ChE 102 Chemistry for Engineers Final Exam December 12, 2001 Instructor Problem Exactly 2,500 kJ is required to heat 1.0 kmol of an ideal gas at constant volume from 300 to 500 K Assuming the heat capacity is constant over the temperature range of 300 to 500 K, how much energy (in kJ) is required to heat 1.0 kmol of the same gas at constant pressure from 300 to 400 K? A) 209 B) 419 C) 2,081 D) 3,010 E) It cannot be determined without knowing whether the gas is monoatomic or diatomic Problem It is well known that, if the environmental conditions remain constant, the rate of evaporation of a pure liquid is directly proportional to its vapour pressure: Rate of Evaporation = α·Pº (Pº = Vapour Pressure) The constant, α, does not depend on the temperature At 10ºC, 98 minutes are required to evaporate 10 g of the unknown liquid At 30ºC, however, only 46 minutes are necessary to evaporate 10 g of the unknown liquid from the same vessel The average enthalpy of evaporation of the unknown liquid between 10ºC and 30ºC in J/mol is: A) 26,988 J/mol B) 3,300 J/mol C)76,020 J/mol D) 85,837 J/mol E) 1,886 J/mol Problem A saturated solution is prepared at 70ºC containing 32.0g CuSO4 per 100.0 g solution A 335 g sample of this solution is then cooled to 0ºC and CuSO4·5H2O precipitates If the concentration of a saturated solution at 0ºC is 12.5 g CuSO4/100 g solution, what mass of CuSO4·5H2O precipitate would be obtained? (Hint: Note that the solution composition is stated in terms of CuSO4 and that the solid that precipitates is the copper sulphate hydrate, CuSO4·5H2O.) A) 130 g B) 220 g C) 55 g D) 310 g E) g Problem The partial pressure of CO2 gas in a bottle of carbonated water is atm at 25ºC How much CO2 gas (in g) will be released from 1.0 L of the carbonated water when the partial pressure of CO2 is lowered to 1.0 atm? At 25ºC, the Henry’s law constant for CO2 dissolved in water is 1.65×103 atm, and the density of water is 1.0 g/cm3 A) 2.4 g B) 3.4 g C) 4.4 g D) 5.4 g E) 6.4 g 1/1 ChE 102 Chemistry for Engineers Final Exam December 12, 2001 Instructor Problem Styrene is used in the manufacture of polystyrene plastics and is made from ethylbenzene The liquid mixture obtained contains about 38% styrene (C8H8) and 62% ethylbenzene (C8H10), by mass The mixture can be separated by fractional distillation at 90ºC Determine the molar fraction of styrene in the vapour phase in equilibrium with this liquid mixture at 90ºC given the vapour pressures of the two components: ethylbenzene, 182 mmHg; styrene 134 mmHg A) 0.25 B) 0.38 C) 0.32 D) 0.40 E) 1.00 Problem When 0.0250 g of an unknown compound with an empirical formula of CH2 is dissolved in 5.00 g of benzene (Kf = 5.12 ºC/m), the freezing point of the benzene is depressed from 5.510ºC to 5.280ºC What is the molecular formula of the unknown compound? A) C3H6 B) C4H8 C) C5H10 D) C7H14 E) C8H16 Problem Consider the decomposition of arsene gas (AsH3) to solid arsenic and hydrogen that occurs as follows: AsH 3(g ) ↔ As (s ) + H 2(g ) If “f” is defined as the fraction of AsH3 converted and “PT” is defined as the total pressure of the system, then the equilibrium constant, KP can be expressed as: f3 PT2 A) 27 (1 − f ) D) 27 f3 B) 27 P2 T (1 − f )(1 + f ) f3 P2 T (1 − f )(1 + f ) E) ( 1− f ) f C) 27 P (1 + f )2 T f3 P2 (1 − f )(0.5 + f ) T 2/2 ChE 102 Chemistry for Engineers Final Exam December 12, 2001 Instructor Problem An important exothermic reaction for the production of hydrogen is: The following statements refer to the ratio of the partial pressure of hydrogen to the partial pressure of carbon monoxide ( ) at equilibrium The single correct or single incorrect statement is: PH PCO A) At a constant temperature, the partial pressure ratio increases if the gas mixture at equilibrium is compressed B) At constant volume, the partial pressure ratio increases if the temperature increases C) At constant volume, the partial pressure ratio does not change if an inert gas (nitrogen for example) is added to the container D) At constant volume, the partial pressure ratio decreases if carbon dioxide (CO2) is removed from the system E) At constant pressure, the partial pressure ratio increases if a catalyst is added to the system Problem Nitrogen dioxide obtained as a cylinder gas is always a mixture of NO2(g) and N2O4(g) N O 4(g) ↔ NO 2(g) A 5.00 g sample obtained from such a cylinder is sealed in a 0.5 L flask at 298K Knowing that Kc = 4.61×10-3 mol/L for this reaction at 298 K, calculate the mole fraction of NO2(g) in equilibrium inside the 0.5 L flask A) 1.13×10-3 B) 0.131 C) 0.177 D) 0.531 E) 0.782 3/3 ChE 102 Chemistry for Engineers Final Exam December 12, 2001 Instructor Problem 10 Consider the following standard potentials in an acidic medium where [H+] = M εº (volts) Mn 3+ ( aq ) − + e ↔ Mn 2+ ( aq ) 1.51 + MnO 2(s ) + H + + e − ↔ Mn 3(aq ) + H 2O 0.95 Ag (+aq ) + e − ↔ Ag ( s ) 0.80 Ag (2aq+ ) + e − ↔ Ag (s ) -0.76 (i) Mn3+(aq) is the strongest reducing agent (ii) The reaction between Ag(s) and Zn2+(aq) proceeds spontaneously under standard conditions as shown below (iii) The εº value for Ag (+aq ) + e − ↔ Ag ( s ) is 1.6 volts (iv) The equilibrium constant at 25ºC for the reaction + + − Mn 3(aq ) + H O ↔ MnO (s ) + H + e is greater than (v) In a galvanic cell, oxidation occurs at the anode and reduction occurs at the cathode The total number of correct statements is: A) B) C) D) E) Problem 11 Consider the following concentration cell Pb (s ) Pb 2+ (saturated PbI ) Pb 2+ (0.100 M ) Pb ( s ) At the anode, a lead electrode is placed in a saturated aqueous solution of lead iodide At the cathode, a second lead electrode is placed in a solution with [Pb2+] = 0.100 M At 25ºC, the cell voltage is measured to be 0.0567 V Determine the Ksp (in (mol/L)3 ) for PbI2 in aqueous solution at 25ºC A) 1.28×10-5 B) 1.48×10-6 C) 2.95×10-6 D) 1.79×10-9 E) 7.17×10-9 Problem 12 It takes 3.0 using a current of 2.00 A to deposit all the silver onto the electrode from 0.250 L of a solution containing Ag+ What was the original molar concentration of Ag+ in the solution? A) 0.0037 B) 0.0025 C) 1.61 D) 144 E) 0.015 4/4 ChE 102 Chemistry for Engineers Final Exam December 12, 2001 Instructor Problem 13 For the reaction A + B Ỉ C + D the following initial rates of reaction were found What is the numerical value of the reaction rate constant for this reaction in terms of moles, litres, and minutes? Exp [A] mol/L [B] mol/L Initial rate, mol L-1 min-1 0.5 1.5 5.24×10-3 1.5 1.5 1.57×10-2 3.0 3.0 8.89×10-2 A) 5.2×10-4 B) 1.7×10-3 C) 5.7×10-3 D) 7.2×10-2 E) 1.5×10-1 Problem 14 Di-t-butyl peroxide, DTBP, (C8H18O2) decomposes in the gaseous state into acetone and ethane (C2H6) by the first order reaction: C H18 O 2( g ) → C H O ( g ) + C H 6( g ) In an experiment, pure gaseous DTBP is placed inside a closed reactor at an initial pressure of 800 mmHg and temperature of 147ºC Knowing that the rate constant for the decomposition reaction of DTBP at 147ºC is k = 8.7×10-3 min-1, determine the time at which the total gas pressure inside the reactor is 2100 mmHg A) 58 B) 100 C) 153 D) 192 E) The pressure will never reach 2100 mmHg Problem 15 The half-life of a first order reaction decreases from 92.4 to 5.2 as the temperature increases from 25 to 102ºC At what temperature (in ºC) would the half-life be 20.0 min, assuming the activation energy is constant over this temperature range? A) 33.4 B) 41.8 C) 61.5 D) 82.1 E) 88.9 5/5 ChE 102 Chemistry for Engineers Final Exam December 12, 2001 Instructor Problem 16 Consider the chemical reaction occurring in the gas phase in a constant volume reactor A ( g ) + B( g ) → C ( g ) (i) Assuming that this chemical reaction is first order with respect to A and first order with respect to B, the reaction mechanism must consist of more than one elementary process (ii) Assuming that the reaction takes place in one elementary step as written in the above equation, it will have a second order dependence with respect to A and a first order dependence with respect to A and a first order dependence with respect to B (iii) The activation energy for the above reaction is the minimum energy barrier the reactants must overcome for the reaction to take place (iv) If the reaction is first order with respect to A and first order with repect to B, the differential rate law can be expressed as follows: − dPA = kPA PA dt Where PA represents the partial pressure of A, PB represents the partial pressure of B and k is the rate for the reaction (v) If the reaction is second order with respect to A, the half-life of the reaction is independent of the concentration of A The total number of correct statements is: A) B) C) D) E) 6/6 ... ) D) 27 f3 B) 27 P2 T (1 − f )(1 + f ) f3 P2 T (1 − f )(1 + f ) E) ( 1− f ) f C) 27 P (1 + f )2 T f3 P2 (1 − f )(0.5 + f ) T 2/ 2 ChE 1 02 Chemistry for Engineers Final Exam December 12, 20 01 Instructor... mol L-1 min-1 0.5 1.5 5 .24 ×10-3 1.5 1.5 1.57×10 -2 3.0 3.0 8.89×10 -2 A) 5 .2? ?10-4 B) 1.7×10-3 C) 5.7×10-3 D) 7 .2? ?10 -2 E) 1.5×10-1 Problem 14 Di-t-butyl peroxide, DTBP, (C8H18O2) decomposes in the... solution with [Pb2+] = 0.100 M At 25 ºC, the cell voltage is measured to be 0.0567 V Determine the Ksp (in (mol/L)3 ) for PbI2 in aqueous solution at 25 ºC A) 1 .28 ×10-5 B) 1.48×10-6 C) 2. 95×10-6 D)