FCH 152: General Chemistry II Final Exam Review Thursday, May 4th 8:00 - 10:00 AM Marshall Auditorium / 140 Baker Additional Survey Questions 14. Based on my Instructor’s recommendation, I spent 2-3 hours after every lecture reviewing the class notes and working problems from the text. 15. My expectation for a challenging course such as FCH152 is that most of my “learning” is done in class. 16. Baker 140 is a significant improvement over Marshall Aud. for General Chemistry classes. 17. I frequently used the tutorials and quizzes available on the CD accompanying the text to prepare for exams. 18. Weekly quizzes would be a good way to improve student performance in FCH152. FCH 152: General Chemistry II Disclaimer !!! This study guide does not contain all of the material likely to be on the final exam ….. It is just a compendium of subjects that will form the basis of Exam questions. Problems from Exams, Homework's and Workshops might show up again ! 1 Exam Questions (Non-Binding Instructors Estimate !) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. Kinetic Theory of Gases No Nukes ! Ideal Gas Law Ionic Compounds Stoichiometry / Balancing Equations Empirical Formulae Solutions / Solubility Product (2) Colligative properties of solutions (2) Thermodynamics (2) Kinetics (2) Reaction Equilibria – Equilibrium Constant Acids and Bases (2) Electrochemistry More on Kinetic Molecular Theory... • Gases: More K.E. than liquids or solids. • K.E. is directly proportional to absolute Temperature (T, K). • T increases, K.E. increases • At a given T, every gas has the same K.E. but different speed. • K.E. = 1/2 Mu2 , where M = molar mass and u = “root mean square” speed of the molecule. Temperature in °K Influence of Temperature on Molecular Velocity in the Gas Phase u2 = (3.R.T)/M (Speed ->) 2 (M = 32) (M = 28) K.E. = 1/2Mu2 so… u2 = 2K.E./M M = molar mass u = “root mean square” speed (rms) (M = 4) (M = 2) Speed Review Ideal Gases… PV = nRT If T and n are fixed, then: P1V1=P2V2 If P and n are fixed, then V1/T1=V2/T2 If V and n are fixed, then P1/T1=P2/T2 R is the Gas Constant = 0.082 atm.L/mol.K 1 mole of ideal gas = 22.4 L Ideal Gases… Not on Exam Henry’s Law (Solubility on liquids) Raoult’s Law (Partial Pressure and Mole Fraction) 3 Ionic Compounds Polyatomic Ions and Their Charges…… Sulfate, carbonate, etc. Know: Lattice Energy (U) and what atomic factors are responsible for higher or lower energy. Relationship between lattice energy and ionic material properties (melting point , density, etc) Balancing the Automobile Air Bag Equation Active Ingredient: Sodium Azide (NaN3) NaN3(s) → Na(s) + N2(g) NaN3(s) → Na(s) + [NaN3(s) 2 → Na(s) + NaN3(s) → 2 1.5 1.5 N2(g) N2(g)] x Na(s) + 3 2 N2(g) 2 x 65 g → 67.2 L of nitrogen gas ! Empirical Formulae for Dummies Analytical data is usually in weight % Assume you have 100 g of a sample, then % of each element corresponds to grams of that element. • For example: Compound W is 60% N, then 100 grams of W contains 60 g of N Calculate the moles of each element by dividing its weight in grams by its molar mass. Divide the moles of each element by smallest value of moles in the compound. Adjust results to end up with whole numbers for each element….. Voila! 4 Analytical Data Calculating Reaction Yield… The combustion of 58 g of butane (C4H10) yields 158 g of CO2. What is the yield of this reaction ? 2 C4H10 + 13 O2 → 10 H2O + 8 CO2 Theoretical yield is 8 moles of CO2 for each 2 moles of butane or, 4 moles of CO2 for each 1 mole of butane. 1 mole of butane = 58 g ; 4 moles of CO2 = 176 g Actual Yield (Given) = 158 g CO2 Theoretical yield for 1 mole of butane (58 g) = 176 g CO2 % Yield = Actual/Theoretical = 158/176 = .897 = 89.7% Solution Concentrations Molarity (M; moles / Liter of solvent) Molality (m; moles / kg of solvent) Percent (%): • Grams / 100 g of solvent (w/w) • Grams / 100 ml of solvent (w/v) • Milliliters / 100 ml (v/v) Parts per million (ppm): grams per 1,000,000 grams or ml of solvent ppb, ppt, etc. (Very dilute) 5 Concentration Conversions Solution Dilution ! For Dilutions: Voriginal x Moriginal = Vdiluted x Mdiluted 50 ml = 0.050 L Say it’s 5.0M = 0.250 mol 250 ml = 0.250 L 0.250 mol / 0.250 L = 1.0 M Types of Solutes Electrolyte: Solute that dissociates into ions in solution, enhancing the electrical conductivity of the solvent (water mostly). Ex. NaCl → Na+ + ClWeak Electrolyte: A solute that only partially dissociates in water and weakly enhances conductivity. Ex. Acetic Acid: CH3COOH ↔ CH3COO- + H+ Nonelectrolyte: None of the above. No dissociation, no conductivity. Ex. Scotch and soda (ethanol in water) 6 Colligative Solution Properties Properties that depend on the number of moles of solute present in solution and not solute composition (1 mole of sugar has the same effect as one mole of ethanol, for example). 1mol NaCl 1 mol Na+ + 1 mol Cl- = 2 moles total in solution ! Typical “colligative” properties: • • • Boiling Point Elevation Freezing Point Depression Osmotic Pressure Calculating Boiling Point Elevation ΔTb = Tb - Tbo = Kb.m, where: • • • • • ΔTb = Change in Boiling Point Tb = Observed Boiling Point of solution Tbo = Pure Solvent Boiling Point Kb = 0.52°C/m - water boiling point elevation constant. m = Molality = moles of Solute / kg of Solvent For chloride ion in seawater: 0.558M or 0.565m - Almost the same! Example: For a 1.14m seawater solution, its change in boiling point is: (0.52 °C / m).(1.14m) = 0.60°C Tb = ΔTb + Tbo Tb = 0.60°C + 100°C = 100.6 °C Calculating Freezing Point Depression ΔTf = T0f - Tf = Kf.m, where: • • • • • ΔTf = Change in Freezing Point Tf = Observed Freezing Point Tfo = Pure Solvent Freezing Point Kf = 1.86°C/m - water freezing point depression constant. m = Molality = moles of Solute / kg of Solvent Example: For a 1.14m seawater solution, its change in freezing point is: (1.86 °C / m).(1.14m) = 2.12°C Tf = Tfo - ΔTf Tf = 0°C - 2.12 °C = -2.12 °C 7 Osmotic Pressure: π Calculating Osmotic Pressure (π) π = MRT where: •M = Molarity (mol/L) •R = 0.082 atm.L / mol.K •T = Temperature (K) Units of π: atm Note similarity to PV=nRT π across a membrane Example: Calculate separating pure water from seawater at 25ºC. π = MRT = 1.14 mol/L x 0.0821(L.atm)/(mol.K) x (25+273 K) = 27.9 atm “Solubility Product” (Ksp) More Generally: Ionic Compound Dissolves: MmXx ↔ mM+ + xXDefinition of Ksp = [M]m . [X]x Ksp values are tabulated for many compounds ….. See Appendix Table A5.3 of text book. CaF2 in water, Ksp = [Ca++] x [F-]2 = 3.9 x 10-11 8 More on “Solubility Product” (Ksp) Caution, Beware, This Gets Tricky Here !! Dissolving CaF2 in water ↔ Ca++(aq) + 2F- (aq) If you start with 1 mol of CaF2 you get one mole of Ca++ and 2 moles of F-, or [s] ↔ [s] + [2s] (Recall [ ] = mol / L) If Ksp = [Ca++] . [F-]2 = 3.9 x 10-11 Then: s . [2s]2 = 4s3 = 3.9 x 10-11 So, s = 2.1 x 10-4 And [s] = 2.1 x 10-4 M = [CaF2 ] = It’s “solubility” Aqueous Solutions of Acids and Bases Bronsted-Lowry Definition (circa 1923) Acid: A proton donor Base: A proton acceptor or OH- producer Lewis Definition Acid: Accepts a pair of electrons Base: Donates a pair of electrons More About Acids / Bases A strong acid or base completely dissociates to ions in solution. Strong Acid: HCl (aq) → H+ (aq) + Cl- (aq) Strong Base: NaOH (aq) → Na+ (aq) + OH- (aq) A weak acid or base does not completely dissociate. (Example to follow) Strong acids can form other strong acids: HNO3 (aq) → H+ (aq) + NO3- (aq) HNO3 (aq) + Cl- → NO3- (aq) + HCl (aq) 9 Water: An Acid and a Base Water can both accept and donate a proton… It’s “amphoteric”. H20 (l) + H20 (l) ↔ OH- + H3O+ (Auto-ionization) Acid + Base ↔ Conjugate Base + Conjugate Acid At auto-ionization “equilibrium”: Kw = [H3O+ ] [OH-] = 1 x 10-14 Where: [H3O+ ] = [OH-] = 1 x 10-7 (Very Low Conc. !) So, in a solution where [H3O+ ] > [OH-], it’s acidic And, in a solution where [H3O+ ] < [OH-], it’s basic Nitric Acid: Strong Nitrous Acid: Weak Degree of Acid Ionization: Ka A strong acid completely dissociates to ions in solution. HCl (aq) → H3O+ (aq) + Cl- (aq) [0.1 M] → [0.1M] + [0.1M] Weak acids only partially dissociate to ions…. Ka values reflect the degree of ionization. Ex: HNO2 (Nitrous Acid; Weak) HNO2 (aq) → H+ (aq) + NO2- (aq) Ka = [NO2- ] [H+] / [HNO2]= 4.0 x 10-4 10 Sample Exercise 16.1: Calculate the value of [H+] of 0.100 M Acetic Acid. (Ka = 1.76x10-5). C2H3OOH (aq) C2H3OO- (aq) + H+ (aq) Ka = [C2H3OO-][H+] [C2H3OOH] = 1.76x10-5 (X)(X) = 1.76x10-5 (0.100 – X) 1. Since Ka is so small and acid concentration relatively large, the value of X will be small compared to 0.100 M. Assume (0.100 – X) = 0.100. (X)(X) (0.100) = 1.76x10-5 2. After some simple algebra, we get: X = [H+] = 1.33 x 10-3 Conjugate pairs ! 16_08.jpg What is pH ? Very simply……the “potential of the hydrogen ion” (SØren SØrenson, 1868-1939). pH = - log [H3O+ ] in water or, generally, pH = - log [H+] So, at “equilibrium”: [H3O+ ] = [OH-] = 1 x 10-7 Then the pH of “neutral” water is: 7 ! 11 What’s a Titration ? An experiment where you add a measured amount of one reactant (for example, an acid or base solution in water) to another reactant (like a solution of acid or base of unknown concentration) to determine the point of equivalence (where equal moles of each reactant are consumed or “neutralized”). Useful for determining the Molarity of solutions of unknown concentration. Titration of a Strong and Weak Acid Original Solutions: 20 ml of 0.10M Acid In General, For Titrations…. Assuming “Monoprotic” Acids Problem: Molarity is unknown for the acid or base … Volume x Molarity = Volume x Molarity Acid Base Volume x Molarity = L x mol / L = moles moles of acid = moles of base For diprotic acids: 0.5 mole acid can neutralize one mole of base 12 Thermodynamics Definition: The study of energy and its transformations. To Begin : Review Dr. Teece’s discussion of Energy, Spontaneity, Free Energy, Enthalpy and Entropy!! Energy of phase transitions Reaction energies • No Calorimetry Internal Energy Let’s call a gas trapped in a vessel a “Chemical System”. Internal energy of a system = Sum of kinetic and potential energies = E Change in Internal Energy going from state A to state B is ΔE = q + w, where q = heat flow into or out of the system and w = work done on or by the system. (Unit of work is the joule (J)). This is the First Law of Thermodynamics: Click on Image Summarizing the Confusion …… • q > 0 if heat is transferred from the surroundings to the system (the system is endothermic) • q < 0 if heat is transferred from the system to the surroundings (the system is exothermic) • w > 0 if work is done by the surroundings on the system . • w < 0 if work is done by the system on the surroundings. Remember These ! • Therefore: The value of ΔE depends on the signs and magnitude of q and w. 13 Internal Energy and Enthalpy For a chemical system at constant pressure, a new “State” function is defined where: H = E +PV, where H = Enthalpy If this system experiences a change (say work is done on it or by it), then ΔH = ΔE + PΔV. However, since ΔE = q +w = q - PΔV. Then ΔH = q -PΔV + PΔV. Then, at constant pressure, ΔH = qp, where qp = heat flow at constant pressure. Click on Image Require input of heat ΔH positive11_06.jpg ΔH negative Some Definitions….. Exothermic: If a chemical reaction or physical change results in heat flow from a system to its surroundings, its exothermic Endothermic: Reactions and physical changes that absorb heat from their surroundings are endothermic. Example: H2O(l) →H2O(g) ? q is heat flow: By definition, if q < 0, reaction / change is exothermic, and if q> 0, its endothermic. 14 Entropy Entropy (S): measurement of disorder • More disordered, larger entropy • Disorder increases = Entropy increases • Entropy changes during reactions, phase changes and other chemical processes: ΔS = Sfinal - Sinitial ΔS = Sproducts - Sreactants ΔS is positive, increased disorder ΔS is negative, increased order Entropy Changes (ΔS) Examples: (a) If the reaction of a solid and a liquid yields a gas for a product, then the product molecules have more freedom (kinetic theory !) and more disorder than the reactants… Entropy increases. (ΔS is positive) (b) If two gases react to form a liquid, then entropy decreases (ΔS is negative) (c) If a ice melts (solid – liquid phase change) entropy increases (ΔS is positive) (d) If one mole of a compounds dissociates into two moles of product, entropy increases. (ΔS is positive) (e) Dissolving ammonia, a gas, in water decreases its entropy (ΔS is negative) S solid < S liquid < S gas Gibbs Free Energy ΔG For just the “system”, a new function called Gibbs Free Energy (ΔG) can be defined at a constant pressure (1 atm) and a specific temperature: ΔG = ΔH – TΔS For a reaction/event (just the system) to be spontaneous, ΔG must be negative (-ve) S(s) + O2(g) → SO2(g); ΔH = -300 kJ This is an Exothermic Reaction: ΔH is negative (–ve) and Entropy increases: ΔS is +ve ΔG = ΔH - TΔS = (-) - [T(+)] = -ve (SPONTANEOUS !!) ΔH -ve and ΔS +ve = Reaction is SPONTANEOUS ! 15 Gibbs Free Energy: A Review ΔG = ΔH – TΔS ΔH -ve and ΔS +ve = SPONTANEOUS ΔH +ve and ΔS -ve = NON-SPONTANEOUS Always TRUE at all Temperatures If ΔH and ΔS have SAME SIGN, then temperature is critical Phase Transitions of Water D B C E •Heat flow (q), enthalpy and its changes (ΔH; exo = -; endo =+) •qp = ΔH = n Cp ΔT •ΔH of phase changes; qp = n ΔH fusion or vaporization A Molar Heat Capacity vs. Specific Heat Molar Heat Capacity q = n . Cp .ΔT, where: • n = number of moles • Cp = molar heat capacity of water (=75.3 J/mol.°C) • ΔT = Tfinal - Tinitial = temperature change Specific Heat: q = mass (grams) . C .ΔT, where: C is in J / g-°C or K 16 Heat Flow (q) required to: Stage B → C Melt ice at 0°C; q = n . ΔHfusion , where: • n = number of moles • ΔHfusion = molar heat of fusion of water (heat of fusion is the enthalpy change that takes place when one mole of a substance is melted) = 6.01 kJ/mol for water Ex.: q = (15.0 mol)(6.01 kJ/mol) = 90.0 kJ Enthalpy Changes During Chemical Reactions Bonds break ! (energy required) Bonds form !! (energy released) For a specific bond, like C-H, the energy of bond breaking is the same as the energy required for formation. ΔHreaction = Energy required + Energy liberated (-) Bond Energy = Energy required to break a mole of bonds • Bond Breaking: ΔH is positive (+) • Bond Formation: ΔH is negative (-) Changed from Online Version 17 Enthalpy of Reaction (ΔHrxn) from Standard Enthalpies ΔH0 reaction = Σ nΔH0formation, products - Σ mΔH0formation, reactants n, m = number of moles in the balanced equation ΔH0formation values for a compound or element in its ionic non-standard state are found in “tables” like Appendix A4.3 in your text. Example: Calculate the Heat of Reaction (ΔHrxn) for the combustion of propane (C3H8 (g)) from standard enthalpies of formation… Table 11.3: Standard Enthalpies of Formation at 298 K Compound Compound CH4 (g) ΔHf0 (kJ/mol) -74.8 CO (g) ΔHf0 (kJ/mol) -110.5 C2H6 (g) -84.7 CO2 (g) -393.5 C3H8 (g) -103.8 H2O (g) -241.8 C4H10 (g) -125.7 H2O (l) -285.8 O2 (g) 0.0 H2 (g) 0.0 Thermodynamics Refresher … Let’s “wake up” those resting brain cells For a chemical reaction or a process, like freezing or boiling: ΔG = ΔH -TΔS. ΔG = The change in Gibbs Free Energy, ΔH = enthalpy (heat) change, and ΔS = entropy change. If ΔG < O, reaction is spontaneous (One possibility: ΔH < 0 and ΔS is >0) If ΔG > O, reaction is non-spontaneous (ΔH > 0, ΔS < 0) If ΔG = O, reaction or process is in “equilibrium” (ΔH= -TΔS) If ΔS > O, More system disorder: S solid < S liquid < S gas ΔH = heat flow = qp at constant pressure • • Endothermic: ΔH is positive (+) Exothermic: ΔH is negative (-) ΔH = qp = n Cp ΔT where Cp = molar heat capacity or = mass (g) x C x ΔT where C = specific heat in kJ / g ; (n =moles) qp for a phase transition = ΔH molar heat of fusion or vaporization xn 18 Chemical Kinetics Definition: The area of chemistry that deals with speed of reactions, or the reaction rate, is called “Chemical Kinetics”. Reaction rates typically depend on: The concentration of reactants Physical state (gas > liquid > solids ) Temperature The presence of a catalyst (enzymes in natural systems) • The surface area of solid or liquid reactants and catalysts • • • • Effect of Concentration on Rate • Reaction: 2 NO + O2 (g) → 2 NO2 • Rate ∝ [O2] • Rate ∝ [NO]2 • Rate ∝ [O2].[NO]2 • Rate = k [O2].[NO]2 (Rate Law) • Where k = Rate Constant • Generalized Rate Law: k [O2]m Reaction Intermediate → is formed (“Activated Complex”) . [NO]n Activation Energy (Ea) Exothermic → 19 Arrhenius Equation Doing the “math”: ln k = - Ea/R (1/T) + ln A is in the form of y = mx + b, so, y intercept = ln A and slope =-Ea / R Ea and A can then be used to calculate k at any other temperature …. Slower Catalyst Effect: Homogeneous Catalysis Faster Chemical Equilibrium Chemical Equilibrium: The state in which the rate of a reaction in the forward direction matches its rate in the reverse direction….. And… the concentrations of the reactant(s) and product(s) do not change a.k.a “Dynamic Chemical Equilibrium” A + B ↔ C + D 20 Reaction: N2 (g) + O2 (g) ↔ 2 NO 15_01.jpg Equilibrium has been reached before all oxygen has been consumed ! Generic “Equilibrium Constant” General Reaction: aA + bB ↔ cC + dD Kc = [C]c [D]d / [A]a [B]b (For a specific temperature) If the products and reactants are all gases, then [concentration] = partial pressure (P) of each gas. Then, Kp = [PC]c [PD]d / [PA]a [PB]b • K >> 1: Lots of Product • K<< 1: Little product, lots of un-reacted reactants “Equilibrium Constant” • 2 NO2 (g; brown) ↔ N2O4 (gas; colorless) • Rate Forward = kf [NO2]2 • Rate Reverse = kr [N2O4] • At Equilibrium: Rate Forward = Rate Reverse • kf [NO2]2 = kr [N2O4] • Or, kf / kr = [N2O4] / [NO2]2 = K • K = Equilibrium Constant 21 Impact of K on ΔG: What Does K Mean ??? ΔG0 = -RT ln K, R = 8.314 J/mol.K, T = 298 K K = e-ΔG/RT ΔG K ln K 17.1 kJ 10-3 -6.9 10-1 -2.3 Not much product 5.7 kJ More Product 0 0 1 Equilibrium -5.7 kJ 10 2.3 Lots of Product ☺ Equilibrium LeChâtelier’s Principle A system at equilibrium responds to a stress in such a way that it relieves the stress ! Stress: Temperature, Pressure, Concentration, Precipitation, pH ☺ Acid / Base Equilibria….. Let’s Look at Nitrous Acid: HNO2 (aq) ↔ H+ (really, H3O+) + NO2Ka = [NO2- ] [H+ ] / [HNO2] = 4.0 x 10-4 (Book value) 0.1M HNO2 (aq) ↔ 0.0061M H+ + 0.0061M NO2Degree of ionization or Degree of dissociation = 0.0061/0.1 = 6.1% Small values of Ka suggests that the equilibrium favors the “reactant” and not products. For nitric acid (a strong acid) HNO3 (aq) → H+ + NO3- 0.1M HNO3 (aq) → 0.1M H+ + 0.1M NO3- 22 So What’s Happening ? • Acetic Acid in Water (A Weak Acid): – Initially: CH3COOH ↔ (←) CH3COO- + H30+ – Ka = [ H3O+] [CH3COO- = conjugate base] / [CH3COOH] – Finally: CH3COOH + NaOH → CH3COO-Na+ + H20 (Products sodium acetate plus water) • At the “mid-point” (pH = 4.75): – [CH3COOH] = [CH3COO- ] – [Acid] = [ Conjugate Base] So What’s Happening II ? • From: Ka = [ H3O+] [conjugate base] / [acid] • Then pKa = pH – log [conjugate base] / [acid] • Henderson-Hasselbach Equation: pH = pKa + log [conjugate base] / [acid] • At the “mid-point” (pH = 4.75): – – – – Where [CH3COOH] = [CH3COO-] [CH3COO- ] / [CH3COOH] = 1 Log 1 = 0 Then, pH = pKa So Who Cares ? • pKa (or pKb) is a useful property to know about since it reflects how strong or weak an acid or base is. • Lower pKa means a stronger acid. • Lower pKb means a stronger base. • Higher pKa means a more basic. 23 Buffer Composition • Typical Buffer Composition: A solution containing a weak acid (acetic) and a salt of its conjugate base. Example: Acetic Acid plus Sodium Acetate (pH range near 4.75) • Or,: A weak base and a salt of its conjugate acid (like ammonia and ammonium ion, say ammonium chloride). pH ~ 9 • Blood Buffer: Carbonic Acid / bicarbonate ion (H2CO3 and HCO3 –) H3O+ (aq) + HCO3 – (aq) ↔ H2CO3 (aq) ↔ H2O + CO2 (g) CO2 is then expelled ! No Nukes …… Redox Reactions Definition: Reactions where there is a simultaneous transfer of electrons from one chemical species to another…. Oxidation: Loss of electrons Reduction: Gain of electrons Half Reactions: Two reactions which combine to give an overall “Redox” reaction 24 Oxidation - Reduction Neither can take place without the other. Consider the reaction between zinc metal and an aqueous copper (II) sulfate solution: Zn(s) + Cu2+ Zn2+ + Cu(s) The overall reaction may be decomposed into two half-reactions: Zn(s) Zn2+ + 2e- (oxidation – loss of electrons) 2+ Cu + 2eCu(s) (reduction – gain of electrons) How much voltage does this cell generate ?? E°cell = E°cathode - E°anode = 0.34 V – (-0.76 V) = 1.10 Volts ! Which is Anode, Which is Cathode !! Reductions: Gain Electrons Reactions above hydrogen, will occur at the cathode, and hydrogen electrode becomes the anode Preference For Being Reduced 2 Cu+2 + 2 e- → Cu 2 H+ + 2 e- → H2 2 2 0.342 (cathode) 0.000 (anode) 25