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Questions and Answers of Physical Chemistry

What fraction of the total current is carried by Li+ when current flows through an aqueous solution of LiBr at 25°C?
The limiting molar conductivities of KCl, KNO3, and AgNO3 are 14.99 mS m2 mol−1, 14.50 mS m2 mol−1, and 13.34 mS m2 mol−1, respectively (all at 25°C). What is the limiting molar conductivity
What is the proportion of gas molecules having(a) More than,(b) Less than the root mean square speed?(c) What are the proportions having speeds greater and smaller than the mean speed?
At 25°C the molar ionic conductivities of Li+, Na+, and K+ are 3.87 mS m2 mol−1, 5.01 mS m2 mol−1, and 7.35 mS m2 mol−1, respectively. What are their mobilities?
The mobility of a NO3− ion in aqueous solution at 25°C is 7.40 × 10−8 m2 s−1 V−1. Calculate its diffusion coefficient in water at 25°C.
Calculate the fractions of molecules in a gas that have a speed in a range ∆v at the speed nc* relative to those in the same range at c* itself? This calculation can be used to estimate the
The diffusion coefficient of CCl4 in heptane at 25°C is 3.17 × 10−9 m2 s−1. Estimate the time required for a CCl4 molecule to have a root mean square displacement of 5.0 mm.
Derive an expression that shows how the pressure of a gas inside an effusion oven (a heated chamber with a small hole in one wall) varies with time if the oven is not replenished as the gas escapes.
Estimate the effective radius of a sucrose molecule in water 25°C given that its diffusion coefficient is 5.2 × 10−10 m2 s−1 and that the viscosity of water is 1.00 cP.
The diffusion coefficient for molecular iodine in benzene is 2.13 × 10−9 m2 s−1. How long does a molecule take to jump through about one molecular diameter (approximately the fundamental jump
What are the root mean square distances travelled by an iodine molecule in benzene and by a sucrose molecule in water at 25°C in 1.0 s?
Use mathematical software to calculate P in a one-dimensional random walk, and evaluate the probability of being at x = nλ for n = 6, 10, 14, . . . , 60. Compare the numerical value with the
Interstellar space is a medium quite different from the gaseous environments we commonly encounter on Earth. For instance, a typical density of the medium is about 1 atom cm−3 and that atom is
The diffusion coefficient of a particular kind of t-RNA molecule is D = 1.0 × 10−11 m2 s−1 in the medium of a cell interior. How long does it take molecules produced in the cell nucleus to reach
The rate of the reaction A + 2 B → 3 C + D was reported as 1.0 mol dm−3 s−1. State the rates of formation and consumption of the participants.
The data below apply to the reaction, (CH3)3CBr + H2O → (CH3)3COH + HBr. Determine the order of the reaction, the rate constant, and the molar concentration of (CH3)3CBr after 43.8 h. t/h 0 3.15
The rate of formation of C in the reaction 2 A + B → 2 C + 3 D is 1.0 mol dm−3 s−1. State the reaction rate, and the rates of formation or consumption of A, B, and D.
The following data have been obtained for the decomposition of N2O5(g) at 67°C according to the reaction 2 N2O5(g) → 4 NO2(g) + O2(g). Determine the order of the reaction, the rate constant, and
The gas-phase decomposition of acetic acid at 1189 K proceeds by way of two parallel reactions: What is the maximum percentage yield of the ketene CH2CO obtainable at this temperature? (1)
A first-order decomposition reaction is observed to have the following rate constants at the indicated temperatures. Estimate the activation energy. k/(10-s-) Ꮎ/°C 2.46 0 45.1 20.0 576 40.0
The rate law for the reaction in Exercise 22.2a was reported as d[C]/dt = k[A][B][C]. Express the rate law in terms of the reaction rate; what are the units for k in each case?Data in Exercise
The ClO radical decays rapidly by way of the reaction, 2 ClO → Cl2 + O2. The following data have been obtained:Determine the rate constant of the reaction and the half-life of a ClO radical.
At 518°C, the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 Torr, was 1.07 Torr s−1 when 5.0 per cent had reacted and 0.76 Torr s−1 when 20.0 per cent
Sucrose is readily hydrolysed to glucose and fructose in acidic solution. The hydrolysis is often monitored by measuring the angle of rotation of plane polarized light passing through the solution.
The second-order rate constant for the reactionis 0.11 dm3 mol−1 s−1. What is the concentration of ester after(a) 10 s,(b) 10 min when ethyl acetate is added to sodium hydroxide so that the
At 518°C, the half-life for the decomposition of a sample of gaseous acetaldehyde (ethanal) initially at 363 Torr was 410 s. When the pressure was 169 Torr, the half-life was 880 s. Determine the
The rate constant for the first-order decomposition of N2O5 in the reaction 2 N2O5(g) → 4 NO2(g) + O2(g) is k = 3.38 × 10−5 s−1 at 25°C. What is the half-life of N2O5? What will be the
Cyclopropane isomerizes into propene when heated to 500°C in the gas phase. The extent of conversion for various initial pressures has been followed by gas chromatography by allowing the reaction to
A second-order reaction of the type A + B → P was carried out in a solution that was initially 0.050 mol dm−3 in A and 0.080 mol dm−3 in B. After 1.0 h the concentration of A had fallen to
Consider the dimerization 2 A ⇌ A2, with forward rate constant ka and backward rate constant kb.(a) Derive the following expression for the relaxation time in terms of the total concentration of
A reaction 2 A → P has a second-order rate law with k = 3.50 × 10−4 dm3 mol−1 s−1. Calculate the time required for the concentration of A to change from 0.260 mol dm−3 to 0.011 mol dm−3.
The reaction mechanism involves an intermediate A. Deduce the rate law for the reaction. A₂A+A (fast) A+B → P (slow)
Show that t1/2 ∝ 1/[A]n−1 for a reaction that is nth-order in A.
The rate constant for the decomposition of a certain substance is 2.80 × 10−3 dm3 mol−1 s−1 at 30°C and 1.38 × 10−2 dm3 mol−1 s−1 at 50°C. Evaluate the Arrhenius parameters of the
Set up the rate equations for the reaction mechanism: Show that the mechanism is equivalent to under specified circumstances. A А ka, К В Кы, К, С ka, B C
The base-catalysed bromination of nitromethane-d3 in water at room temperature (298 K) proceeds 4.3 times more slowly than the bromination of the undeuterated material. Account for this difference.
The effective rate constant for a gaseous reaction that has a Lindemann–Hinshelwood mechanism is 2.50 × 10−4 s−1 at 1.30 kPa and 2.10 × 10−5 s−1 at 12 Pa. Calculate the rate constant for
Consider the dimerization A ⇔ A2 with forward rate constant ka and backward rate constant kb. Show that the relaxation time is: T= 1 kb + 4k₁ [A]eq
Derive an integrated expression for a second-order rate law v = k[A][B] for a reaction of stoichiometry 2 A + 3 B → P.
Derive an equation for the steady-state rate of the sequence of reactions A ⇌ B ⇌ C ⇌ D, with [A] maintained at a fixed value and the product D removed as soon as it is formed.
One of the hazards of nuclear explosions is the generation of 90Sr and its subsequent incorporation in place of calcium in bones. This nuclide emits β rays of energy 0.55 MeV, and has a half-life of
Bearing in mind distinctions between the mechanisms of stepwise and chain polymerization, describe ways in which it is possible to control the molar mass of a polymer by manipulating the kinetic
Distinguish between competitive, non-competitive, and uncompetitive inhibition of enzymes. Discuss how these modes of inhibition may be detected experimentally.
Discuss experimental procedures that make it possible to differentiate between quenching by energy transfer, collisions, or electron transfer.
When benzophenone is illuminated with ultraviolet light it is excited into a singlet state. This singlet changes rapidly into a triplet, which phosphoresces. Triethylamine acts as a quencher for the
The enzyme-catalysed conversion of a substrate at 25°C has a Michaelis constant of 0.035 mol dm−3. The rate of the reaction is 1.15 × 10−3 mol dm−3 s−1 when the substrate concentration is
The number of photons falling on a sample can be determined by a variety of methods, of which the classical one is chemical actinometry. The decomposition of oxalic acid (COOH)2, in the presence of
In a photochemical reaction A → 2 B + C, the quantum efficiency with 500 nm light is 2.1 × 102 mol einstein−1 (1 Einstein = 1 mol photons). After exposure of 300 mmol of A to the light, 2.28
In an experiment to measure the quantum efficiency of a photochemical reaction, the absorbing substance was exposed to 490 nm light from a 100 W source for 45 min. The intensity of the transmitted
The following mechanism has been proposed for the thermal decomposition of acetaldehyde (ethanal): (1) CH3CHO → ·CH3 + CHO(2) ·CH3 + CH3CHO → CH4 + ·CH2CHO(3) ·CH2CHO → CO + ·CH3(4)
Calculate the ratio of the mean cube molar mass to the mean square molar mass in terms of(a) The fraction p,(b) The chain length.
Calculate the average polymer length in a polymer produced by a chain mechanism in which termination occurs by a disproportionation reaction of the form M· + ·M → M + :M.
Derive an expression for the time dependence of the degree of polymerization for a stepwise polymerization in which the reaction is acid catalysed by the -COOH acid functional group. The rate law is
The photochemical chlorination of chloroform in the gas has been found to follow the rate law d[CCl4]/dt = k[Cl2] 1/2Ia1/2. Devise a mechanism that leads to this rate law when the chlorine pressure
Nitrogen dioxide reacts bimolecularly in the gas phase to give 2 NO + O2. The temperature dependence of the second-order rate constant for the rate law d[P]/dt = k[NO2]2 is given below. What are the
The light-induced electron transfer reactions in photosynthesis occur because chlorophyll molecules (whether in monomeric or dimeric forms) are better reducing agents in their electronic excited
Calculate the collision frequency, z, and the collision density, Z, in ammonia, R = 190 pm, at 25°C and 100 kPa. What is the percentage increase when the temperature is raised by 10 K at constant
Distinguish between a diffusion-controlled reaction and an activation controlled reaction.
Collision theory demands knowing the fraction of molecular collisions having at least the kinetic energy Ea along the line of flight. What is this fraction when(a) Ea = 10 kJ mol−1,(b) Ea = 100 kJ
Calculate the percentage increase in the fractions in Exercise 24.2a when the temperature is raised by 10 K. Data in Exercise 24.2aCollision theory demands knowing the fraction of molecular
Discuss the physical origin of the kinetic salt effect.
Describe how the following techniques are used in the study of chemical dynamics: infrared chemiluminescence, laser-induced fluorescence, multiphoton ionization, resonant multiphoton ionization,
A typical diffusion coefficient for small molecules in aqueous solution at 25°C is 5 × 10−9 m2 s−1. If the critical reaction distance is 0.4 nm, what value is expected for the second-order rate
The rate constant of the reaction I−(aq) + H2O2(aq) → H2O(l) + IO−(aq) varies slowly with ionic strength, even though the Debye–Hückel limiting law predicts no effect. Use the following data
Justify the following statements:(a) Reactions with attractive potential energy surfaces proceed more efficiently if the energy is in relative translational motion.(b) Reactions with repulsive
Calculate the magnitude of the diffusion-controlled rate constant at 298 K for a species in(a) Water,(b) Pentane.The viscosities are 1.00 × 10−3 kg m−1 s−1 , and 2.2 × 10−4 kg m−1 s−1 ,
Calculate the magnitude of the diffusion-controlled rate constant at 298 K for the recombination of two atoms in water, for which η = 0.89 cP. Assuming the concentration of the reacting species is
Discuss how the following factors determine the rate of electron transfer in homogeneous systems: the distance between electron donor and acceptor, and the reorganization energy of redox active
For the gaseous reaction A + B → P, the reactive cross-section obtained from the experimental value of the pre-exponential factor is 9.2 × 10−22 m2. The collision cross-sections of A and B
Two neutral species, A and B, with diameters 588 pm and 1650 pm, respectively, undergo the diffusion-controlled reaction A + B → P in a solvent of viscosity 2.37 × 10−3 kg m−1 s−1 at 40°C.
The reaction of propylxanthate ion in acetic acid buffer solutions has the mechanism A− + H+→ P. Near 30°C the rate constant is given by the empirical expression k2 = (2.05 × 1013)e−(8681
The gas-phase association reaction between F2 and IF5 is first-order in each of the reactants. The energy of activation for the reaction is 58.6 kJ mol−1. At 65°C the rate constant is 7.84 ×
Determine the ratios of(a) The mean speeds,(b) The mean kinetic energies of H2 molecules and Hg atoms at 20°C.
Provide a molecular interpretation for each of the following processes: diffusion, thermal conduction, electric conduction, and viscosity.
A 1.0 dm3 glass bulb contains 1.0 × 1023 H2 molecules. If the pressure exerted by the gas is 100 kPa, what are(a) The temperature of the gas,(b) The root mean square speeds of the molecules?(c)
The element polonium crystallizes in a cubic system. Bragg reflections, with X-rays of wavelength 154 pm, occur at sin θ = 0.225, 0.316, and 0.388 from the (100), (110), and (111) sets of planes.
What are the relative populations of the states of a two-level system when the temperature is infinite?
Explain how the internal energy and entropy of a system composed of two levels vary with temperature.
Calculate the translational partition function at(a) 300 K and(b) 600 K of a molecule of molar mass 120 g mol−1 in a container of volume 2.00 cm3.
Consider 1.00 × 1022 4He atoms in a box of dimensions 1.0 cm × 1.0 cm × 1.0 cm. Calculate the occupancy of the first excited level at 1.0 mK, 2.0 K, and 4.0 K. Do the same for 3He. What
Enumerate the ways by which the parameter β may be identified with 1/kT.
Calculate the ratio of the translational partition functions of D2 and H2 at the same temperature and volume.
Distinguish between the zipper and Zimm–Bragg models of the helix–coil transition.
A certain atom has a threefold degenerate ground level, a nondegenerate electronically excited level at 3500 cm−1, and a threefold degenerate level at 4700 cm−1. Calculate the partition function
By what factor does the number of available configurations increase when 20 m3 of air at 1.00 atm and 300 K is allowed to expand by 0.0010 per cent at constant temperature?
Calculate the electronic contribution to the molar internal energy at 1900 K for a sample composed of the atoms specified in Exercise 16.4a.Data in Exercise 16.4a.A certain atom has a threefold
A certain molecule has a non-degenerate excited state lying at 540 cm−1 above the non-degenerate ground state. At what temperature will 10 per cent of the molecules be in the upper state?
Consider a system of distinguishable particles having only two nondegenerate energy levels separated by an energy that is equal to the value of kT at 10 K. Calculate(a) The ratio of populations in
The four lowest electronic levels of a Ti atom are: 3F2, 3F3, 3F4, and 5F1, at 0, 170, 387, and 6557 cm−1, respectively. There are many other electronic states at higher energies. The boiling point
At what temperature would the population of the first excited vibrational state of HCl be 1/e times its population of the ground state?
Calculate the standard molar entropy of neon gas at(a) 200 K,(b) 298.15 K.
Calculate the vibrational contribution to the entropy of Cl2 at 500 K given that the wavenumber of the vibration is 560 cm−1.
Identify the systems for which it is essential to include a factor of 1/N! on going from Q to q:(a) A sample of helium gas,(b) A sample of carbon monoxide gas,(c) A solid sample of carbon
A certain molecule can exist in either a non-degenerate singlet state or a triplet state (with degeneracy 3). The energy of the triplet exceeds that of the singlet by ε. Assuming that the molecules
Consider Stirling’s approximation for ln N! in the derivation of the Boltzmann distribution. What difference would it make if(a) A cruder approximation, N! = NN,(b) The better approximation in
Explore whether a magnetic field can influence the heat capacity of a paramagnetic molecule by calculating the electronic contribution to the heat capacity of an NO2 molecule in a magnetic field.
Explain the origin of the symmetry number.
Estimate the values of γ = Cp/CV for gaseous ammonia and methane. Do this calculation with and without the vibrational contribution to the energy. Which is closer to the expected experimental value
Estimate the rotational partition function of HCl at(a) 25°C and(b) 250°C.
Calculate the temperature dependence of the heat capacity of p-H2 (in which only rotational states with even values of J are populated) at low temperatures on the basis that its rotational levels J =

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