Answers included: 1. Solubility and Precipitation Reaction worksheet 2. Thermodynamics Worksheet 3. Problem Set 3b 4. Problem Set 3a CHEM 1412 Solubility and Precipitation Reaction 1. Mg(OH)2 2. Ag3PO4 a. reaction for dissolving (dissolution) Mg(OH)2(s) Mg2+ + 2OH- b. Algebraic expression of Ksp and (S) Ksp = S(2S)2=4S3= 1.5x10-11 S= molar solubility Dr. Ya-Ping Huang 3. Fe4[Fe(CN)6]3 Ag3PO4(s) 3Ag+ + PO43- Fe4[Fe(CN)6]3 4Fe3+ + 3 [Fe(CN) 6] 4- c. Molar 10 Ksp = [Ag+]3[PO43-] = (3S)3S =27S4 = 1.3x10-20 Ksp 3 1.5 x10 11 1.55 x10 4 M 4 4 solubility S= 3 d. Molar mass 58.33 e. Solubility, 1.55x10-4M)(58.33g/mol)= 9.04 x10-3 g/L S= 4 Ksp 4 1.3x10 20 4.68 x10 6 M 27 27 11 Ksp = (4S)4(3S)3 = 6912 S7 = 3.0 E-41 Ksp 7 3.0 x10 41 4.59 x10 7 M 6912 6912 S= 7 418.58 859.24 1.96 E-3 3.95 E-4 0.0049 g 9.9 x10-4g skip g/L f. g in 2.50 L sat’d solution M.V.MM = g. given solution 0.10 M HCl in 0.1 M AgNO3 Possible reaction or effect WB + SA, 100 % neutralization Common-ion (Ag+) effect on Ag3PO4(s) 3Ag+ + PO43- Molar solubility (1.55x10-4M)(2.5L)(58.33g/mol)= 0.0226g Mg(OH)2 + 2H+Mg2++ 2H2O Neutralization between WB, Mg(OH)2 and SA (HCl) is almost 100%, Solubility of Mg(OH)2 is based on how many moles of Mg(OH)2 reacts w/ HCl, and is limited by the amount H+ available Ksp = (3S+0.1)3 S = 1x 10-3 S S= 1.3 E-17 M skip Solubility = ½ (.01MH+)=.005M Given the combination of solutions,: (25.0 mL 0.010M of 1st solution and 50.0 mL 0.020 M 2nd solution) After dilution, [Solution1] = 0.010M(25.0mL)/75.0mL = 0.0033M, [Solution2] = 0.020M(50.0mL)/75.0mL = 0.0133M Solution combination 116108348 4. Cu(NO3)2 + NaOH 12 5. CaCl2 + Na3PO4 6. AgNO3 + K2CrO4 2/13/2016 Cu(NO3)2 + 2 HCl Cu(OH)2 + 2 HNO3 Cu(OH)2 Cu(OH)2(s) Cu2+ + 2OH- 3CaCl2 +2 Na3PO4 Ca3(PO4)2(s) + 3 NaCl Ca3(PO4)2 Ca3(PO4)2(s) 3Cu2+ + 2PO43- 2AgNO3 + K2CrO4 Ag2CrO4(s) +2 KNO3 Ag2CrO4 Ag2CrO4(s) 2Ag+ + CrO42- b. Ksp of the ppt 1.6x10-19 1.0x10-25 9.0x10-12 c. Qsp in solution (0.0033)(0.0133)2 =5.83x10-7 (0.0033)3(0.0133)2 =6.36x10-12 (0.0033)2(0.0133) =1.45x10-7 d. Will ppt form? Yes yes reaction a. formula of ppt Thermodynamics Worksheet Reactions Dr. Ya-Ping Huang 1. Decomposition of a fertilizer 2. Habor process 3. Ionization of water 2NH4NO3(s) 2N2(g) + 4H2O(g) + O2(g) N2(g) + 3H2(g) 2NH3(g) H2O(ℓ) H+ (aq) + OH-(aq) a H kJ/ mol rxn -236 -92.22 /mol rxn 55.8 kJ/mol rxn b qp for 500 g (kJ) NH4NO3(s) -737.5 NH3(g) -1356 kJ H2O(ℓ): 1550 kJ c n 7 -2 0 d E kJ/ mol rxn -253.35 -87.26 kJ/mol rxn 55.8kJ/mol rxn e S 1.0406 -0.1987 kJ/mol.K -0.0806 kJ/mol.K f Transition Temp Does not exist = 464.1 K = 190.9 C Does not exist g G -546.1 **a. -40.0 (by H & S) b. -32.38 (Gf) 79.9 kJ h Keq 4.53 x 1095 a.1.0 x 107 b. 4.7 x 105 1.01 x 10-14 kJ/mol.K 25 C 116108348 kJ/mol rxn 12 2/13/2016 i Spontaneous? yes yes 300 C pH value for pure water: 7.00 90 C j G kJ/mol rxn -832.47 21.64 kJ/mol rxn 85.06 kJ k Keq 7.08 x 1075 0.0107 5.78 x 10-13 l Spontaneous? yes No pH value for pure water; 6.12 ** There is discrepancy in G calculated by Gf and by G = H -T S for this reaction (2) at 25 C (1). 2NH4NO3(s) 2N2(g) + 4H2O(g) + O2(g) always spontaneous H = 2HfN2(g) + 4HfH2O(g) + HfO2(g) - 2HfNH4NO3(s) = 2(0) +4(-241.8) + 0 –2(-365.6) = -236 kJ/mol rxn 500 g mole.of . lim iting .reagent n ceofficient.in.balanced .equation 80 g / mol 3.125mole.reaction 2 qp = 3.125 mol rxn x (-236 kJ/mol rxn) = -737.5 kJ H = E +nRT, n=mole of gas on RHS – mole of gas on LHS = 7 -0 =7 E = H -nRT = -236 kJ – (7)(8.314E-3)(298.15) = -737.5 kJ –17.35 = -253.35 kJ S = 2S.N2(g) + 4S.H2O(g) + S O2(g) – 2S.NH4NO3(s) = 2(191.5) +4(188.7) + 205 –2(151.1) = 1040.6 J/mol.K = 1.0406kJ/mol.K H o 236kJ / mol.rexn Ttransition 227 K ( Dose.not.exist , Temp.can.not.be.lower.than.0 K ) o 1.0406kJ / k .mole.rexn S (In this reaction, reaction is always spontaneous, favored by lower enthalpy, H < 0 and increased entropy, S> 0) 25 C :G = H -T S = -236kJ – 298(1.0406) = -546.1 kJ/mol rxn (or G = 2GfN2(g) + 4GfH2O(g) + GfO2(g) - 2GfNH4NO3(s) = 2(0) +4(-228.6) + 0 –2(-184) = -546.4 kJ/mol rxn) 116108348 12 2/13/2016 G = -5.709logK G o 546.1 log K 95.66 5.709 5.709 K 10 95.66 4.53x10 95 , 300 C :G = H -T S = -236 – (300+273)(1.0406) = -832.47 kJ G = -2.303RT(logK) G o 832.47 log K 75.85 2.303RT 2.303(8.314 x10 3 )(573) K 10 75.85 7.08 x10 75 (2) Habor Process N2(g) + 3H2(g) 2NH3(g) H = 2HfNH3(g) – (HfN2 (g) + 3HfH2(g) = 2(-46.11)-0 = -92.22 kJ/mol reaction 500 g mole.of . lim iting .reagent n ceofficient.in.balanced .equation 17.03g / mol 14.7mole.reaction 2 qp = 14.7 mol rxn x (-92.22 kJ/mol rxn) = -1356 kJ (3) H2O(ℓ) H+ (aq) + OH-(aq) always nonspontaneous H = HfH+ (aq) + HfOH-(aq) - HfH2O(l) = 0 + (-230.0) –(-285.8) = 55.8kJ/mol rxn qp = [500g/(18)]mol x 55.8 = 1550 kJ S = SH+ (aq) + SOH-(aq) - SH2O(l) = 0 + (-10.7) –(69.91) = -80.6J/K.mol rxn = -0.0806kJ/K.mol rexn 25 C G = GfH+ (aq) + GfOH-(aq) - GfH2O(l) = 0 + (-157.3)-(-237.2) = 79.9 kJ/mol rexn logK = G /-5.709 = 79.9/-5.709 = -13.995 K = Kw = 10-13.995 = 1.01 x 10-14 Kw = [H+][OH-] = [H+]2, [H+] = 1.01x10 14 1.005x10 7 , pH =-log(1.005x10-7) =6.998 (If use G = H -T S = 55.8kJ/mol - 298(-0.0806) = 79.8 kJ ) 90 C: G = H -T S =55.8kJ/mol - 363(-0.0806) = 85.06 kJ 116108348 12 2/13/2016 G = -2.303RT(logK) G o 85.06 log K 12.24 2.303RT 2.303(8.314 x10 3 )(363) Kw = [H+][OH-] = [H+]2, [H+] = K 10 12.24 5.78 x10 13 5.78x10 13 = 7.5 x 10-7, pH = 6.12 Problem Set 3b: (2) qH2O = (4.184 J/goC)(100 mL)(1.02 g/mL)(26.65 – 23.35oC) = 1408 J qCal = (24.0 J/oC)(26.65 – 23.35oC) = 79.2 J (Total heat evolved = qH2O + qCal = 1487 J) qtotal= qH2O+ qCal+ qrexn = 0 qrexn = -1487 J = nH To find n, you have to find moles of each reagent and find which reactant is the limiting reagent. mol of CuSO4 = (0.400M)(0.050L) = 0.020 mol x 1molrexn 0.0200molrexn 1molCuSO4 mol of NaOH = (0.600M)(0.0500L) = 0.030 mol x 1molrexn 0.0150molrexn 2molNaOH So NaOH is limiting reagent, and n = 0.0150 mole reaction qrexn = -1487 J = nH = (0.0150 mole reaction) H H = -1487 J/(0.0150 mole reaction) = - 99133 J/mole rexn = -99.13 kJ/mole rexn Complete thermochemical equation includes balanced chemical equation and H CuSO4(aq) + 2NaOH(aq) Cu(OH)2(s) + Na2SO4(aq) H = -99.13 kJ/mol rxn 4. The thermite reaction, used for welding iron, is as following: 8 Al(s) + 3Fe3O4(s) 9 Fe(s) + 4Al2O3(s) A. To calculate H, the best method is using Hf: 8 Al(s) + 3Fe3O4(s) 9 Fe(s) + 4Al2O3(s) H = 9Hf, Fe(s) + 4 Hf,Al2O3(s) – 3 Hf,Fe3O4(s) –8 Hf, Al(s) = 4(-1676) – 3(-1118) = -3350 kJ/mol rxn B. To find the energy released, given both reactants, it’s a limiting reagent type of problem. The approach is to calculate 116108348 12 2/13/2016 the energy released by the reaction of each reactant. The smaller value is the answer. a. H based on 8.0 g Al(s): 8.0 gAlx 1molAl 1molrexn 3350kJ x x 124kJ 27 gAl 8molAl 1molrexn b. H based on 20.0 g Fe3O4 1molFe3O 4 1molrexn 3350kJ 20.0 gFe3O 4 x x x 96.3kJ 232 gFe3O 4 3molFe3O 4 1molrexn The answer is therefore 96.3 kJ released. And Fe3O4(s) is the limiting reagent. c. Grams of Fe produced is based on the limiting reagent Fe3O4(s) 1molFe3O4 9molFe 55.8gFe x x 14.4 gFe 232 gFe3O4 3molFe3O4 1molFe Q7. Estimate G° and determine if the following reaction is spontaneous at 25, 1000 and 2000°C? 20.0 g Fe3O4 x N2(g) + O2(g) 2NO(g) [Ans]: G° = H° - TS° H° = Hf°,RHS - Hf°,LHS = 2Hf°,NO(g) – (Hf°N2(g) + Hf°,O2(g)) = 2(90.25) – (0+0) = 180.5 kJ/mol rxn S° = S°,RHS - S°,LHS = 2S°,NO(g) – (Hf°N2(g) + Hf°,O2(g)) = 2(210.7) – (191.5 + 205) = 24.9 J/K.mol rxn = 24.9x10-3 kJ/K.mol rxn G° = H° - TS° At 25°C (298.15 K) G° = 180.5 kJ/mol rexn –(298.15)( 24.9x10-3 kJ/K.mol rxn) = 173.08 kJ/mol rxn (non-spontaneous) At 1000°C (1273 K) G° = 180.5 kJ/mol rexn –(1273)( 24.9x10-3 kJ/K.mol rxn) = 148.80 kJ/mol rxn (non-spontaneous) At 2000°C (2273 K) G° = 180.5 kJ/mol rexn –(2273)( 24.9x10-3 kJ/K.mol rxn) = 123.90 kJ/mol rxn (non-spontaneous) At 25°C (298.15 K) G° can be calculated by GHf° 116108348 12 2/13/2016 G° = Gf°,RHS - Gf°,LHS = 2Gf°,NO(g) – (Gf°N2(g) + Gf°,O2(g)) = 2(86.57) –(0+0) = 173.14 kJ/mol rxn, almost identical to the one calculated by G° = H° - TS° Transition temperature, Ttransition = H 180.5kJ / mol.rxn 7249 K 6976C S 24.9 x10 3 kJ / K .mol.rxn CHEM 1412 Problem Set #3a Dr. Ya-Ping Huang Solubility Equilibrium 1. Calculate the molar solubility of CaF2 at 25oC in: a. pure water (2.1 x 10-4 M) b. in 0.010M Ca(NO3)2 solution (3.1 x 10-5 M) c. in 0.010M KF solution (3.9 x 10-7 M) [Ans]: The 1st step is to write the equation for dissolution, and find the relationship between Ksp and molar solubility. . a. R CaF2(s) Ca2+(aq) + 2F-(aq) E S 2+ S - Ksp = [Ca ]eq [F S3 K sp 4 3 ]eq2 Let S represent the molar solubility 2S 2 = (s)(2s) = 4S3 = 3.9x10-11 3.9 x1011 3 9.75x1012 2.14 x10 4 M 4 b. In 0.010M Ca(NO3)2 solution, there is the common –ion effect. The extra Ca2+ from Ca(NO3)2 will reduce the solubility of CaF2(s) (Le Chatelier’s principle) –the common-ion effect R CaF2(s) Ca2+(aq) + 2F-(aq) E S S Let S represent the molar solubility 2S +0.010 2+ [F-]eq = 2S [Ca ]eq = 0.010+ S Ksp = [Ca2+]eq [F-]eq2 = (S+0.010)(2S)2 (0.010)(2S)2 = 0.04S2 = 3.9x10-11 (s is dropped from s+0.010, because when there is common-ion effect , the solubility will be severely reduced such that the s term is negligible compared to the concentration of commen-ion) 116108348 12 2/13/2016 S Ksp 3.9 x1011 3.12 x10 5 M 0.04 0.04 Ksp = [Ca2+]eq [F-]eq2 = (s)(2s)2 = 4S3 = 3.9x10-11 c. in 0.010M KF solution: there is the common –ion effect. The extra F- from KF will reduce the solubility of CaF2(s) (Le Chatelier’s principle) R CaF2(s) Ca2+(aq) + 2F-(aq) E S S Let S represent the molar solubility 2S +0.010 [Ca2+]eq = S [F-]eq = 0.010+ 2S Ksp = [Ca2+]eq [F-]eq2 = (S)(0.01+2S)2 (S)(0.01)2 = 1.0x10-4S = 3.9x10-11 S = Ksp/1.0x10-4 = 3.9x10-7 M 2. Calculate the molar solubility of BaSO4 at 25oC: a. in pure water b. in 0.10M Na2SO4 solution c. Grams of BaSO4 dissolved in 2.0 Liters of water e. LD50 of Ba2+ for rat is around 20 mg/Kg body weight of rats. Would the Ba2+ in part (d) dangerous if ingested? (1.05 x 10-5M, 1.1 x 10-9 M, 4.9 x 10-3 g, 2.16 mg) [Ans]: a. In pure water (no common-ion or other effects) BaSO4(s) Ba2+(aq) + SO42-(aq) Let S represent the molar solubility, then [Ba2+] = S and [SO42-] = S Ksp = [Ba2+] [SO42-] = (S)( S)= S2 = 1.1x10-10 S= 1.1x1010 1.05x105 M b. in 0.10M Na2SO4 solution, the additional SO42- ions from Na2SO4 will reduce solubility of BaSO4 through common-ion effect Ksp = [Ba2+] [SO42-] = (S)(0.10+S)= S(0.10) = 1.1x10-10 S=1.1x10-9 M d. mg of Ba2+ in 1.5 L of saturated BaSO4 solution. 1.05x105 mol 137 g 1000mg mg of Ba2+ = (M)(V)(MM) = x(1.5L)( 2.16mg ) L 1mol.Ba 1g 116108348 12 2/13/2016 e. LD50 refers to lethal dose for 50% population exposed. Assume a typical adult weighs 50kg, then LD50 = (20mg/Kg body weight)(50 kg) = 1000mg. So 2.16 mg is quite safe. 3. How would the solubility of the following substances be affected by pH of a solution? a. Ni(OH)2 b. CaCO3 c. BaSO4 d. AgCl [Ans]: The key to see how does pH of a solution affect the solubility is to see if additional H+ will affect the dissolution process a. Ni(OH)2 (s) Ni2+(aq) + 2OH-(aq) Dissolution reaction Rexn w/ H+ dissolution solubility A Ni(OH)2 (s) Ni(OH)2 (s) Ni2+(aq) + 2OH-(aq) H + OH H2O B CaCO3 CaCO3 Ca2+(aq) + CO32- 2H++CO3 2- H2O + CO2 C BaSO4 BaSO4(s) Ba2+(aq) + SO42-(aq) H++SO42HSO4- Slightly favored barely d AgCl AgCl Ag+(aq) + Cl-(aq) No reaction Not affected same + - 4. A solution is 0.10 M in Mg(NO3)2 and the pH is adjusted to 8.0. Would Mg(OH)2 precipitate? (No) 5. A solution is 0.10M in Mg(NO3)2. What concentration of OH- is required to just start precipitation of Mg(OH)2? If NH3-NH4+ buffer is used to control the pH, and [NH3] = 0.10 M. What concentration of NH4+ is required to prevent the precipitation of Mg(OH)2? (1.2 x 10-5M, >0.15 M) [Ans]: To find out conditions for ppt, compare the requirements for different situation: The easiest way is to calculate conditions for saturated solution and modify condition for different situation Qsp = [Mg2+][OH-]2 - Saturated soln, equilibrium Unsaturated soln, = Ksp = 1.5x10-11 < Ksp no ppt -5 > Ksp [OH ] 1.2x10 M < 1.2x10 M > 1.2x10-5 M [NH4+] 0.15M > 0.15 M, need more CA (NH4+] to keep solution acidic < 0.15M, need less CA (NH4+] to keep solution basic For saturated solution, Qsp = [Mg2+] [OH-]2 116108348 ppt -5 (0.10) [OH-]2 = 1.5x10-11 12 2/13/2016 1.5 x10 11 1.2 x10 5 M 0.10 [OH-] = If [OH-] is maintained by buffer: you can either use Handerson-Hasselbalch equation or Kb of NH3 Kb of NH3 will be more straight forward: NH3 + H2O NH4+ + OH- Kb= [ NH 4 ][OH ] [ NH 3 ] 1.8 x10 5 [ NH 4 ][1.2 x10 5 ] 0.10 (1.8 x10 5 )(0.10) 0.15M 1.2 x105 [ NH 4 ] 6. 100mL 0.020 M NaF is mixed with 200 mL of 0.050 M Ca(NO3)2. What would be the possible reaction? Would there be any precipitate? Will the ppt be visible with naked eyes? (yes, yes) 7. Solid AgNO3 is slowly added to a solution that is 0.0010M in NaCl, NaBr and NaI. Calculate the [Ag+] required to initiate the ppt of each silver salt. Assume the solution volume does not change in the process. (AgCl, requires [Ag +] = 1.8 x 10-7M, AgBr: [Ag+] = 3.3 x 10-10M, AgI: [Ag+] = 1.5 x 10-13M) [Ans]; For each ppt, 1st calculate the [Ag+] required for saturation. All 3 ppts (AgCl, AgBr, AgI) follow the same dissolution process: AgX(s) Ag+(aq) + X-(aq) (X= Cl, Br or I) In saturated solutions, Qsp = [Ag+]eq [X-]eq = Ksp X Ksp [Ag+]eq = K sp [X ] [Ag+]eq= K sp K sp Order of ppt [X ] 0.001 AgCl Cl 1.8x10-10 1.8x10-7 M 3rd, requires most amt of Ag+ AgBr Br 3.3x10-13 3.3x10-10 M 2nd, requires 2nd amt of Ag+ AgI I 1.5x10-16 1.5x10-13 M 1st, requires least amt of Ag+ ** Since all three ppts have the same ion ratio, the Ksp indicates the relative molar solubility AgI has lowest Ksp, therefore the lowest molar solubility, will be the 1st to ppt AgCl has highest Ksp, therefore the highest molar solubility, will be the last to ppt 8. Solid AgNO3 is slowly added to a solution that is 0.0010M in NaCl and Na2CrO4. Which one will ppt 116108348 12 2/13/2016 first, AgCl or Ag2CrO4? Calculate the [Ag+] required to initiate the ppt of each silver salt. (AgCl 1st, requires [Ag+] = 1.8 x 10-7, Ag2CrO4 requires [Ag+] = 9.5 x 10-5) [Ans]: AgCl and Ag2CrO4 have different ion ratio, values of Ksp does not indicates the relative molar solubility AgCl Ion ratio Ksp Ksp and conc [Ag+]eq= K sp K sp 1:1=1 1.8x10-10 Ksp= [Ag+]eq [Cl-]eq 9.0x10-12 Ksp=[Ag+]2eq [CrO42-]eq [X ] Ag2CrO4 2:1 = 2 [Ag+]eq = Order of ppt 0.001 K sp [Cl ] 1.8 x10 10 1.8 x10 7 0.001 K sp 2 4 [CrO ] 9.0 x10 12 9.5 x10 5 M 0.001 1st, requires less Ag+ 2nd, requires more Ag+ 9. Refer to problem 7, what is [Cl-] and [I-] when AgBr just starts to precipitate? ([Cl-] = 0.001, [I-] = 4.5 x 10-7 when AgBr starts to ppt. [Ans]: When AgBr starts to ppt, [Ag+ ] = 3.3x10-10 M. AgCl has not ppt’d yet. All Cl- remains in solution. [Cl-] = 0.001M AgI ppt’d before AgBr starts to ppt. Once pptn starts, the Qsp of the compound that has ppt’d always equals to its Ksp. I K[ Ag sp, AgI ] 1.5 x1016 4.5 x107 M 10 3.3x10 10. A 0.010 M solution of AgNO3 is made 0.50 M in NH3 and Ag(NH3)2+ complex forms. Ag+(aq) + 2 NH3(aq) Ag(NH3)2+(aq) Kf = 1.7 x 107. a. What is the equilibrium concentration of Ag+ in the solution? R Ag+(aq) + 2 NH3(aq) Ag(NH3)2+(aq) Kf = 1.7 x 107 I 0.010 0.50 . 0 C -x -2x +x E 0.01-x 0.5-2x (2.56 x 10-9 M) x K f 1.7 x10 7 116108348 [ Ag ( NH 3 ) 2 ] x 2 [ Ag ][ NH 3 ] (0.01 x)(0.5 2 x) 2 12 2/13/2016 This is a relatively complicated equation to solve. But the large size of Kf, it is reasonably to assume that the reaction is almost 100%, and the limiting reagent, Ag+, will be completely used up in the reaction. We can re-write the RICE as following R Ag+(aq) + 2 NH3(aq) Ag(NH3)2+(aq) Kf = 1.7 x 107 I 0.010 0.50 . 0 C -0.01 -0.02 +0.01 0.48 0.01 E 0 K f 1.7 x10 7 [ Ag ( NH 3 ) 2 ] 0.01 [ Ag ][ NH 3 ]2 [ Ag ](0.48) 2 [ Ag ] 0.01 2.56 x109 M (1.7 x107 )(0.48) 2 b. What % of the total silver is in the form of Ag+ (aq)? (2.56 x 10-5 %) 9 % of silver as Ag+= [ Ag ] x100 2.56 x10 x100 2.56 x10 5% 0.01 0.01 Most of Ag exists in the form of complex ion, only very small % stays as Ag+ This in fact drives the dissolution of AgCl forward and greatly increase the solubility of AgCl 116108348 12 2/13/2016