CHEM N-2 November 2006

Transcription

1 CHEM N- November 006 High-purity benzoic acid, C 6 H 5 COOH, (H comb = 37 kj mol 1 ) is used to calibrate a bomb calorimeter that has a L capacity. A g sample of C 6 H 5 COOH is placed in the bomb calorimeter, along with 750 ml of pure H O(l), and the remaining 50 ml cavity is filled with pure O (g) at atm. The C 6 H 5 COOH is ignited and completely burned, causing the temperature of the water and the bomb calorimeter to rise from 7.0 ºC to ºC. Write the chemical equation corresponding to the standard enthalpy of combustion (H comb ) of C 6 H 5 COOH. 6 C 6 H 5 COOH(s) + 15 O (g) 7CO (g) + 3H O(l) Given that H O(l) has a heat capacity of J K 1 g 1 and a density of g ml -1, calculate the heat capacity of the bomb calorimeter itself (in units of J K 1 ). Ignore the heat capacity of the gases and of C 6 H 5 COOH. The molar mass of C 6 H 5 COOH is ( (C))+( (H))+( (O)) = Therefore g corresponds to: amount of C 6 H 5 COOH = mass mol molar mass As combustion of 1 mol gives out 37 kj of heat, this amount gives out: q = = 6.4 kj = J This heat leads to a temperature increase of ( ) = 5.96 C for the combination of the calorimeter and the water. As water has a density of g ml -1, 750 ml has a mass of g. q = (mc water + C calorimeter ) T = (( ) + (C calorimeter )) 5.96 = C calorimeter = 1305 J K -1 Answer: 1305 J K -1 ANSWER CONTINUES ON THE NEXT PAGE

2 CHEM N- November 006 If 30.0% of the CO produced dissolves in the water, calculate the final total pressure (in atm) inside the 50 ml cavity of the bomb calorimeter. Assume oxygen is insoluble in water and ignore the vapour pressure of water. Initially, atm of oxygen is present in a volume of 50 ml and a temperature of 7.0 C. Using the ideal gas equation, PV = nrt, initial no (g) = PV (10.00) (0.50) mol RT (0.0806) (73 7.0) From the chemical equation, 15 mol of O are required for the combustion of every mole of C 6 H 5 COOH. As mol of C 6 H 5 COOH is present, consumed no (g) = = mol Therefore, final no (g) = = mol From the chemical equation, 7 moles of CO are produced for the combustion every mole of C 6 H 5 COOH. As mol of C 6 H 5 COOH is present, total nco = = mol As 30% of this dissolves, n CO (g) = = mol The total number of moles of O (g) and CO (g) is therefore = This is present in 50 ml at C. Using the ideal gas law, P = nrt (0.0801) (0.0806) ( ) 8.05atm V 0.50 Answer: 8.05 atm

3 CHEM N-3 November 006 The specific heat capacity of water is 4.18 J g 1 K 1 and the specific heat capacity of copper is 0.39 J g 1 K 1. If the same amount of energy were applied to a 1.0 mol sample of each substance, both initially at 5 C, which substance would get hotter? Show all working. Using q = C m T, the temperature change for a substance of mass m and specific heat capacity C when an amount of heat equal to q is supplied is given by: T = q C m The atomic mass of copper is Hence, the temperature change for 1.0 mol of copper is T (copper) = q q ( ) 4.8 C The molar mass of H O is ( (H)) (O) = Hence, the temperature change for 1.0 mol of water is T (water) = q = ( ) q 75.3 C Hence, T (copper) > T (water) Answer: Copper Explain why the acidity of hydrogen halides increases with increasing halogen size (i.e., K a (HCl) < K a (HBr) < K a (HI)), while the acidity of hypohalous acids decreases with increasing halogen size (i.e., K a (HOCl) > K a (HOBr) > K a (HOI)). 3 For the hydrogen halides, the length of the H-X bond increases and hence gets weaker as the halogen gets bigger,. The weaker the bond, the more easily the H + dissociates. For the hypohalous acids, as the electronegativity of the halide increases, the more electron density it pulls from the O-H bond towards itself. This results in the O-H bond becoming more polar and increasing the ease with which the H + will be lost.

4 CHEM N-4 November 006 The K a of benzoic acid is M at 5 C. Calculate the ph of a M aqueous solution of sodium benzoate (C 6 H 5 COONa). 5 As benzoic acid is a weak acid, its conjugate base, C 6 H 5 COO -, is a weak base and so [OH ] must be calculated using the reaction table: C 6 H 5 COO H O OH C 6 H 5 COOH initial large 0 0 change -x negligible +x +x final x large x x The equilibrium constant K b is given by: K b = [OH ][C6H5COOH] [C6H5COO ] x x For an acid and its conjugate base in aqueous solution, K a K b = K w = Hence, K b = = As K b is very small, x ~ and hence: x = ( ) or x = M = [OH (aq)] Hence, the poh is given by: poh = log 10 [OH ] = log 10 [ ] = 5.9 Finally, ph + poh = 14.0 so ph = = 8.1 Answer: ph = 8.1 Answer: ph = 4.1 ANSWER CONTINUES ON THE NEXT PAGE

5 CHEM N-4 November 006 A buffer solution is prepared by adding 375 ml of this M aqueous solution of sodium benzoate to 5 ml of M aqueous benzoic acid. Calculate the ph of the buffer solution. 375 ml of a of benzoate contains, moles of benzoate = volume concentration = = mol 5 ml of a of benzoic acid contains, moles of benzoic acid = = mol The mixture has a volume of ( ) = 600 ml so the concentrations of benzoate (base) and benzoic acid (acid) are: [base] = number of moles volume = M [acid] = M As pk a = -log 10 K a, pk a = -log 10 ( ) = 4. The ph of the buffer can be calculated using the Henderson-Hasselbalch equation, [base] ph = pk a + log10 [acid] = 4. + log = 4.1 Answer: ph = 4.1

6 CHEM N-5 November 006 Water gas is a mixture of combustible gases produced from steam and coal according to the following reaction: C(s) + H O(g) CO(g) + H (g) H = 131 kj mol 1 The equation for the complete combustion of 1 mol of water gas (i.e. 0.5 mol CO(g) and 0.5 mol H (g)) can be written as: ½CO(g) + ½H (g) + ½O (g) ½CO (g) + ½H O(g) Calculate the standard enthalpy of combustion of water gas, given the following thermochemical data. H vap (H O) = 44 kj mol 1 H f (H O(l)) = 86 kj mol 1 H f (CO (g)) = 393 kj mol 1 3 o o o Using rxn H mf H (products) nf H (reac tan ts) for the vaporization of water (H O(l) H O(g)) gives o o o vaph [ f H (HO(g))] [ f H (HO(l))] o [ fh (HO(g))] ( 86) 44 Hence Using o 1 fh (HO(g)) ( 44) ( 86) 4kJmol o o o rxn H m f H (products) n f H (reac tan ts) for the reaction, as C(s) + H O(g) CO(g) + H (g) gives o o o rxnh [ f H (CO(g)] [ f H (HO(g))] o [ f H (CO(g)] ( 4) 131 o f H (H (g)) and states. Hence o f H (C(s)) are both zero for elements in their standard o = -111 kj mol-1 f H (CO(g) Using o o o rxn H m f H (products) n f H (reac tan ts) for the reaction, ½CO(g) + ½H (g) + ½O (g) ½CO (g) + ½H O(g) gives o 1 o 1 o 1 o combh [ f H (CO (g)) f H (HO(g))] [ f H (CO(g))] as the enthalpy of formation of H (g) and O (g) are both zero for elements in their standard states. Hence, o combh [( 393) ( 4)] [( 111)] = -6 kj mol -1 Answer: -6 kj mol -1 THIS QUESTION CONTINUES ON THE NEXT PAGE.

7 CHEM N-6 November 006 The CO(g) in water gas can be reacted further with H O(g) in the so-called watergas shift reaction: CO(g) + H O(g) CO (g) + H (g) 4 At 900 K, K c = 1.56 for this reaction. A sample of water gas flowing over coal at 900 K contains a 1:1 mole ratio of CO(g) and H (g), as well as 0.50 mol L 1 H O(g). This sample is placed in a sealed container at 900 K and allowed to come to equilibrium, at which point it contains mol L 1 CO (g). What was the initial concentration of CO(g) and H (g) in the sample? The reaction table is CO(g) H O(g) CO (g) H (g) initial x x change equilibrium x x The equilibrium constant in terms of concentrations, K c, is: K c = [CO (g)][h (g)] (0.070)(x 0.070) [H O(g)][CO(g)] (0.180)(x 0.070) 1.56 x = [CO(g)] initial = [H (g)] initial = 0.1 mol L -1 [CO] = [H ] = 0.1 mol L -1 If the walls of the container are chilled to below 100 ºC, what will be the effect on the concentration of CO (g)? At temperatures below 100 C, the water vapour will condense to form H O(l). Following Le Chatelier s principle, the equilibrium will shift to the left as [H O(g)] is reduced by this process and so [CO (g)] will decrease.

8 CHEM N-7 November 006 The isomerisation of glucose-6-phosphate (G6P) to fructose-6-phosphate (F6P) is a key step in the metabolism of glucose for energy. At 98 K, 6 G6P F6P G = 1.67 kj mol 1 Calculate the equilibrium constant for this process at 98 K. Using G = -RTlnK, = -(8.314) (98) lnk K = Answer: K = What is the free energy change (in kj mol 1 ) involved in a mixture of 3.00 mol of F6P and.00 mol of G6P reaching equilibrium at 98 K? The reaction quotient, for the reaction, is Q = [F6P] [G6P] = Using G = G + RTlnQ, G = ( ) + ( ) ln(1.50) = +670 J mol -1 = +.67 kj mol -1 Answer: +.67 kj mol -1 Sketch a graph of G sys versus extent of reaction, with a curve showing how G sys varies as G6P is converted to F6P. Indicate the position on this curve corresponding to 3.00 mol of F6P and.00 mol of G6P.

9 CHEM N-8 November 006 Assume that NaCl is the only significant solute in seawater. A L sample of seawater at 5 ºC and 1 atm has a mass of kg and contains 33.0 g of NaCl. At what temperature would this seawater freeze? The freezing point depression constant of water is 1.86 ºC kg mol 1. 6 The formula mass of NaCl is.99 (Na) (Cl) = Therefore, 33.0 g corresponds to: number of moles of NaCl = mass mol formula mass As each mole of NaCl dissolves to give moles of particles (Na + (aq) and Cl - (aq)), the number of moles of solute is = 1.19 mol. If salt water contains only water and NaCl, mass of water = = kg Hence, the molality is m = moles of solute mol kg -1 mass of solvent The freezing point depression is then: T f = K f m = =.11 C As water normally freezes at 0 C, this saltwater will freeze at -.11 C. Answer: -.11 C ANSWER CONTINUES ON THE NEXT PAGE

10 CHEM N-8 November 006 The vapour pressure above pure H O is 3.76 mmhg at 5 ºC and 1 atm. Calculate the vapour pressure above this seawater under the same conditions. The molar mass of H O is ( (H)) (O) = Therefore, kg of water corresponds to moles of water = 3 mass ( ) molar mass mol As 1.19 mol of solute is also present, the mole fraction, X, of water is X water = numberof moles of water total number of moles ( ) From Raoult s law, P water = X water P o water = = 3.3 mmhg Answer: 3.3 mmhg The desalination of seawater by reverse osmosis has been suggested as a way of alleviating water shortages in Sydney. What pressure (in Pa) would need to be applied to this seawater in order to force it through a semi-permeable membrane, yielding pure H O? The concentration of solute is: concentration = c = number of moles of solute M volume The osmotic pressure, Π, required is given by Π = crt = (1.19) (0.0806) (5 + 73) = 7.6 atm As 1 atm = Pa, Π = 7.6 ( ) = Pa = Pa Answer: Pa

11 CHEM N-9 November 006 The molar solubility of lead(ii) fluoride, PbF, is found to be M at 5 C. Calculate the value of K sp for this compound at this temperature. The solubility equilibrium and constant for PbF (s) are, PbF (s) Pb + (aq) + F - (aq) K sp = [Pb + (aq)][f - (aq)] As one moles of Pb + (aq) and two moles of F - (aq) are produced for every mole of PbF (s) which dissolves, [Pb + (aq)] = M and [F - (aq)] = ( ) = M. Hence, K sp = ( ) ( ) = K sp = Draw all stereoisomers of the complex ion of [Co(en) 3 ]Br 3. (en = ethylenediamine = NH CH CH NH ) NH NH NH Co NH NH NH NH NH Co NH NH NH NH Name the following complexes. [Co(H O) 4 Br ]Cl K[Au(CN) ] tetraaaquadibromocobalt(iii) chloride potassium dicyanoaurate(i)

12 CHEM N-10 November 006 Write the chemical equation for the formation of the complex ion [Cd(NH 3 ) 4 ] +. Cd + + 4NH 3 [Cd(NH 3 ) 4 ] + Write the associated stability constant expression (K stab ). [[Cd(NH 3) 4] ] K stab 4 [Cd ][NH 3 ] The physiological properties of chromium depend on its oxidation state. Consider the half reaction in which Cr(VI) is reduced to Cr(III). CrO 4 (aq) + 4H O(l) + 3e Cr(OH) 3 (s) + 5OH (aq) E o = 0.13 V Calculate the potential for this half reaction at 5 o C, where ph = 7.40 and [CrO 4 (aq)] = M. 3 As ph + poh = and poh = -log 10 ([OH - (aq)]), at ph = 7.40, poh = = 6.60 = -log 10 ([OH - (aq)]) [OH - (aq)] = The reaction quotient for the half-cell reaction is, Q = [OH (aq)] [CrO 4 5 (aq)] = (10 ) 6 (1.010 ) = Using the Nernst equation for this three electron process, E = E o RT lnq = (-0.13) nf (5+73) ln( ) = V Answer: E = V

13 CHEM N-11 November 006 Consider the following reaction at 98 K. Ni + (aq) + Zn(s) Ni(s) + Zn + (aq) Calculate ΔG o for the cell. (Relevant electrode potentials can be found on the data page.) 5 The half-cell reduction reactions and potentials are: Ni + (aq) + e - Ni(s) Zn + (aq) + e - Zn(s) E 0 = -0.4 V E 0 = V In the reaction above, the Zn is undergoing oxidation so its potential is reversed and the overall cell potential is: 0 E cell = (-0.4) (-0.76) = +0.5 V Using G 0 = -nfe 0 for this two electron reaction: G 0 = -() (96485) (+0.5) = J mol 1 = -100 kj mol 1 Answer: -100 kj mol -1 What is the value of the equilibrium constant for the reaction at 98 K? Using E 0 = RT lnk, nf +0.5 = (8.314) (98) lnk () (96485) so K = Alternatively, using G 0 = -RTlnK, = -(8.314) (98) lnk so K = Express the overall reaction in voltaic cell notation. Answer: In the reaction, Zn is being oxidized and hence is the anode. Ni + is being reduced and so Ni is the cathode. In the standard cell notation, the anode is written on the left and the cathode on the right: Zn(s) Zn + (aq) Ni + (aq) Ni(s) ANSWER CONTINUES ON THE NEXT PAGE

14 CHEM N-11 November 006 Using a current of.00 A, how long (in minutes) will it take to plate out all of the silver from 0.50 L of a M Ag + (aq) solution? The number of moles of Ag + (aq) in a 0.50 L of a M solution is, number of moles = volume concentration = = mol The reduction of Ag + (aq) is a one electron process, Ag + (aq) + e - Ag(s), so this number of moles of electrons are required. As the number of moles of electrons delivered by a current I in a time t is, number of moles of electrons = It F =.00 t = t = 137 s =.9 minutes

15 CHEM N-1 November 006 If a medical procedure calls for.0 mg of 48 V, what mass of isotope would be required to be able to use it exactly one week later? The half life of 48 V is 1.61 days. The decay constant is related to the half life as t 1/ = ln λ. Thus, ln λ = days The number of radioactive nuclei decreases with time according to the equation, N ln N 0 t = λt If N t =.0 mg after t = 7 days, N0 ln = (0.431) 7.00 so N 0 = g = 41 mg Answer: 4.1 mg Describe how hydrophilic and hydrophobic colloids are stabilised in water. 3 They can be stabilised via electrostatic and steric stabilisation. Hydrophilic colloids may have a charge on their surface that attracts oppositely charged ions (H + or OH present in water) to form a tightly bound layer known as the Stern Layer. The Stern layer is surrounded by a diffuse layer which contains an excess of counter-ions (opposite in charge to the Stern layer) and a deficit of co-ions. The Stern layer and diffuse layer are collectively known as a double layer. Coagulation of a hydrophilic colloid is prevented by mutual repulsion of the double layers. Hydrophobic colloids may be stabilised by the use of a surfactant, e.g. a long chain fatty acid with a polar head and a non-polar tail. When dispersed in water these molecules arrange themselves spherically so that the polar (hydrophilic) heads are interacting with the polar water molecules and the non-polar (hydrophobic) tails are interacting with each other. This arrangement is called a micelle. The hydrophobic colloid can be stabilized by dissolving in the non-polar interior of the micelle. ANSWER CONTINUES ON THE NEXT PAGE

16 CHEM N-1 November 006 Calculate the standard free-energy change for the following reaction at 98 K. Au(s) + 3Mg + (1.0 M) Au 3+ (1.0 M) + 3Mg(s) The half-cell reduction reactions and potentials are: Au 3+ (aq) + 3e - Au(s) Mg + (aq) + e - Mg(s) E 0 = V E 0 = -.36 V In the reaction above, the Au is undergoing oxidation so its potential is reversed and the overall cell potential is: 0 E cell = (-.36) (+1.50) = V Using G 0 = -nfe 0 for this six electron reaction: G 0 = -(6) (96485) (-3.86) = J mol 1 = kj mol 1 Answer: kj mol -1

17 CHEM N-13 November 006 The major pollutants NO(g), CO(g), NO (g) and CO (g), which are emitted by cars, can react according to the following equation. 5 NO (g) + CO(g) NO(g) + CO (g) The following rate data were collected at 5 o C. Experiment [NO ] 0 (M) [CO] 0 (M) Initial rate (d[no ]/dt, M s 1 ) Determine the rate law for the reaction. Between experiments (1) and (), [NO ] 0 is constant and [CO] 0 is halved. The rate does not change. The rate is independent of [CO]: zero order with respect to [CO]. Between experiments () and (3), [CO] 0 is kept constant and [NO ] 0 is doubled. The rate increases by a factor of four: the rate is second order with respect to [NO ]. Overall, rate [NO ] = k[no ] Calculate the value of the rate constant at 5 o C. Answer: M -1 s -1 Calculate the rate of appearance of CO when [NO ] = [CO] = M. When [NO ] = M, rate = d[no ] dt = ( ) (0.500) = M s -1 From the chemical equation, one mole of CO is produced for every mole of NO that is removed. Thus, rate of appearance of CO = rate of loss of NO. Answer: M s -1 Suggest a possible mechanism for the reaction based on the form of the rate law. Explain your answer. A possible mechanism is: NO (g) + NO (g) NO(g) + NO 3 (g) (slow) NO 3 (g) + CO(g) NO (g) + CO (g)...(fast) The first step is slow and is rate determining. For this step, rate [NO ], as observed. The second step is fast and does not affect the overall rate of the reaction and so the rate is independent of [CO(g)].

18 CHEM N-13 November 006