Chemistry 0 Spring 07 Discussion #3, Chapter 7 Student name TA name Section Things you should know when you leave Discussion today:. ΔSsys = ΔrS = Σ [ni (S )]product - Σ [nj (S )]reactants. ΔGº = -T ΔSnet = ΔH sys - TΔS sys a. ΔG rxn ( at 5 C only) = n P (G o f ) - product b. ΔGº = - RT lnk = -.3 RT log K -( ΔGº/RT.3) c. K= 0 d. ΔG = -ne F E = -q E Q 3. ΔG = RT ln( ) =.3 RT log K reactants ( K Q ) = ΔG + RT ln Q a. ΔG = -T ΔSnet = ΔHsys - TΔSsys b. ΔG= -ne FE = -q E i. ΔG<0 process is Spontaneous ii. ΔG>0 process is Not Spontaneous iii. ΔG=0 process is at Equilibrium n R (G f o ). Circle the value of ΔG when both products and reactants are in their standard states. (Note: Q=) Circle the value of ΔG when Q = K. Circle the value of ΔG when Q = K. ΔG = ΔG = 0 ΔG = ΔG None of these ΔG = ΔG = 0 ΔG = ΔG None of these ΔG = ΔG = 0 ΔG = -RT lnk None of these Circle the value of ΔG when Q > K. When would ΔG = 0? ΔG = ΔG = 0 ΔG = -RT lnk None of these. a) If ΔG= 5 kj/mol and ΔGº= 4 kj/mol circle everything that must be true: Q= Q> Q< Q<K Q=K Q>K b) ( at home ) Assuming temperature of 98 K calculate the values of K and Q. (Useful Hint: at T=98K value of.3rt =.3 8.34(J.(mol K) 98K =5698J/mol 6kJ/mol)
3. a) If ΔG= -5kJ/mol and ΔGº= 3kJ/mol circle everything that must be true: Q = Q > Q < Q < K Q = K Q > K b) At home : Assuming temperature of 98 K, calculate the values of K and Q. 4. The standard free energy change for the process A (aq) + B (aq) 3C (aq) is ΔG = +54 kj/mol. If the concentration of B is decreased from M to 0.50 M (but concentrations of A and C stay at standard states) circle the value of the free energy change, ΔG, relative to ΔG. ΔG < ΔG ΔG = ΔG ΔG > ΔG 5. Remember that ΔGº = - RT ln K = ΔHºsys TΔSºsys and so we can derive ln K= RT H sys + S sys R ln Keq Reaction Reaction 0 High T region /T 0 T Reaction 3 Low T region /T T 0 /T Reaction 4 a. When ln K is positive. What does it mean? Why? b. When ln K is negative. What does it mean? Why? c. When ln K is zero. What does it mean? Why? H sys Using that lnk= + RT following questions: S sys R and that equations of the line is y = mx + b answer the
d. What is the y-intercept of the expression for lnk? e. What is slope of the expression for lnk? f. The slope is positive. What does it mean? Why? g. The slope is negative. What does it mean? Why? For Reactions,, 3 and 4 in the plot above, answer the following questions. a. Is the reaction endothermic or exothermic and at what temperatures? Reaction : Reaction : Reaction 3: Reaction 4: b. If the reaction above are redox reactions, which ones will have positive standard voltages and at what temperatures? Reaction : Reaction : Reaction 3: Reaction 4: c. Does the reaction increase or decrease entropy of the system and at what temperatures? Reaction : Reaction : Reaction 3: Reaction 4: d. For each reaction choose at what temperatures the ratio of product to reactants will be greater than or smaller than? Reaction : Products/ Reactants >: High T Low T never always Products/ Reactants <: High T Low T never always Reaction : Products/ Reactants >: High T Low T never always Products/ Reactants <: High T Low T never always Reaction 3: Products/ Reactants >: High T Low T never always Products/ Reactants <: High T Low T never always Reaction 4: Products/ Reactants >: High T Low T never always Products/ Reactants <: High T Low T never always 3
e. It is a well-known fact that mixing any group metal and water leads to an explosion. The plot of which reaction corresponds to the reaction between Na and water: Na(s) + HO(l) Na + (aq) + OH - (aq) + H(g) Reaction Reaction Reaction 3 Reaction 4 f. The plot of which reaction corresponds to freezing of water? Reaction Reaction Reaction 3 Reaction 4 6. For the following combustion reaction calculate ΔG at 5 C. : ΔG f(kj/mol) C6HO6 (s) + 6O (g) 6 CO (g) + 6 HO (l) (only at 5 C) O(g) 0 C6HO6 (s) -900. CO (g) -400. HO(l) -40. Without doing a calculation, at what temperatures will this process cease to be spontaneous? 7. For autoionization of water at 330 K, Kw=0-3 and at 300K, Kw=0-4. Calculate the value of ΔH and ΔS. Do your calculations to significant figure. 8. You have a buffer with a ph = 5 at two different temperatures: T = 300 K and T = 330 K HA(aq) + HO (l) A - (aq) + H3O + (aq) You need to have the following ratios of weak acid and conjugate base to make this happen: at T [A - ]/[HA] = / at T [A - ]/[HA] = /4 To answer the following questions you need to draw the plot of lnk verses /T. (Hint:lnK=.303logK) 4
a. Will this reaction be exothermic, endothermic or neither. Circle one: ΔH > 0 ΔH = 0 ΔH < 0 b. The system entropy change will be: Circle one: ΔS > 0 ΔS = 0 S < 0 9. Your body needs glutamine (an amino acid used to make proteins) for your survival. While glutamate is useless to you as-is, you need to make glutamine out of glutamate and ammonium ions through the following reaction: Glutamate + NH4 + glutamine (ΔG rxn=+4.kj/mol) What problem(s) do you see with this process? A wise man once said, Don t panic! You also make glutamine synthetase, an enzyme that helps this process along. If the process of : ATP ADP + PO4-3 (ΔG rxn= -30kJ/mol): were somehow linked to the glutamine synthesis above, what would the new reaction be? (Don t worry about balancing.) What would the ΔG rxn for this new reaction be? 0. Given the two reactions below, find the relationships between ΔGº and ΔGº. A(aq) + B(g) C(s) + D(aq) with Keq=K and ΔGºrxn=ΔGº C(s) + D(aq) A(aq) + B(g) with Keq=K and ΔGºrxn=ΔGº. Given the two reactions below, find the relationships between ΔGº and ΔGº. 3 A(aq) + B(g) C(s) + D(aq) with Keq=K and ΔGº=ΔGº A(aq) + 3 B(g) 3 C(s) + 3 D(aq) with Keq=K and ΔGº=ΔGº. For the following reaction at 5ºC using information below. 3H(g) + N(g) NH3(g) ΔGº kj/mol P (atm) H(g) 0 0.0 N(g) 0 0.04 Calculate value of ΔG NH3(g) -6 0. Calculate value of K Calculate value of Q 5
Calculate value of ΔG Based on your calculation, did the reaction pass an equilibrium point? Based on your calculation, will the reverse reaction be spontaneous or not? 3. For the following reaction: Br(l) Br(g) For the reaction above at 300K, 35K, 340 K use the information given, to calculate ΔHsys, ΔSsys, ΔSsur, ΔSuniv, ΔG and the temperature at which process will cease to be spontaneous. ( Do your calculations to significant figures. Assume that ΔH rxn and ΔS rxn are independent of temperature.) ΔH f (kj/mol) S (J/ Kmol) ΔG f(kj/mol) (only at 5 C) Br(g) 30. 50. 3.0 Br(l) 0 50. 0 Useful information and preparation for chapter 8 not part of exam 3: t. Rate = ; units: M s. Rate of chemical reactions depends on: a. Temperature b. Catalysts c. Initial concentrations d. Magnitude of the rate constant 3. Initial Reaction Rates: a. For a reaction: aa + bb cc + dd [ A] [ B] [ C] [ D] b. Initial Reaction Rate = = = = a t b t c t d t c. Where is an individual rate of loss of A, t [ B] b [ A ] ; [ C] c [ A ] t a t t a t 4. Rate Law: a. Differential Rate Law: rate versus concentration aa + bb cc + dd rate Rate = k [A] x [B] y Where k is a rate constant k= [A] x [B] y Where x is the order of the reaction with respect to species A, and y is the order of the reaction with respect to species B. b. Comparing rates: rate rate k[a] x y [B] k[a] x y [B] c. Units of the rate constant depend on over all reaction order. M ( xy) k = s M where (x+y) is the order of the overall reaction. x y M M s 6
5. Integrated Rate Laws: see attached table for more information a. Zero-Order: [R] t [R] 0 kt b. First-Order: ln [R] t kt [R] 0 c. Second-Order: kt [R] t [R] 0 Questions on the material in chapter 8 not part of exam 3:. A study of the reaction below gave the following result: NO(g)+O(g)NO(g) Fill in the missing information in the table [NO] [O] - d [ NO] dt Ex 0.05 0.085 0.00 Ex 0.050 0.085 0.080 Ex3 0.050 0.0370 0.60 Ex4 0.05 0.0370 0.040 [M/s] Reaction rate What order is the reaction with respect to [NO]? What order is the reaction with respect to [O]? Write the rate law: rate = k [ ] x [ ] y Overall rate order = What are the units of this k? Calculate rate constant: k = What is the reaction rate when [NO] = [O] = 0.00M For each reactant, circle which plot correlating concentration with time will give you a straight line, and what the sign of the slope will be. [NO] vs. time /[NO] vs. time ln[no] vs. time Slope: positive negative zero 7
[O] vs. time / [O] vs. time ln[o] vs. time Slope: positive negative zero. A study of the reaction below gave the following result: [NO] [Cl] NO(g) + Cl (g) NOCl(g) d[no] RXN [M/s] dt rate Ex..5 0.3 Ex 4.8.5 0.5 What order is the reaction with respect to [NO]? Ex3. 5.0 0.9 What order is the reaction with respect to [Cl]? Fill in the table for reaction rate with respect to NO Write the rate law: rate=k [ ] x [ ] y Overall rate order = What are the units of this k? 3. Consider the chemical reaction: 3A + 4B C + D. The experimentally determined rate law is Rate = k[a] [B]. When the concentrations are [A]i = 0.5 M and [B]i = 0.0 M, the rate of consumption of B is 8 x 0-5 M/s. Give the value of the rate constant, k, including the units. 4. Consider the chemical reaction: 3A + 4B C + D. The experimentally determined rate law is Rate = k [A] [B]. When the concentrations are [A]i = 0.3 M and [B]i = 0.0 M, the rate of consumption of B is 6 0-4 M/s. Give the value of the rate constant, k, including the units. 5. Consider the reaction A + B D + C. Three experiments were conducted and the reaction rate of each reaction was determined. For each of the reactants, find the appropriate order Initial conc. (mol/l) Initial Rate Exp [A] [B] (mol/l sec) #.0 0 3.0 0 3 3. 0 7 #.0 0 3 3.0 0 3 9.6 0 7 #3 4.0 0 3 3.0 0 3.9 0 6 8
6. Consider the comproportionation reaction of bromate and bromide to make bromine gas. Four experiments were conducted and the reaction rate was determined. H + (aq) + BrO3 (aq) + 0 Br (aq) 6 Br (g) + 6 HO (l) Initial Concentrations (mol/l) [BrO3 ] [Br ] [H3O + ] Initial Reaction Rate (mol/l sec) Exp. # 0.0 0.0 0.0.0 # 0.0 0.0 0.0.0 #3 0.0 0.30 0.0 3.0 #4 0.0 0.0 0.0 8.0 a) Using the data, determine the order of the reaction with respect to H3O +. b) What is the rate of formation of bromine gas in experiment #? In Peroration for next week 7. In a first order chemical reaction, the concentration of a reactant is observed to fall from.000 M to 0.50 M between t = 6 s and t = 0 s. What is the concentration (in M) at t = s? 8. The first order reaction is 60% complete after 00 seconds. What is rate constant k and t½ for this reaction? 9. Fluorine-8 has a half-life of 0 minutes. After 4 half-lives, how much time has elapsed? What percentage of your original F-8 remains? What percentage has decayed? (Answer: tpass=440minutes, remains=6.5%, decayed=93.75) 0. You are trying to find the half-life of a new, meta-stable compound (X) created in your lab. You analyze the amount of X you have 30 minutes after production of X. You find you have 0% of the original amount. Approximately, what is t½? 6 m. <t½< 7.5 m. 7.5 m. <t½< 0 m. 0 m. <t½< 5 m. 5 m. <t½< 30 m.. For another compound (Y), 94% of an original 00.0 g has decayed in 60.0 minutes. Express your answer to ONE SIGNIFICANT FIGURE. (a) How many grams of Y is remaining? (Answer: 6g) (b) How many half-lives have elapsed? (Answer: n=4 half-lives pass) (c) What is the half-life of this compound? (Answer: t½=5 min) 9
Reaction Order Zero order reaction x = 0, y = 0, x + y = 0 Differential Rate Law Conc. Dependence Rate = k[a] 0 [B] 0 Rate = k Rate is Constant Rate is independent of concentration. Units of the rate constant, k, depend on the reaction order. (M/s) = units of k k = (M/s) are the units of the rate In general the units of k are a good indicator of the reaction order. Half life, t/, Integrated Rate Law [A]final = [A] - ak t When: [A]final = = [A]in- akt/ [ ] t/ = A ak [A] [A]0 Graph Concentration versus time [A]0 is [A] at t = 0 slope= -ak = -k t(s) First order reaction Example: x =, y = 0, x + y = Rate = k[a] [B] 0 Rate = k[a] Rate depends linearly on concentration (ex. doubling [A] doubles the rate) (M/s) = units of k * (M) k = (/s) ln [A]final = ln [A] - ak t final ln = -ak t When: [A]final = t/ = ln/ak =.3log/ak (half life is independent of concentration) t/ is constant ln [A] ln [A]0 slope= -ak = -k t(s) Second order reaction Example: x =, y = 0, x + y = Rate = k[a] [B] 0 Rate = k[a] (M/s) = units of k * (M) k = M s /[A]final = /[A] + ak t When : [A]final = t/ = ak /[A] /[A]0 slope= ak = k t(s) aa + bb cc [ A] [ B] [ C] rate(m/s) = = = = k [A] x [B] y a t b t c t x and y are independent of stoichiometry and can only be determined from experimental data