IChO41th理论试题及答案.docx

1、IChO41th理论试题及答案Problem AuthorsStephen Ashworth University of East AngliaJonathan Burton University of OxfordJon Dilworth University of OxfordNicholas Green University of OxfordPhilip Mountford University of OxfordWilliam Nolan University of CambridgeJeremy Rawson University of CambridgeKathryn Scott

2、 University of OxfordMalcolm Seddon University of East AngliaSimon Titmuss University of OxfordClaire Vallance University of OxfordPeter Wothers University of CambridgeFields of Advanced DifficultyTheoreticalKinetics: integrated first-order rate equation; analysis of moderately complex reactions mec

3、hanisms using the steady state approximation, the use of the Arrhenius equation, simple collision theoryThermodynamics: electrochemical cells, the relationship between equilibrium constants, electromotive force and standard Gibbs energy, the variation of the equilibrium constant with temperatureQuan

4、tum mechanics: calculation of orbital and spin angular momentum, calculation of the magnetic moment using the spin-only formulaSpectroscopy: interpretation of relatively simple 13C and 1H NMR spectra; chemical shifts, multiplicities, coupling constants and integralsMass spectrometry: molecular ions

5、and basic fragmentationTheoretical problemsProblem 1 Dating moon rockThe age of rocks collected from the moon on the Apollo 16 mission has been determined from the 87Rb / 86Sr and 87Sr / 86Sr ratios of different minerals found in the sample.Mineral87Rb / 86Sr87Sr / 86SrA (Plagioclase)0.0040.699B (Qu

6、intessence)0.1800.709a) 87Rb is a emitter, write down the equation of nuclear decay. The half-life for this decay is 4.8 1010 years.b) Calculate the age of the rock. You can assume that the initial 87Sr / 86Sr is the same in A and B and that 87Sr and 86Sr are stable.Problem 2 SnorkellingThe pressure

7、 of a gas may be thought of as the force the gas exerts per unit area on the walls of its container, or on an imaginary surface of unit area placed somewhere within the gas. The force arises from collisions between the particles in the gas and the surface. In an ideal gas, the collision frequency (n

8、umber of collisions per second) with a surface of unit area is given by:Where p is the pressure and T the temperature of the gas, m is the mass of the gas particles, and kB is the Boltzmanns constant (kB = 1.381023 J K1).At sea level, atmospheric pressure is generally around 101.3 kPa, and the avera

9、ge temperature on a typical British summer day is 15C.a) Using the approximation that air consists of 79% nitrogen and 21% oxygen, calculate the weighted averagemass of a molecule in the air.b) Human lungs have a surface area of approximately 75 m2. An average human breath takes around 5 seconds. Es

10、timate the number of collisions with the surface of the lungs during a single breath on a typical British summer day. You should assume that the pressure in the lungs remains constant at atmospheric pressure; this is a reasonable approximation, as the pressure in the lungs changes by less than 1% du

11、ring each respiratory cycle.The human lungs can operate against a pressure differential of up to one twentieth of atmospheric pressure. If a diver uses a snorkel for breathing, we can use this fact to determine how far below water the surface of the water she can swim.The pressure experienced by the

12、 diver a distance d below the surface of the water is determined by the force per unit area exerted by the mass of water above her. The force exerted by gravity on a mass m is F = mg, where g = 9.8 m s2 is the acceleration due to gravity.c) Write down an expression for the mass of a volume of water

13、with cross sectional area A and depth d.d) Derive an expression for the force exerted on the diver by the volume of water in (c), and hence an expression for the difference in pressure she experiences at depth d relative to the pressure at the waters surface.e) Calculate the maximum depth the diver

14、can swim below the water surface, while still breathing successfully through a snorkel.Problem 3 Ideal and not-so-ideal gasesThe force a gas exerts on the walls of its container arises from collisions between the particles in the gas and the surface. In a single collision, the magnitude of the impul

15、sive of the force exerted on the surface is equal to the change in the momentum normal to the surface, mv. The force on the surface is then the impulse, multiplied by the rate at which the particles collide with the surface.Since the motion of particles within a gas is random, the number of collisio

16、ns occurring per unit time is a constant for a gas at constant temperature.The temperature of a gas reflects the distribution of particle velocities within the gas. For a given gas, the particle speeds will be higher, on average, at higher temperatures.a) Given the above information, and assuming th

17、e gas is initially at room temperature and atmospheric pressure, consider how carrying out the following actions would be likely to affect the pressure. Would the pressure double, halve, increase slightly, decrease slightly, or remain unchanged?i) Doubling the number of particles in the gas.ii) Doub

18、ling the volume of the container in which the gas is confined.iii) Doubling the mass of the particles in the gas (assume that the particle velocities remain constant).iv) Increasing the temperature by 10C.The ideal gas model assumes that there are no interactions between gas particles. Particles in

19、a real gas do interact through a range of forces such as dipoledipole forces, dipoleinduceddipole forces, and van der Waals interactions (induceddipoleinduceddipole forces). A typical curve showing the potential energy of interaction between two particles is shown right:The force between two particl

20、es in a gas at a given separation r may be calculated from the gradient of the potential energy curve i.e. F = dV / dr.b) What is the force at the four points marked A, B, C and D on the figure?(attractive / repulsive / approximately zero)The deviation from non-ideality in a gas is often quantified

21、in terms of the compression ratio, Z.where is the molar volume of the (real) gas, and is the molar volume of an ideal gas under the same conditions of temperature, pressure etc.c) Match the following values of Z with the dominant type of interaction in the gas. Z = 1 Z 1 Attractive forces dominateRe

22、pulsive forces dominateNo intermolecular forces, ideal gas behaviourd) The compression ratio is pressure dependent. Consider the average separation between particles in a gas at different pressures (ranging from extremely low pressure to extremely high pressure), and the regions of the intermolecula

23、r potential that these separations correspond to. Sketch the way in which you think the compression ratio will vary with pressure on the set of axes below. Note: do not worry about the actual numerical values of Z; the general shape of the pressure dependence curve is all that is required.Problem 4

24、Coal gasificationIn the process of coal gasification coal is converted into a combustible mixture of carbon monoxide and hydrogen, called coal gasH2O (g) + C (s) CO (g) + H2 (g)a) Calculate the standard enthalpy change for this reaction from the following chemical equations and standard enthalpy cha

25、nges2C (s) + O2 (g) 2 CO (g) rH = 221.0 kJ mol12H2 (g) + O2 (g) 2 H2O (g) rH = 483.6 kJ mol1The coal gas can be used as a fuel :CO (g) + H2 (g) + O2 (g) CO2 (g) + H2O (g)b) Given the additional information, calculate the enthalpy change for this combustionC (s) + O2 (g) CO2 (g) rH = 393.5 kJ mol1Coa

26、l gas can also undergo the process of methanation.3H2 (g) + CO (g) CH4 (g) + H2O (g)c) Determine the standard enthalpy change for the methanation reaction using the additional data.CH4 (g) + 2O2 (g) CO2 (g) + 2 H2O (g) rH = 802.7 kJ mol1Problem 5 The industrial preparation of hydrogenHydrogen gas ma

27、y be prepared industrially by heating hydrocarbons, such as a methane, with steam: CH4 (g) + H2O (g) 3H2 (g) + CO (g) Aa) Given the following thermodynamic data, calculate the rG for reaction A at 298 K and hence a value for the equilibrium constant, Kp.fH (298) / kJ mol1S (298) / J K1 mol1CH4 (g)74

28、.4186.3H2O (g)241.8188.8H2 (g)130.7CO (g)110.5197.7b) How will the equilibrium constant vary with temperature?The industrial preparation can be carried out at atmospheric pressure and high temperature, without a catalyst. Typically, 0.2 vol % of methane gas remains in the mixture at equilibrium.c) A

29、ssuming the reaction started with equal volumes of methane and steam, calculate the value of Kp for the industrial process which gives 0.2 vol % methane at equilibrium.d) Use your answer from (c) together with the integrated form of the vant Hoff isochore to estimate the temperature used in industry

30、 for the preparation of hydrogen from methane.Problem 6 The bonds in dibenzylThis question is a typical application of thermodynamic cycles to estimate a bond dissociation enthalpy.The first step in the pyrolysis of toluene (methylbenzene) is the breaking of the C6H5CH2H bond. The activation enthalp

31、y for this process, which is essentially the bond dissociation enthalpy, is found to be 378.4 kJ mol1.a) Write a balanced equation for the complete combustion of toluene.Standard enthalpies are given below, using the recommended IUPAC notation (i.e. f = formation, c = combustion, vap = vaporisation,

32、 at = atomisation) fH(CO2, g, 298K) = 393.5 kJ mol1 fH(H2O, l, 298K) = 285.8 kJ mol1 cH(C7H8, l, 298K) = 3910.2 kJ mol1 vapH(C7H8, l, 298K) = +38.0 kJ mol1 atH(H2, g, 298K) = +436.0 kJ mol1.i) Calculate fH(C7H8, l, 298K)ii) Estimate fH for the benzyl radical C6H5CH2(g) at 298 K.b) The standard entropy of vapori