Ions in Aqueous Solutions and Colligative Properties

Section 1Compounds in Aqueous Solutions

Dissociation

� When compound made from ions dissolves in water, ions separate

� Dissociation à separation of ions that occurs when an ionic compound dissolves

� Notice number of ions made per formula unit in equations

� 1 formula unit of NaCl gives 2 units of ions in solution

� 1 formula unit of CaCl2 gives 3 units of ions

� Assuming 100% dissociation, solution that contains 1 mol NaCl contains 1 mol Na+ and 1 mol Cl-

� Can assume 100% dissociation of all soluble ionic compounds

Practice Problem

� Write the equation for the dissolution of aluminum sulfate in water. How many moles of aluminum ions are made by dissolving 1 mol aluminum sulfate? What is the total number of moles of ions made by dissolving 1 mol of aluminum sulfate?

1. Analyze

� Given:

� Amount of solute = 1 mol Al2(SO4)3

� Solvent identity = water

� Unknown

� a. moles of aluminum ions and sulfate ions

� Total number of moles of solute ions produced

2. Plan

� The coefficients in the balanced dissociation equation will tell mole relationships

� You can use the equation to find out the number of moles of solute ions produced

3. Compute

� a.

� b.

� Write the equation for the dissolution of each of the following in water, and then determine the number of moles of each ions made as well as the total number of ions made.

� a. 1 mol ammonium chloride

� b. 1 mol sodium sulfide

� c. 0.5 mol barium nitrate

a. 1 mol ammonium chloride

1 mol NH4+

1 mol Cl-

2 mol total ions

b. 1 mol sodium sulfide

2 mol Na+

1 mol S-2

3 mol total ions

c. 0.5 mol barium nitrate

0.5 mol Ba+2

1 mol NO3-

1.5 mol total ions

Precipitation Reactions

� Even though no compound is completely insoluble, compounds of very low solubility can be considered insoluble for practical purposes

� There are general guidelines to help predict whether a compound made of certain combination of ions is soluble

General Solubility Guidelines

1.Sodium, potassium, and ammonium compounds are soluble in water.

2.Nitrates, acetates, and chlorates are soluble.

3.Most chlorides are soluble, except those of silver, mercury (I), and lead. Lead (II) chloride is soluble in hot water.

4.Most sulfates are soluble, except those of barium, strontium, lead, calcium, and mercury.

5.Most carbonates, phosphates, and silicates are insoluble, except those of sodium, potassium, and ammonium.

6.Most sulfides are insoluble, except those of calcium, strontium, sodium, potassium, and ammonium.

� Is calcium phosphate, Ca3(PO4)2 soluble or insoluble?

� Not one of the exceptions, so it is insoluble

� Dissociation equations are not written for insoluble compounds

� Guidelines also useful in predicting what will happen if 2 solutions of 2 different soluble compounds are mixed

� If mixing results in combination of ions that forms insoluble compound, a double-replacement and precipitation reaction will happen

� Will precipitate form when solutions of ammonium sulfide and cadmium nitrate are combined?

� You can tell calcium nitrate is soluble from the guidelines (Most nitrates, acetates, and chlorates are soluble)

� You can also tell ammonium sulfide is soluble (Most sulfides are insoluble, except those of calcium, strontium, sodium, potassium, and ammonium)

� Two possible products: ammonium nitrate and cadmium sulfide

� To decide whether precipitate can form, must know solubilities of two possible products

� Ammonium nitrate – soluble (Most nitrates, acetates, and chlorates are soluble)

� Cadmium sulfide – insoluble (Most sulfides are insoluble, except those of calcium, strontium, sodium, potassium, and ammonium)

� b/c one product is insoluble, double-replacement and precipitation reaction will happen

(NH4)2S (aq) + Cd(NO3)2 (aq) à NH4NO3 (aq) + CdS (s)

Net Ionic Equations

� Reactions of ions in aqueous solution usually represented by net ionic equations instead of formula equations

� Net ionic equation à includes only those compounds and ions that undergo a chemical change in a reaction in an aqueous solution

� To write NIE (net ionic equation) first convert chemical equation into overall ionic equation

� All soluble ionic compounds shown as dissociated ions in solution

� Precipitates shown as solids

� Notice ammonium and nitrate ions appear on both sides

� They haven’t gone through any chemical change

� Spectator ions à ions that do not take part in a chemical reaction and are found in solution both before and after the reaction

� To change ionic equation to NIE, eliminate spectator ions

Cd+2(aq) + S-2(aq) à CdS(s)

� This NIE applies to any reaction in which precipitate of CdS forms

Practice Problem

� Identify the precipitate that forms when aqueous solutions of zinc nitrate and ammonium sulfide are combined. Write the equation for the possible double-replacement reaction. Then write the formula equation, overall ionic equation, and the net ionic equation.

1. Analyze

� Given:

� Identity of reactants: zinc nitrate and ammonium sulfide

� Reaction medium: aqueous solution

� Unknown:

� a. equation for the possible double-replacement reaction

� b. identity of the precipitate

� c. formula equation

� d. overall ionic equation

� e. net ionic equation

2. Plan

� Write the possible double-replacement reaction between Zn(NO3)2 and (NH4)2S

� Use the rules to determine if any of the products will precipitate

� Write a formula equation and overall net ionic equation

� Then cancel spectator ions to make net ionic equation

3. Compute

� a. possible double-replacement reaction:

� b. rules show that zinc sulfide is not soluble so will precipitate (ammonium nitrate is soluble)

� c. formula equation:

� d. overall ionic equation:

� e. net ionic equation:

� Will a precipitate form if solutions of potassium sulfate and barium nitrate are combined? If so, write the net ionic equation for the reaction.

� Yes

� Ba+2(aq) + SO4-2(aq) à BaSO4(s)

� Will a precipitate form if solutions of potassium nitrate and magnesium sulfate are combined? If so, write the net ionic equation for the reaction.

� No

� Will a precipitate form if solutions of barium chloride and sodium sulfate are combined? If so, identify the spectator ions and write the net ionic equation for the reaction.

� Yes; Na+ and Cl-

� Ba+2(aq) + SO4-2(aq) à BaSO4(s)

� Write the net ionic equation for the precipitation of nickel(II) sulfide.

� Ni+2(aq) + S-2(aq) à NiS(s)

Ionization

� Some molecular compounds can also form ions in solution

� Usually polar

� Ionization à ions formed from solute molecules by action of the solvent

� (creation of ions where there were none)

� Ionization different from dissociation

� Dissociation: ionic compounds dissolve and ions already present separate

� Ionization: ions formed where non existed before

� Ions formed are hydrated

� Heat released during hydration of ions gives enough energy to break covalent bonds

� Extent to which solute ionizes depends on strength of bonds within molecules of solute and strength of attraction between solute and solvent molecules

� If strength of bond within solute is weaker than attraction of solvent, bonds break and ions are formed

� HCl – molecular compound that ionizes in aqueous solution

� Contains highly polar bond

� Attraction between polar HCl molecule and polar water strong enough to break HCl bond

The Hydronium Ion

� H+ ions from HCl attracts other molecules or ions so strongly that it doesn’t normally exist alone

� Ionization of HCl better described as direct transfer of proton from HCl to H2O, forming H3O+

H2O(l) + HCl(g) à H3O+(aq) + Cl-(aq)

� Hydration of H+ to form hydronium is highly exothermic

� Energy released gives a lot of energy needed to ionize a molecular solute

� Many molecular compounds that ionize in aqueous solution contain hydrogen and form hydronium ion

Strong and Weak Electrolytes

� Substances that make ions and conduct current in solution are electrolytes

� HCl is one of series of compounds that has hydrogen and halogen

� Hydrogen halides are all molecular compounds with single polar-covalent bonds

� All are gases

� Very soluble in water

� All are electrolytes

� HCl, HBr, HI strongly conduct current in solution

� HF only weakly conducts current at same concentration

� Strength of conduction related to ability to ionize

Strong Electrolytes

� HCl, HBr, HI are 100% ionized in solution

� Strong electrolyte à any compound whose dilute aqueous solutions conduct electricity well; this is due to the presence of all or almost all of the dissolve compound in the form of ions

� HCl, HBr, HI all acids in aqueous solutions

� These acids, several others, and all soluble ionic compounds are all strong electrolytes

� Unique characteristic of strong electrolyte is that they yield only ions

� Ex. Ionic compound may be highly soluble in water and dissociate into ions (NaCl)

� Others may not dissolve much, but amount that does dissolve exists only as ions

Weak Electrolytes

� HF dissolves in water to give acid solution called hydrofluoric acid

� HF bond stronger than bonds between hydrogen and other halogens

� When HF dissolves, some molecule ionize

� Reverse reaction also happens

HF(aq) + H2O(l) ⇄ H3O+(aq) + F-(aq)

HF(aq) + H2O(l) ⇄ H3O+(aq) + F-(aq)

� Concentration of dissolved unionized HF stays high and concentration of ions stays low

� Weak electrolyte à any compound whose aqueous solutions conduct electricity poorly; this is due to the presence of small amount of the dissolved compound in the form of ions

� Different from nonelectrolyte – NO ions at all

� Description of electrolyte as strong or weak not related to concentration of solution

� Electrolytes differ in degree of ionization, not amount of solute dissolved

Section 2Colligative Properties of Solutions

� Presence of solute affects properties of solutions

� Some properties not dependent on nature of dissolved substance but on how may dissolve particles are present

� Colligative properties à properties that depend on the concentration of solute particles but not on their identity

Vapor-Pressure Lowering

� Boiling and freezing point of solution different from pure solvent

� Nonvolatile solute raises boiling point and lowers freezing point

� Nonvolatile substance à one that has little tendency to become gas under existing conditions

� To understand why nonvolatile solute changes boiling and freezing point, consider equilibrium vapor pressure

� Vapor pressure: pressure caused by molecules that have escape liquid phase to gas phase

� Can be thought of a measure of tendency of molecules to escape from a liquid

� Addition of sucrose (nonvolatile solute) lowers concentration of water molecules at surface of liquid

� This lowers tendency of water molecules to leave solution and enter gas phase

� Vapor pressure of solution is lower than vapor pressure of pure water

Aqueous solution of nonvolatile solute

Pure water

� Nonelectrolyte solutions of same molality have same concentration of particles

� Dilute solutions of same solvent and equal molality of any nonelectrolyte solute lower vapor pressure equally

Example

� 1 m aqueous solution of nonelectrolyte glucose lowers vapor pressure of water 5.5 x 10-4 atm at 25℃

� 1  m  aqueous  solution  of  sucrose  also  lowers  water  vapor  pressure  to  5.5 x 10-4 atm at 25℃

� b/c  vapor-­‐pressure  lowering  depends  on  concentration  of  nonelectrolyte  solute  and  doesn’t  depend  on  the  type  of  solute,  it  is  a  colligative  proprerty

� b/c vapor pressure has been lowered, solution remains liquid over larger temperature range

� Lowers freezing point and raises boiling point

� Can assume changes in boiling and freezing point also depend on concentration of solute

� They are colligative properties

Freezing-Point Depression

� Freezing point of 1-molal solution of any nonelectrolyte solute in water is found (by experiment) to be 1.86℃  lower than freezing point of water

� When 1 mol of nonelectrolyte solute dissolved in 1 kg water, freezing point is -1.86℃ , not 0.00℃

� When 2 mol nonelectrolyte solute dissolved in 1 kg water, freezing point is -3.72℃

� For any concentration of nonelectrolyte solute in water, decrease in freezing point can be determined using value of -1.86℃/m

� This value, called the molal freezing-point contstant (Kf) is the freezing-point depression of the solvent in a 1-molal solution of a nonvolatile, nonelectrolyte solute

� Each solvent has own characteristic molal freezing-point constant

� Freezing-point depression (Δtf) à the difference between the freezing points of the pure solvent and a solute of nonelectrolyte in that solvent, and it is directly proportional to the molal concentration of the solution

Δtf = Kfm

Δtf = Kfm

� Kf expressed as ℃/m

� m expressed in mol solute/kg solvent (molality)

Sample Problem

� What is the freezing point depression of water in a solution of 17.1 g of sucrose, C12H22O11 and 200. g of water? What is the actual freezing point of the solution?

1. Analyze

� Given:

� Solute mass and chemical formula � 17.1 g C12H22O11

� Solvent mass and identity � 200.0 g water

� Unknown:

� a. freezing-point depression

� b. freezing point of the solution

2. Plan

Calculate

� Unknown:

� a. freezing-point depression

� b. freezing point of the solution

Practice Problem

� A water solution containing an unknown quantity of a nonelectrolyte solute is found to have a freezing point of – 0.23°C.What is the molal concentration of the solution?

� 0.12 m

� A solution consists of 10.3 g of the nonelectrolyte glucose, C6H12O6, dissolved in 250. g of water. What is the freezing-point depression of the solution?

� −0.426°C

� In a laboratory experiment, the freezing point of an aqueous solution of glucose is found to be −0.325°C.What is the molal concentration of this solution?

� 0.175 m

� If 0.500 mol of a nonelectrolyte solute are dissolved in 500.0 g of ether, what is the freezing point of the solution?

� −118.1°C

� The freezing point of an aqueous solution that contains a nonelectrolyte is −9.0°C.

� a.What is the freezing-point depression of the solution?

� b.What is the molal concentration of the solution?

� a. −9.0°C

� b. 4.8 m

Boiling-Point Elevation

� Boiling point is temp at which vapor pressure is equal to atmospheric pressure

� Change in vapor pressure will cause corresponding change in boiling point

� Vapor pressure of nonvolatile solution is lower than vapor pressure of pure solvent

� More heat will be required to raise vapor pressure of solution

� Boiling point of solution is higher than boiling point of pure solvent

� Molal boiling-point constant (Kb) à boiling-point elevation of the solvent in a 1-molal solution of a nonvolatile, nonelectrolyte solute

� b-p elevation of any nonelectrolyte in water found by experiment to be 0.51℃

� So, molal b-p constant for water is 0.51℃/m

� For different solvents, b-p elevations of 1-molal solutions have different values (Table 14-2)

� Like freezing-point constants, values most accurate for dilute solutions

� Boiling-point elevation, Δtb, à difference between the boiling points of the pure solvent and a nonelectrolyte solution of that solvent, and it is directly proportional to the molal concentration of the solution

� B-p elevation can be calculated using

Δtb = Kbm

� Δtb (boiling point elevation) expressed in ℃/m and m expressed in mol solute/kg solvent

Sample Problem

� What is the boiling-point elevation of a solution made from 20.0 g of a nonelectrolyte solute and 400.0 g of water? The molar mass of the solute is 62.0 g/mol.

1. Analyze

� Given:

� solute mass = 20.0 g

� solute molar mass = 62.0 g/mol

� solvent mass and identity = 400.0 g of water

� Unknown:

� boiling-point elevation

2. Plan

3. Compute

Practice Problem

� A solution contains 50.0 g of sucrose, C12H22O11, a nonelectrolyte, dissolved in 500.0 g of water. What is the boiling-point elevation?

� 0.15°C

� A solution contains 450.0 g of sucrose, C12H22O11, a nonelectrolyte, dissolved in 250 g of water.What is the boiling point of the solution?

� 102.7°C

� If the boiling point elevation of an aqueous solution containing a nonvolatile electrolyte is 1.02°C, what is the molality of the solution?

� 2.0 m

� The boiling point of an aqueous solution containing a nonvolatile electrolyte is 100.75°C.

� a.What is the boiling-point elevation?

� b.What is the molality of the solution?

� a. 0.75°C

� b. 1.5 m

Osmotic Pressure

� Aqueous sucrose solution is separated from pure water by semi-permeable membrane

� Level of sucrose solution rises

� Why?

� Membrane allows water but not sucrose through

� Sucrose allow fewer water molecules through (blocking the path)

� Water enters to the left at faster rate than to the right

� Level rises until pressure applied by height of solution large enough to force water back through

� Osmosis à movement of solvent through semi-permeable membrane from the side of lower solute concentration to the side of higher solute concentration

� Happens when two solutions of different concentrations are separated by semi-permeable membrane

� Osmotic pressure à external pressure that must be applied to stop osmosis

� Because osmotic pressure is dependent on concentration of solute particles and not on type of solute particles, it is a colligative property

� Greater concentration = greater osmotic pressure

� Regulation of osmosis is vital to life of cell b/c cell membranes are semi-permeable

� Cells lose water and shrink in solution of higher concentration

� Gain water and swell when placed in lower concentration

� Cells protected from shrinking and swelling by blood and lymph (fluid) that surrounds cells

� Blood and lymph are equal in concentration to concentration inside cell

Electrolytes and Colligative Properties� Early investigators confused by experiments where

certain substances depressed freezing point or elevated boiling point more than expected

� Ex. 0.1 m solution of NaCl lowers freezing point of solvent almost twice as much as 0.1 m solution of sucrose

� 0.1 m CaCl2 lowers f.p. almost 3 times as much as 0.1 m solution of sucrose

� To understand why this happens, contrast behavior or sucrose with NaCl in aqueous solution

� Each sucrose dissolves to make only 1 particle in solution

� So 1 mol sucrose dissolves to 1 mol particles

� 1 mol NaCl dissolves to make 2 moles of particles (1 mol Na+ and 1 mol Cl-)

Calculated Values for Electrolyte Solutions

� Colligative properties depend on total concentration of solute particles regardless of their identity

� Electrolytes cause changes in colligative properties proportional to total molality in terms of all dissolves particles instead of formula units

� For same molal concentrations of sucrose and NaCl, you expect effect on colligative properties twice as large for NaCl than for sucrose

� What about barium nitrate, Ba(NO3)2?

� Each mole of barium nitrate yields 3 mol of ions in solution

Ba(NO3)2(s) → Ba2+(aq) + 2NO3−(aq)

� You would expect solution of given molality to lower f.p. of solvent 3 times as much as nonelectrolytic solution of same molality

Sample Problem

� What is the expected change in the freezing point of water in a solution of 62.5 g of barium nitrate, Ba(NO3)2 , in 1.00 kg of water?

1. Analyze

� Given:

� solute mass and formula = 62.5 g Ba(NO3)2

� solvent mass and identity = 1.00 kg water

� Δtf = Kfm

� Unknown:

� expected freezing-point depression

2. Plan

� The molality can be calculated by converting the solute mass to moles and then dividing by the number of kilograms of solvent

� That molality is in terms of formula units of Ba(NO3)2 and must be converted to molality in terms of dissociated ions in solution

� It must be multiplied by the number of moles of ions produced per mole of formula unit

� This adjusted molality can then be used to calculate the freezing-point depression

3. Compute

Practice Problem

� What is the expected freezing-point depression for a solution that contains 2.0 mol of magnesium sulfate dissolved in 1.0 kg of water?

� −7.4°C

� What is the expected boiling-point elevation of water for a solution that contains 150 g of sodium chloride dissolved in 1.0 kg of water?

� 2.7°C

� The freezing point of an aqueous sodium chloride solution is −20.0°C. What is the molality of the solution?

� 5.4 m NaCl

Actual Values for Electrolyte Solutions� Remember values calculated are only expected values

� Actual values of colligative properties for all strong electrolytes are almost what would be expected

� Difference between expected and actual values caused by attractive forces that exist between dissociated ions in aqueous solution

� Attraction between hydrated ions in solution is small compared with those in crystalline solid

� However, forces of attraction don’t interfere with movements of aqueous ions

� More concentrated solution means ions closer together and attraction is greater

� Also depends on charge of ions – higher charge, greater attraction