 7.65 atm at 37°C. If blood were considered a solution of NaCl, what is the molar concentration of NaCl in blood? Assume an ideal van’t Hoff factor.
  9. What is the vapour pressure of an aqueous solution of 36.4 g of KBr in 199.5 g of H2O if the vapour pressure of H2O at the same temperature is 32.55 torr? What other solute(s) would give a solution with the same vapour pressure? Assume an ideal van’t Hoff factor.
  10. Assuming an ideal van’t Hoff factor, what mole fraction is required for a solution of Mg(NO3)2 to have a vapour pressure of 20.00 torr at 25.0°C? The vapour pressure of the solvent is 23.61 torr at this temperature.

Answers

  1. Ionic solutes separate into more than one particle when they dissolve, whereas molecular solutes do not.
  1. 101.9°C
  1. −7.5°C
  1. 30.3 atm
  1. 30.86 torr; any two-ion salt should have the same effect.

Annotate

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Copyright © 2014

                                by Jessie A. Key

            Introductory Chemistry - 1st Canadian Edition by Jessie A. Key is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.
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