EXERCISES. 16. What is the ionic strength in a solution containing NaCl in c=0.14 mol/dm 3 concentration and Na 3 PO 4 in 0.21 mol/dm 3 concentration?

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1 EXERISES 1. The standard enthalpy of reaction is 512 kj/mol and the standard entropy of reaction is 1.60 kj/(k mol) for the denaturalization of a certain protein. Determine the temperature range where the reaction is spontaneous. 2. What is the best coefficient of performance of an air conditioner if we want to cool down the room to 20 and the temperature outside is 35? 3. A photo is exhibited where it is stated that there is a single point where four phases (ice I, ice II, liquid water and water vapor) are stable in a system with a single component. Is it possible based on the phase rule? 4. The fugacity coefficient of a real gas is 0.72 at T=200 K under 50 atm pressure. What is the change in the Gibbs free energy compared to the ideal gas for 5 mol real gas? 5. The boiling point of ethanol is 78.3 at Pa and the enthalpy of evaporation is 39.3 kj/mol. alculate the vapor pressure of ethanol at Mt. Blanc is 4807 m high. At the summit the pressure is 55.5 kpa. Determine the boiling point of water at that elevation. The enthalpy of evaporation is kj/mol. The boiling point of water is 100 at Pa. 7. The highest point in Hungary is Kékestető (1015 m) where the pressure is 90.0 kpa. Determine the boiling point of water at that elevation. The enthalpy of evaporation is kj/mol. The boiling point of water is 100 at Pa. 8. The vapor pressure of dichloromethane is 400 torr at 24.1 and the enthalpy of evaporation is 28.7 kj/mol. What is the temperature of the vapor when its vapor pressure is 500 torr? (760 torr = Pa) 9. We mix 2 mol O 2 gas, 4 mol N 2 gas, and 0.5 mol Ar gas under 1 atm pressure and at 293 K in a vessel with 5 dm 3 in volume. What is the change in entropy, enthalpy, and Gibbs energy during mixing if the gases behave as ideal gases? R=8.314 J/(mol K) 10. The vapor pressure of pure ethanol is 48 torr at 20, while that of pure diethyl ether is 450 torr. The vapor pressure of diethyl ether is 260 torr in the diethyl ether ethanol mixture when the mole fraction of ethanol is 0.6 in the mixture. Is this an ideal mixture? If not, what is it? (760 torr = Pa) 11. The mixture of benzene and toluene behaves ideally. What is the vapor pressure of the mixture when x toluene = 0.35 in the solution? The vapor pressure of pure toluene is torr and that of pure benzene is torr. (760 torr = Pa) 12. The vapor pressure of pure acetone is torr and that of pure chloroform is 293 torr at The total vapor pressure is 286 torr of a solution with mol acetone and mol chloroform. The mole fraction of the acetone in the vapor is The Henry s law constant for chloroform in acetone is 145 torr at this temperature. alculate the activity and the activity coefficient, defined in terms of mole fraction, for acetone and for chloroform. (760 torr = Pa) 13. alculate the number of moles of nitrogen dissolved in 5.00 l blood at a depth of 200 m, where the partial pressure of nitrogen is 16 atm. The Henry s law constant is 1430 atm mol 1 l at these conditions. alculate the volume of this amount of nitrogen at 1.00 atm and at 20. (1 atm = Pa) 14. The dilute solution of bromine in l 4 is an ideal dilute solution. alculate the chemical composition of the solution in terms of mole fraction if the vapor pressure of bromine is 8 torr. alculate the vapor pressure of l 4 at this chemical composition. The Henry s law constant is torr for bromine. The vapor pressure of pure l 4 is torr. (760 torr = Pa) 15. The following data give the pressures for carbon disulfide/dimethyl oxymethane solutions at 298 K: X S2 p S2 /kpa p DMO /kpa alculate the activities and activity coefficients of S 2 for a solution with x S2 = mole fraction. 16. What is the ionic strength in a solution containing Nal in c=0.14 mol/dm 3 concentration and Na 3 PO 4 in 0.21 mol/dm 3 concentration? 17. alculate the mean activity coefficient for a(no 3 ) 2 solution with mol/dm 3 concentration using the Debye- Hückel limiting law at 298 K. 18. The concentration of glucose inside a cell is 0.12 mm and that outside is 12.3 mm. alculate the Gibbs energy change for the transport of 3 moles of glucose into the cell at 37. 1

2 19. The concentration of K + is 400 mm in the intracellular fluid of a nerve cell, while that in the extracellular fluid is 20 mm. alculate the Gibbs free energy change for the transfer of 3 moles of ions outside at 37 if the electric potential inside the cell is E cell = -70 mv relative to the outside. 20. The height of Redwood tree in alifornia is 105 m. alculate the osmotic pressure necessary for water to be transported from the roots to the top if the density of water is 1 g/cm 3 and g=9.81 m/s The osmotic pressure of a 100 cm 3 aqueous solution containing 0.80 g protein is 275 Pa at 25. What is the molar mass of the protein? 22. The freezing point depression due to an unknown solute is 10.5 K when 100 g of unknown was added to 750 g of l 4. What is the molar mass of the unknown? The molal freezing point depression coefficient is K M,f = 30 K kg mol The concentration of the apolar chlorobenzene is ppm in the fatty acid of a fish while that in water is 15 ppm. Determine K o/w for the chlorobenzene mg of antibiotics is dissolved in 30.0 ml water. The antibiotics was extracted by 15 ml diethyl ether. Evaporation of ether yields 37.5 mg antibiotics while the rest is left in water. alculate the partition coefficient of the antibiotics for ether with respect to water. 25. One mole of unknown can be dissolved in 47 ml of water, 8.1 ml of chloroform, 370 ml of diethyl ether or 86 ml benzene. What is the best solvent to extract the unknown from its aqueous solution? (Hint: alculate K o/w for each solvent) 26. Determine the equilibrium constant for the N 2 (g)+3h 2 (g) 2NH 3 (g) reaction at T=300 K if the standard enthalpy of reaction is kj/mol and the standard entropy of reaction is J/(mol K). 27. The alcohol dehydrogenase reaction removes ethanol from the blood at 37 according to the following equation: NAD + + ethanol NADH + acetaldehyde alculate the equilibrium constant for the reaction. The standard Gibbs energies of formation are G 0 f (NAD+ ) = kj/mol, G 0 f (NADH) = kj/mol, G0 f (ethanol) = 63.0 kj/mol, and G 0 f (acetaldehyde) = 24.1 kj/mol. Solutions: 1. T > 320 K = c m = K=1 therefore F cannot be 4 4. G = kj 5. p=11.9 kpa 6. T = T = T = mix H=0, mix S=46.40 J/K, mix G= kj 10. For an ideal solution p diethyl ether = 270 torr; it is a real solution with positive deviation from Raoult s law 11. p = torr 12. for acetone: a= and γ= and for chloroform: a=0.382 and γ= n= mol and the volume is 1.34 dm x Br2 =0.0654, x l4 =0.9346, p l4 =31.64 torr 15. a S2 = and γ S2 = I=1.40 mol/dm γ ± = G= kj 19. G= -2.9 kj 20. π=1.03 MPa 21. M=72.1 kg/mol 22. M= 381 g/mol 23. K o/w = K o/w = chloroform, because K o/w =5.80 is the largest 26. K= K=

3 KINETI PROBLEMS The goal of the problems is to derive the experimentally determined rate law based on the reaction mechanism. 1. The rate law for the formation of HBr(g) is given as H 2 (g) + Br 2 (g) 2HBr(g) d[hbr] = k[h 2][Br 2 ] 3/2 [Br 2 ] + k [HBr] The following reaction mechanism yields the rate law above Br 2 2Br v i = k i [Br 2 ] Br + H 2 HBr + H v f,1 = k f,1 [Br][H 2 ] H + Br 2 HBr + Br v f,2 = k f,2 [H][Br 2 ] H + HBr H 2 + Br v k = k k [H][HBr] 2Br + M Br 2 + M v l = k l [Br] 2 Identify the initiation, propagation and termination steps. Give the expression for the rate of the product. Give the expression for the rate of H. Give the expression for the rate of Br. Express the concentration of Br applying the steady-state approximation. Express the concentration of H applying the steady-state approximation. Substitute the previous expressions obtained for [H] and [Br] into the rate expression for HBr. (The expression should only contain the concentrations of reactants and/or products and the rate constants.) 2. The reaction mechanism of a dimerization reaction for a protein is given as F F v a = k a [F] 2F F 2 v b = k b [F ] 2 where F represents the protein, F the denaturated protein, and F 2 the protein dimer. Give the expression for the rate of protein dimer. Substitute the previous expression into the rate expression for the protein dimer. (The expression should only contain the concentrations of reactants and/or products and the rate constants.) The empirical rate law is given as d[f 2] = k obs [F]. Show that the rate law based on the reaction mechanism is equivalent with the empirical rate law. 3

4 3. The empirical rate law for enzyme-catalyzed reactions is S T [S] v = k [S] + K, where S represents the reactant (substrate), while T the product. The reaction mechanism suggested is where E corresponds to the enzyme. Give the expression for the rate of product T. E + S ES v a = k a [E][S] ES E + S v b = k b [ES] ES T + E v c = k c [ES] Express the concentration of the intermediate by applying the steady-state approximation and utilizing the mass balance for the enzyme, i.e., [E] 0 = [E] + [ES], where [E] 0 is the initial concentration of the enzyme. Substitute the previous expression into the rate expression for the product T. (The expression should only contain the concentrations of reactants and/or products and the rate constants.) 4. The empirical rate law for the reaction of nitrogen monoxide with hydrogen is The reaction mechanism suggested is 2H 2 (g) + 2NO(g) N 2 (g) + 2H 2 O(g) v = d[n 2] = k obs [NO] 2 H 2 (g) + 2NO(g) N 2 O(g) + H 2 O(g) v a = k a [H 2 ][NO] 2 H 2 (g) + N 2 O(g) N 2 (g) + H 2 O(g) v b = k b [H 2 ][N 2 O] Give the expression for the rate of N 2. State the steady-state approximation. Under what conditions does the steady-state approximation apply? Substitute the previous expression into the rate expression for N 2. (The expression should only contain the concentrations of reactants and/or products and the rate constants.) 4

5 5. The decomposition of reactant A to product T can be described by the following equation The reaction mechanism is determined as Give the expression for the rate of product T. Give the expression for the rate of reactant A. A T A B v a = k a [A] B T v b = k b [B] By solving the previous differential equation, give the concentration of reactant as a function of time. (The initial concentration of reactant should be indicated by a subscript 0.) State the steady-state approximation. Under what conditions does the steady-state approximation apply for the reaction mechanism above? Give the the expression for the rate of the intermediate. State when the steady-state approximation is not valid. Why? mix G = RT The following equations are necessary to solve the exercises n i lnx i = nrt r G 0 = r H 0 T r S 0 T h c max = T m T h F = P + 2 G mreal = G mideal + RT lnγ G = n G m ln p 2 = H ( m 1 1 ) p 1 R T 1 T 2 p i = x i p i, x i lnx i, mix S = nr p solution = p i i p 2 = K 2 x 2 a i = γ i x i, a 2,m = γ 2,m ( m 2 / m 0 ), a 2,c = γ 2,c (c 2 /c 0 ) r G 0 = I = 1/2 c i z 2 i lgγ ± = 0,509 z + z I/(mol dm 3 ) G = G out G in = RT ln [X] i [X] o + zfe cell n ν i G 0 f,i, π = c solute RT T f = T M, f m B K m,c = c X,A c X,B ν i : stoichiometric number x i lnx i, mix H = 0 5

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