Unit 2: Equilibria and Thermodynamics Chem 1B Name__ANSWERS____ Chapters 16, 6, 17 Equilibrium Problems 1. Of what does a buffer consist and why are buffers useful? Buffers are a special case of the common ion effect, calculate the change in pH of a) 0.020 mole HCl added to 1.0 liter of water, and b) 0.020 mole HCl added to a 1.0 L solution of 0.10 M NaF and 0.10 M HF. Ka of HF = 7.2 x 10-4 Buffers consist of a weak acid and a salt that has its conjugate base or a weak base and a salt that has its conjugate acid. Ratios are between 1:10 and 10:1. Relatively high concentrations of each will make a stronger buffer capacity. Buffers resist change in pH even when a strong acid or base is added. a) change in pH after adding 0.020 mole of HCl to 1.0 L H2O = 5.30 pH 7.00 for neutral water to pH 1.70 for 0.020M [H+] b) change in pH after adding 0.020 mole of HCl to buffer solution = 0.18 pH 3.14 for the buffer with 0.10 M HF and 0.10M F-1 to pH 2.96 for the buffer with 0.12M HF and 0.08M F-1 2. What is more basic a) 1.0 M NH3 solution or b) 1.0 M NH3 and 1.0 M NH4Cl solution? Explain your answer before any calculations are done. Given that K b = 1.8 x 10-5 calculate the pH of each solution. The 1.0 M NH3 solution in (a) is more basic since it contains only the weak base and none of the conjugate acid. When a salt containing the conjugate acid is added the pH will go down (lower pH, more acidic and closer to neutral) (a) pH = 11.63 (b) pH = 9.26 3. Choose an appropriate weak acid and conjugate base pair to prepare 1.0 L of buffered solution with a pH of 4.50. What molarity of the conjugate base is needed if 0.10 M of the weak acid is used? Several weak acids may be appropriate, I chose acetic acid, HC2H3O2, whose pKa = 4.74. molarity of NaC2H3O2 required will be 0.058 M 4. a) Describe or draw a simplified picture of a strong acid/strong base titration curve where you start with 0.10 M NaOH, the y axis is pH and the x axis is the volume of strong acid added. b) Describe or draw a picture for a weak acid/strong base titration curve. As the strong base is added what initially happens? Is the equivalence point on the basic or acidic side? after equivalence what happens? Be able to find pH when given initial concentration of contents in a flask and the quantity of various amounts of solution added from the buret and any time. SA + SB a) WA + SB b) 13 pH equivalence point at 7.0 equivalence point above 7.0 pH buffered ml of acid added ml of base added In part b) a buffer is initially made when adding the strong base to a weak acid. The equivalence point is basic since there is a conjugate base from the weak acid that is not neglible. after the equivalent point the curve loses its buffer and a sharp rise in pH occurs as in the strong acid strong base curve. 5. An acid-base titration experiment begins with 10.0 ml of 0.30 M NH3 in the flask and 0.10 M HCl in the burette. Kb for the ammonia = 1.8 x 10-5 . a) What is the initial [OH-], pOH, and pH for the 0.30 M ammonia solution in the flask before any acid is added? [OH-]=2.3 x 10-3 M, pOH = 2.63, pH= 11.37 b) What is the pOH and the pH after 10.0 ml of 0.10 ml of HCl has been added to the ammonia in the flask? pOH = 4.44, pH= 9.56 The half equivalence pOH = 4.74, pH = 9.26 (not asked here) c) What total volume in ml of the 0.10 M HCl must be added to the 10.0 ml of 0.30 M NH3 solution to reach the equivalence point? 30.0 ml d) What is the Ka for NH4 ? Ka = 5.56 x 10-10 for NH4+1 e) What is the numerical value of the pH at the equivalence point when the solution contains only the salt and water? pH= 5.19 Is this basic, acidic or neutral? acidic f) Which is the best indicator to use for this titration methyl orange (pH range 3-5), or phenolphthalein (pH range 8-10)? methyl orange (pH range 3-5) + g) 6. Draw a graph where pH is the y-axis and ml of HCl added is the x-axis. Sketch the titration curve including points of the previously calculated numbers from parts above. Indicate where there is a buffered solution if relevant. Inverse of 4b a) If you would like to make a buffered solution with a pH of 3.60, which one of the following weak electrolyte--salt combinations is best to make the buffer? 1) 2) H2SO3 and NaHSO3 CH3NH2 and CH3NH3Br 3) 4) HF and NaF H3AsO4 and NaCl Ka of H2SO3 = 1.2 x 10-2 Kb of CH3NH2 = 5.0 x 10-4 Ka of HF = 7.2 x 10-4 Ka of H3AsO4 = 2.5 x 10-4 -4 b) #3 HF and NaF, Ka of HF = 7.2 x 10 , pKa = 3.14 (close to the desired pH) and the acid is monoprotic. Using your chosen combination, what molarity of the weak acid is needed to make this a buffer of pH 3.60 if the conjugate base used has a concentration of 0.75 M? 0.26 M HF 7. Choose an appropriate weak acid and conjugate base pair to prepare 1.0 L of buffered solution with a pH of 4.50. What molarity of the conjugate base is needed if 0.12 M of the weak acid is used? Repeat of question #3 with a change in concentration. Several weak acids may be appropriate, I chose acetic acid, HC2H3O2, whose pKa = 4.74. The molarity of NaC2H3O2 required will be 0.069 M 8. If 2.0 mol NH3 and 1.50 mol Ca(NO3)2 are added to enough water to make 1.0 liter -5 -6 solution, will Ca(OH)2 precipitate out? Kb = 1.8 x 10 for NH3 and Ksp = 6.5 x 10 for Ca(OH)2. If a precipitate forms, how many moles of NH4Cl must be added to prevent precipitation of the calcium hydroxide? [OH-1] from 2.0 M NH3 = 6.0 x 10-3 M OH-1 [Ca+2] from Ca(NO3)2 = 1.50 M Qsp for Ca(OH)2 = 5.4 x 10-5 Qsp>Ksp so solid Ca(OH)2 does form, but you cannot see it with the human eye since the Qsp/Ksp ratio is less than 1000 Maximum of 2.1 x 10-3 M OH-1 allowed to avoid precipitation A minimum of 0.017 moles of NH4Cl must be added 9. Experimental evidence shows 1.00 liter of saturated CaF2 solution contains 0.0167 g CaF2 at 25°C calculate the molar solubility and the Ksp. 0.0167g/L /x(1mol/78.08 g) = 2.1 x 10-4 M Ksp = (x) (2x)2 = 3.9 x 10-11 10. Calculate the molar solubility of Mg3(AsO4)2, [Mg ], and [AsO4 ]. Ksp= 2.1 x 10 Ksp = (3x)3 (2x)2 = 2.1x 10-20 = 108x5 Molar solubility x = 4.5 x 10-5M [Mg+2] = 1.4 x 10-4 M; [AsO4-3] = 9.0 x 10-5M 11. Adding a common ion decreases the solubility. Ksp for lead (II) chloride, 1.7 x 10 . Calculate and compare the molar solubility, (x), of PbCl2 for a) a saturated solution of PbCl2 in just water (x) = 0.016 M b) A solution of 1.0 M Pb(NO3)2 in which excess solid PbCl2 is added to saturate. Molar solubility = 2.1 x 10-3 M 12. What is Kd? What is Kf? How are they different from Ksp? +2 -3 -20 -5 Kd is the dissociation constant of a complex ion Kf is the formation constant of a complex ion and is the inverse of Kd Ksp is for the dissociation of a solid and the solid activity is 1 13. Calculate the concentration of ammonia and cobalt(II) ions in 0.30 M [Co(NH3)6]+2 solution. Kd=1.3 x 10-5 Kd = [Co+2][NH3]6/[Co(NH3)6+2]= (x)(6x)6/(0.30) Molar solubility and [Co+2] = 0.036 M 6x = [NH3] = 0.22 M 14. An acid-base titration experiment begins with 20.0 ml of 0.300 M HF in the flask and 0.150 M NaOH in the buret. Ka for HF = 6.8 x 10-4. a) Draw the expected titration graph where pH is the y axis and ml of NaOH added is the x axis, Sketch and label the titration curve including WA or WB, SA or SB, salt, equivalence pt, pH at equiv pt <, =, or > 7, buffer, where color change of indicator should occur. See picture in 4b b) What are the initial [H+], [OH-], pH, pOH, and % ionization for the 0.300 M HF in the flask? Clearly identify answers. Ka for HF = 6.8 x 10-4 [H+] = 0.014 M; [OH-] = 7.0 x 10-13 M , pH = 1.85, pOH = 12.15, and 4.7 % ionization c) What is the pH of the titrated solution at the half equivalence point? What volume of NaOH must be added to reach this point? pH = pKa = 3.17 volume = 20.0 ml d) What is the pH after 18.0 ml of 0.150 M NaOH has been added to the flask containing 20.0 ml of 0.300 M HF? pH = 3.08 e) What volume of 0.150 M NaOH must be added to the original flask of 20.0 ml of 0.300 M HF to reach the equivalence point? volume = 40.0 ml f) Write the balanced whole, complete ionic, and net ionic equations of hydrolysis of the salt sodium fluoride (NaF) and indicate whether the salt is acidic, basic, or neutral. All species aqueous unless otherwise indicated NaF + H2O (l) NaOH + HF Na+1 + F- + H2O (l) Na+1 + OH- + HF F- + H2O (l) OH- + HF Basic g) Solve for the numerical Kb value for the net ionic equation in the previous step. Kb = 1.5 x 10-11 h) What is the pH of the solution in the flask at the equivalence point? [F-1] = 6.0 mmol/(20.0+40.0 ml) = 0.10 M F-1 [OH-1] = 1.2 x 10-6 M ; pOH = 5.91; pH = 8.09 i) Which is the best indicator to use for determining the endpoint of this titration Bromocresol green (pH 4-6) or phenolphthalein (pH 8-10)? phenolphthalein (pH 8-10) j) What is the pH after 45.0 ml of 0.150 M NaOH has been added to the original flask containing 20.0 ml of 0.300 M HF? 0.75 mmol OH-1/65.0 ml = 0.0115 M [OH-1]; pOH = 1.94; pH = 12.06 k) Check your pH answers and compare to the expected pH titration curve you predicted in part (a). Fill in your calculated values. Thermochemistry Problems 15. Give a brief description of each of the laws of thermodynamics. (Zeroth, first, second, third) Laws of thermodynamics are useful in predicting outcomes, but unlike a theory do not explain the expected behavior. Zeroth Law: Temperature Concept: Temperature measures the intensity of hotness or coldness of an object. When two objects are brought together heat always flows spontaneously from a hotter object to a colder object until thermal equilibrium is reached. Think of the heat flow direction when placing your hand in ice water verses hot water. First Law: Law of Conservation of Energy: Energy cannot be created or destroyed. The energy of the universe is constant. This law works for ordinary chemical and physical processes. It was later combined with another (conservation of matter) to include nuclear reactions after E =mc2. It was changed to the Law of Conservation of Matter and Energy Second Law: Entropy Principle: Every spontaneous change increases the entropy of the universe. This does not mean local decreases in entropy cannot take place. For the entropy of a system to decrease, the entropy of the surroundings must increase more. Third Law: Zero Entropy Established: The entropy of a pure, perfect, crystalline substance (no disorder) is zero at the temperature of absolute zero, 0 Kelvin. It is impossible to reach absolute zero. It has been tried in the lab and gets close. 16. A certain system change releases 3462 J of heat and at 1.00 atm pressure expands its volume from 12.9 L to 46.8 L. Solve for the E, H, and w for the system. (include the correct sign +/-, and units) . H = -3462 J, w = -33.9 L atm must convert to joules = -3434 J, 17. When gasoline burns in an automobile engine, the heat released causes the CO 2 and H2O vapor (this is gas) produced to expand, which pushes the pistons outward. Excess heat is removed by the car's cooling system. Determine the change in internal energy if the expanding gases do 451J of work on the pistons and the system looses 325 J to the surroundings as heat. H = -325 J, w = -451 J, 18. E = -6896 J E = -776 J Before the days of refrigerators and icemakers, drinking water in hot countries was often cooled by storage in clay pots. Evaporation of water through the pot cooled the remaining water. How many grams of water must evaporate to cool 3790 grams (1 gallon) of water from 34.8°C to 21.0°C? For water, specific heat is 4.184 J/g°C; Hvap is 44.0 kJ/mol. Qrxn = -218.8 kJ heat removed from the 1 gallon of water 4.97 moles of water, 89.5 g of water must evaporate 19. Is there a difference between the heat (q) determined in a coffee-cup calorimeter and the heat determined in a bomb calorimeter? Explain your answer. Heat in a coffee-cup calorimeter is under constant pressure and one measures change in enthalpy, in a bomb calorimeter the volume is constant and you measure internal energy change. 20. 50.0 ml of 1.00 M NaOH (aq) at 25.4 °C was added to 50.0 ml of a 0.50 M H 2SO4 (aq) solution also at 25.4°C in a coffee-cup calorimeter with a heat capacity of 20 J/°C. The 2 solutions were mixed thoroughly and the temperature rose to 31.9°C. What is the heat of neutralization of 1 mole of H2SO4? (Assume the density of both liquids to be 1.00 g/ml and the specific heat to be 4.184 J/g°C) Qcal + water = 2719.6 J + 130 J = 2849.6J, reverse sign for the reaction and divide by moles of H2SO4 H = -114 kJ/mol H2SO4 21. A manufacturer claims that its new dietetic dessert has fewer than 10 Calories per serving. An independent laboratory uses a bomb calorimeter with a heat capacity of 8.151 kJ/K to test the claim. When one serving of the dessert is burned in excess O 2, the temperature rises from 22.153 °C to 27.080°C. Is the manufacturer's claim correct? YES 22. The major source of Al in the world is bauxite (mostly Al2O3) Al2O3 (s) 2Al (s) + 3/2 O2 (g); Hrxn = 1676 kJ How many grams of Al can be produced utilizing 1000. kJ of heat? 32.2 g Al 23. Using Hess' Law and the 2 equations below, solve for the Hrxn of P4 (s) + 10 Cl2 (g) 4 PCl5 (s) 1) P4 (s) + 6Cl2 (g) 4 PCl3 (l) H = -1277.2 kJ 2) PCl5 (s) Cl2 (g) + PCl3 (l) H = +123.8kJ H = -1772.4 kJ 24. x1 x -4 Write the balanced formation equation of solid aluminum bicarbonate Al(HCO3)3. Al (s) + 3/2 H2 (g) + 3 Cgraphite (s) + 9/2 O2 (g) Al(HCO3)3 (s) 25. What is a state function? Give several examples of both state functions and those that are not. State Function: a property that depends only on the present state and not the path the system took to reach the state. In Thermochemistry state functions are generally capitalized. Some examples of state functions include: E, H, V, P, T. Time and work are not state functions. 26. Why is it important to show the physical phase in thermochemical equations? Different states of matter have different energies. 27. The first step in the production of nitric acid is the oxidation of ammonia. 4NH3 (g) + 5O2 (g) 4NO (g) + 6H2O (g) Calculate Hrxn from the Hf values found in the appendix. Hrxn = 4(90.37) + 6(-241.82) – 4(-46.19) – 5(0) = -904.68 kJ/mol 28. A 48.3 g sample of NH3 is produced according to the following reaction done under constant pressure and 450°C. Solve for the amount of work done on the system. N2 (g) + 3 H2 (g) 2 NH3 (g) w = - nRT = +12.0 kJ/mole reaction as written, for 48.3 g NH3, work = 17.0 kJ 29. Estimate the heat of reaction below using the bond energies given : CH4 (g) + 3Cl2 (g) CHCl3 (g) + 3 HCl (g) Bond Energies: C - H = 414 kJ/mol: Cl-Cl = 243 kJ/mol: C-Cl = 330 kJ/mol: H Cl = 431 kJ/mol Hrxn = -312 kJ/mol rxn 30. Given the Hf° of ammonia gas is - 46.11 kJ/mol, and the following bond energies: N - H is 389 kJ; H - H is 435 kJ/mol. Estimate the bond energy of a nitrogen nitrogen triple bond. Bond Energy for the triple bond in N2 = 937 kJ/mol 31. List and explain the factors (such as phase changes) that help in predicting the sign of the change in entropy of a system. Try to think of a type of example for each. (these factors interrelate so the same example may be used more than once with a combined explanation.) Predicting the sign for S: 1) Phase changes: s l g… + S H2O (l) H2O (g) 2) Temp: warming… + S O2 (g) 25°C O2 (g) 80°C 3) Volume: expanding… + S 10 ml gas 1.0 liter of same gas 4) Mixing: dissolving ... + S NaCl (s) + H2O (l) NaCl (aq) 5) Rearrange to create more ways of being… + S H2 (g) + Cl2 (g) 2 HCl (g) 6) # parts: increase… + S 10 g rock 10 g sand 7) More moles gas… + S N2O4 (g) 2 NO2 (g) 32. Choose the one with the higher entropy in each of the following pairs and justify your choice. a) 1 mole of SO2 gas or 1 mole of SO3 gas more atoms b) 1 mole CO2 solid or 1 mole CO2 gas gas vs solid c) 3 moles O2 gas or 2 moles O3 gas more moles gas d) 1 mole KBr crystal or 1 mole KBr aqueous more mixed e) Sea water at 2°C or Sea water at 23°C higher temp f) 1 mole HF gas or 1 mole HI gas more subatomic particles 33. Calculate S°rxn for the combustion of 1 mole of methane, CH4, at 25.0°C using S° in Appendix S°rxn = nS°products nS°reactants CH4 (g) + 2 O2 (g) CO2 (g) +2 H2O (l) S°rxn = 213.6 + 2(69.91) – 186.3 – 2(205) = -242.9 J/mol K 34. Estimate the normal boiling point (the temperature at which liquid and vapor are in equilibrium with each other and G = 0) for CCl4 at 1 atm pressure. ( H° and S° do not vary much with temperature, so often they may be used to estimate G at temperatures other than 25°C) CCl4(l) CCl4 (g) H°= 32.6 kJ/mol, S° = 95.0 J/mol K, Teq= 343K, 70°C 35. Use H°f and S° values to calculate G° at 25 °C for the reaction 2 CH3OH (l) + 3 O2 (g) 2 CO2 (g) + 4 H2O (l) Under which conditions is this reaction spontaneous? H°= -1453.1 kJ/mol, S° = -161.76 J/mol K, G° = -1404.9 kJ/mol, Teq= 8983 K, 8710 °C, This reaction is spontaneous under 8710°C, in other words, for all reasonable temperatures this will be a spontaneous reaction. 36. Answer positive, negative or zero for each blank Exothermic reactions have a negative enthalpy. The change in entropy of a spontaneous reaction is usually positive , this means more disorder. A reaction that is nonspontaneous has a positive G, while a system at equilibrium has a zero G, and a spontaneous reaction has a negative G. 37. What is the value of Keq when G = -98.0 kJ/mol at 25°C? Keq = 1.5 x 1017 38. In the Haber process NH3 is manufactured from N2 and H2. At 25°C, Kp = 3.6 x 108. To increase the rate of reaction the reaction is run at a higher temperature. Use the van't Hoff equation to calculate Kp at 450°C N2 (g) + 3 H2 (g) 2NH3 (g) H° = -92.2 kJ Van't Hoff eq. ln(KT2/KT1) = H/R (1/T1 - 1/T2) At 450°C, Kp = 0.11 39. For the following question on this problem refer to the equation below. 2 Cl2 (g) + 2 H2O (g) 4 HCl (g) + O2 (g) ; H° = +115 kJ At 25°C, the equilibrium partial pressures in a 5.00 liter container are as follows; [P(Cl2)] = 3.1 atm, [P(H2O)] = 3.1 atm, [P(HCl)] = 1.3 x 10-3 atm and [P(O2)] = 1.5 atm. a) Calculate Kp at 25°C Kp = 4.6 x 10-14 b) c) d) e) 40. Estimate G° from the Kp value G° = 76.1 kJ/mol Using the values of Kp and G° explain your prediction of whether products or reactants are favored. Reactants are favored, forward is nonspontaneous Is this reaction spontaneous at 25°C? NO You solved for Kp in the original reaction at 25°C . Use the van't Hoff equation to estimate Kp at 400°C. Kp = 7.9 x 10-3 The reaction for the enthalpy of formation of H2O (g) has H°f = -242 kJ/mol. a) Write the balanced formation equation. H2 (g) +1/2 O2 (g) H2O (g) b) Is the change in entropy expected to be positive or negative. Explain Negative, since fewer moles of gas are in products. c) How much PV work is done in kJ/mol and what is the value of E in kJ/mole for the formation equation of H2O (g) formed, given that when 0.50 moles of H2 gas reacts with 0.25 mol of O2 gas at 1.00 atmospheric pressure the volume compresses by 5.6 L. Work = -P V = +5.6 L atm = 567 J for 0.50 moles H2 w = 1.13 kJ/mol H2O E = -242 kJ + 1.13 kJ = -240.9 kJ/mol d) Under what conditions will this be spontaneous? Explain. Spontaneous at temperatures below the equilibrium temp since bothe enthalpy and entropy changes are negative. 41. Specific Heat A 7.82 g sample at 99.2 C is added to 30.0g of water at 22.10 C in a coffee-cup calorimeter. The final temperature is 24.20 C. The specific heat capacity of water is 4.184 J/g C. a) Solve for the specific heat of the metal 0.449 J/g C b) Determine which metal it is. (Al = 0.903 J/g C, Fe = 0.449 J/g C, Pb = 0.128 J/g C) c) Test the Law of Dulong and Petit which states that the molar heat capacity of elements are all approximately 25 J/mol C by solving for the molar heat capacities of Al, Fe, Pb. Al = 0.903 J/g C x 27.0 g/mol = 24.4 J/mol C Fe = 0.449 J/g C x 55.85 g/mol = 25.1 J/mol C Pb = 0.128 J/g C x 207.2 g/mol = 26.5 J/mol C The law seems to work, answers come to approximately 25 J/mol C 42. Heat of Reaction 50.0 ml of 0.500 M NaOH and 50.0 ml of 0.500 M HC2H3O2 both initially at 20.00 C are added together in a coffee-cup calorimeter and the final temperature is found to be 23.37 C. Assume the volumes are additive, the density of the solutions are 1.00 g/ml, the specific heat of the solution is 4.18 J/g C and it is an isolated system in which no matter or energy is exchanged outside of the calorimeter. a) Solve for the Qcalorimeter and the Qrxn. Qcalorimeter = 1409 J , Qrxn = -1409 J b) Solve for the molar enthalpy of neutralization in kJ/mol, Hrxn Hrxn= -56.3 kJ/mol 43. Bomb Calorimeter Calibration A known compound that generates 15.1 kJ of energy is burned in a bomb calorimeter and the temperature increased from 21.80 C to 23.28 C. a) Solve for the Qcalorimer Qcalorimeter = +15.1 kJ b) Is this experiment under constant pressure or constant volume? Is this H or U Constant volume, measuring internal energy, written as E or U c) Solve for the Heat Capacity of this bomb calorimeter in kJ/ C. Heat capacity = 10.2 kJ// C 44. Bomb Calorimeter Problem For the combustion of 1 mole of ethanol in kJ/mol use the following data and the above calibrated bomb calorimeter. 1.000 ml of ethanol (C2H5OH) is pipeted into the sample chamber of the bomb calorimeter and then 25 atm pressure of oxygen are added to insure complete combustion. The initial temperature is 22.185 C, the final temperature is 24.469 C. The density of the ethanol is 0.789 g/ml. a) Write the balanced combustion reaction for 1 mole ethanol C2H5OH (l) + 3 O2 (g) 2 CO2 (g) +3 H2O (l) b) Solve for Qcalorimeter and the Qrxn. Qcalorimeter = 23.3 kJ , Qrxn = -23.3kJ c) Solve for internal energy E = -29.5 kJ/g , -1358 kJ/mol d) Solve for work and enthalpy in kJ/mol under standard conditions. w = 2.48 kJ/mol, Hrxn= -1356 kJ/mol 45. Work Predict the sign for work, determine if the system is expanding or compressing and state if work is done on or by the system. a) 2 NO (g) + O2 (g) 2 NO2 (g) compression, (+) b) PCl5 (g) PCl3 (g) + Cl2 (g) expansion, (-) c) 2 C4H10 (g) + 13 O2 (g) 10 H2O (l) + 8 CO2 (g) compression, (+)