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chemistry
physical chemistry

Questions and Answers of Physical Chemistry

Nuclear magnetic resonance can be used to determine the mobility of molecules in liquids. A set of measurements on methane in carbon tetrachloride showed that its diffusion coefficient is 2.05 x
In a series of observations on the displacement of rubber latex spheres of radius 0.212 urn, the mean square displacements after selected time intervals were on average as follows: These results
A. Fenghour, W.A. Wake ham, V. Vesovic, I.T.R. Watson, I. Millet, and E. Vogel. Phys. Chem. Ref Data 24, 1649 (1995)) have compiled an extensive table of viscosity coefficients for ammonia in the
Start from the Maxwell-Boltzmann’s distribution and derive an expression for the most probable speed of a gas of molecules at a temperature T. Go on to demonstrate the validity of the equipartition
A specially constructed velocity-selector accepts a beam of molecules from an oven at a temperature T but blocks the passage of molecules with a speed greater than the mean. What is the mean speed of
Calculate the fractions of molecules in a gas that have a speed in a range t. v at the speed ne relative to those in the same range at c itself? This calculation can be used to estimate the fraction
Show how the ratio of two transport numbers t' and t" for two cautions in a mixture depends on their concentrations c' and c" and their mobilities u' and UN.
The diffusion equation is valid when many elementary steps are taken in the time interval of interest, but the random walk calculation lets us discuss distributions for short times as well as for
Supply the intermediate mathematical steps in Justification 21.7.
Calculate the escape velocity (the minimum initial velocity that will take an object to infinity) from the surface of a planet of radius R. What is the value for? (a) The Earth, R = 6.37 X 106 m, g=
The principal components of the atmosphere of the Earth are diatomic molecules, which can rotate as well as translate. Given that the translational kinetic energy density of the atmosphere is 0.15 J
Enrico Fermi, the great Italian scientist, was a master at making good approximate calculations based on little or no actual data. Hence, such calculations are often called 'Fermi calculations'. Do a
In this problem, we examine a model for the transport of oxygen from air in the lungs to blood. First, show that, for the initial and boundary conditions c(x, t) = c(x, 0) = co (0 < x < ∞] and c(0,
Consult literature sources and list the observed timescales during which the following processes occur radiative decay of excited electronic states, molecular rotational motion, molecular vibrational
Describe the main features, including advantages and disadvantages, of the following experimental methods for determining the rate law of a reaction: the isolation method, the method of initial
Assess the validity of the following statement: the rate-determining step is the slowest step in a reaction mechanism.
Distinguish between kinetic and thermodynamic control of a reaction.
Distinguish between a primary and a secondary kinetic isotope effect. Discuss how kinetic isotope effects in general can provide insight into the mechanism of a reaction.
The rate of the reaction A + 3 B --7 C + 2 D was reported as 1.0 mol dm-1 S-1. State the rates of formation and consumption of the participants.
The rate of consumption of B in the reaction A + 3 B → 7 C + 2 D is 1.0 mol dm3 S-1. State the reaction rate, and the rates of formation or consumption of A, C, and D.
The rate law for the reaction in Exercise 22.1b was found to be v = k[A][BF, What are the units of k? Express the rate law in terms of the rates of formation and consumption of (a) A, (b) C.
The rate law for the reaction in Exercise 22.2b was reported as d[C]/dt = k[A] [B][C]-l Express the rate law in terms of the reaction rate; what are the units for k in each case?
At 400 K, the rate of decomposition of a gaseous compound initially at a pressure of 12.6 kPa was 9.71 Pa S-1 when 10.0 per cent had reacted and 7.67 Pa S-I when 20.0 per cent had reacted. Determine
At 400 K, the half-life for the decomposition of a sample of a gaseous compound initially at 55.5 kPa was 340 s. When the pressure was 28.9 kPa, the half-life was 178 s. Determine the order of the
The rate constant for the first-order decomposition of a compound A in the reaction 2 A --7 P is k = 2.78 X 10.7 S·1 at 25°C. What is the half-life of A? What will be the pressure, initially 32.1
A second-order reaction of the type A + 2 B --7 P was carried out in a solution that was initially 0.075 mol dm3 in A and 0.030 mol dm3 in B. After 1.0 h the concentration of A had fallen to 0.045
If the rate laws are expressed with (a) Concentrations in molecules per meter cubed, (b) Pressures in newtons per meter squared, what are the units of the second-order and third-order rate constants?
The second-order rate constant for the reaction A + 2 B --7 C + D is 0.21 dm 3 mol-J S-1. What is the concentration of C after? (a) 10 s, (b) 10 min when the reactants are mixed with initial
A reaction 2 A --7 P has a third-order rate law with k = 3.50 X 10-4 dm3 mol3 S-1. Calculate the time required for the concentration of A to change from 0.077 mol dm-3 to 0.021 mol dm-3.
Deduce an expression for the time it takes for the concentration of a substance to fall to one-third its initial value in an nrh-order reaction.
The equilibrium Ac=' B + C at 25°C is subjected to a temperature jump that slightly increases the concentrations of Band C. The measured relaxation time is 3.0 us. The equilibrium constant for the
The rate constant for the decomposition of a certain substance is 1.70 x 10-2 dm3 mol-1 S-1 at 24°C and 2.01 X 10-2 dm3 mol-1 S-1 at 37"C. Evaluate the Arrhenius parameters of the reaction.
Predict the order of magnitude of the isotope effect on the relative rates of displacement of (a) IH and 3H, (b) 160 and ISO. Will raising the temperature enhance the difference? Take kr(C-H) = 450 N
The effective rate constant for a gaseous reaction that has a Lindemann-Hinshelwood mechanism is 1.7 X 10-3 s-I at 1.09 kPa and 2.2 X 10-4 S-1 at 25 Pa. Calculate the rate constant for the activation
The data below apply to the formation of urea from ammonium cyanate, NH4CNO --7 NH2CONH2. Initially 22.9 g of ammonium cyanate was dissolved in enough water to prepare 1.00 dm3 of solution. Determine
The thermal decomposition of an organic nitrile produced the following data: Determine the order of the reaction and the rate constant.
A first -order decomposition reaction is observed to have the following rate constants at the indicated temperatures. Estimate the activation energy.
Sucrose is readily hydrolyzed 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.
Show that the following mechanism can account for the rate law of the reaction in Problem 22.11:What further tests could you apply to verify this mechanism?
In the experiments described in Problems 22.11 and 22.13 an inverse temperature dependence of the reaction rate was observed, the overall rate of reaction at 70°C being roughly one-third that at
In Problem 22.10 the isomerization of cyclopropane over a limited pressure range was examined. If the Lindemann mechanism of first €“order reactions is to be tested we also need data at low
Two products are formed in reactions in which there is kinetic control of the ratio of products. The activation energy for the reaction leading to Product 1 is greater than that leading to Product 2.
The equilibrium A ( B is first -order in both directions. Derive an expression for the concentration of A as a function of time when the initial molar concentrations of A and Bare [A]0 and [B]0. What
Derive the integrated form of a third-order rate law v = k[A f [B] in which the stoichiometry is 2 A + B ( P and the reactants are initially present in (a) Their stoichiometric proportions, (b) With
Show that the ratio t1/2/t3/4 where 1112 is the half-life and 13/4is the time for the concentration of A to decrease to t of its initial value (implying that t3/4 < t1/2) can be written as a function
For a certain second-order reaction A + B -7 Products, the rate of reaction, v, may be written where x is the decrease in concentration of A or B as a result of reaction.Find an expression for the
The half-life for the (first-order) radioactive decay of 14Cis 5730 y (it emits B rays with an energy of 0.16 MeV). An archaeological sample contained wood that had only 72 per cent of the 14Cfound
Pharmacokinetics is the study of the rates of absorption and elimination of drugs by organisms. In most cases, elimination is slower than absorption and is a more important determinant of
Consider a mechanism for the helix-coil transition in which nucleation occurs in the middle of the chain:We saw in Impact 122.1 that this type of nucleation is relatively slow, so neither step may be
Consider the following mechanism for renaturation of a double helix from its strands A and B:Derive the rate equation for the formation of the double helix and express the rate constant of the
Methane is a by-product of a number of natural processes (such as digestion of cellulose in ruminant animals, anaerobic decomposition of organic waste matter) and industrial processes (such as food
T. Gierczak, R.K. Talukdar, S.C. Herndon, G.L. Vaghjiani, and A.R. Ravish Ankara (J. Phys. Chem. A 101, 3125 (1997)) measured the rate constants for the bimolecular gas-phase reaction of methane with
The CIO radical decays rapidly by way of the reaction, 2 CIO ---7Cl, + Oz.The following data have been obtained:Determine the rate constant of the reaction and the half-life of a CIO radical.
The addition of hydrogen halides to alkenes has played a fundamental role in the investigation of organic reaction mechanisms. In one study (M.J. Haugh and D.R. Dalton, J. Amer. Chem. Sac. 97, 5674
Identify any initiation, propagation, retardation inhibition, and termination steps in the following chain mechanisms:
Discuss the features, advantages, and limitations of the Michaelis-Menten mechanism of enzyme action.
Distinguish between the primary quantum yield and overall quantum yield of a chemical reaction. Describe an experimental procedure for the determination of the quantum yield.
Summarize the main features of the Forster theory of resonance energy transfer. Then, discuss FRET in terms of Forster theory.
On the basis of the following proposed mechanism, account for the experimental fact that the rate law for the decomposition 2 N2O5 (g) → 4 NO2 (g) + O2 (g) is v=k [N205]'
Consider the following mechanism for the thermal decomposition ofR2:Where R2, PA' PB are stable hydrocarbons and Rand R' are radicals. Find the dependence of the rate of decomposition of R, on the
Refer to Fig. 23.3 and determine the pressure range for a branching chain explosion in the hydrogen-oxygen reaction at (a) 700 K,(b) 900 K.
Consider the acid-catalyzed reactionDeduce the rate law and show that it can be made independent of the specific term [H+].
Consider the following chain mechanism:Use the steady-state approximation to deduce that the rate law for the consumption of A2.
The enzyme-catalyzed conversion of a substrate at 25°C has a Michaelis constant of 0.042 mol dm-3. The rate of the reaction is 2.45 x 10-4 mol dm-3 s-1 when the substrate concentration is 0.890 mol
In a photochemical reaction A -7 B + C, the quantum efficiency with 500 nm light is 1.2 x 102 mol einstein-1, After exposure of 200 mmol A to the light, 1.77 mmol B is formed. How many photons were
In an experiment to measure the quantum efficiency of a photochemical reaction, the absorbing substance was exposed to 320 nm radiation from an 87.5 W source for 28.0 min. The intensity of the
Studies of combustion reactions depend on knowing the concentrations of H atoms and HO radicals. Measurements on a flow system using EPR for the detection of radicals gave information on the
I.D. Chapple-Sokol, Cl Giunta, and R.G. Gordon (J Electrochem Sac 136,2993 (1989)) proposed the following radical chain mechanism for the initial stages of the gas-phase oxidation of silane by
For many years the reaction Hz (g) + I2 (g) →7 2 HI (g) and its reverse were assumed to be elementary bimolecular reactions. However, I.H. Sullivan (J. Chem. Phys. 46, 73 (1967)) suggested that
Dansyl chloride, which absorbs maximally at 330 nm and fluoresces maximally at 510 nm, can be used to label amino acids in fluorescence microscopy and FRET studies. Tabulated below is the variation
An electronically excited state of Hg can be quenched by N, according toHg* (g) + Nz (g, V = 0) -7 Hg (g) + N, (g, v = 1) in which energy transfer from Hg* excites Nz vibrationally. Fluorescence
The Rice-Herzfeld mechanism for the dehydrogenation of ethane is specified in Section 23.1, and it was noted there that it led to first-order kinetics. Confirm this remark, and find the
Express the root mean square deviation {(M2) - (M} 2} 1/2 of the molar mass of a condensation polymer in terms of p, and deduce its time dependence.
Calculate the average polymer length in a polymer produced by a chain mechanism in which termination occurs by a disproportionate reaction of the form M• +•M → M + M.
Autocatalysis is the catalysis of a reaction by the products. For example, for a reaction A -> P it may be found that the rate law is v = k[A] [P] and the reaction rate is proportional to the
Derive an expression for the rate of disappearance of a species A in a photochemical reaction for which the mechanism is:Hence, show that rate measurements will give only a combination of k2 and k3
Photolysis of Cr (CO)6 in the presence of certain molecules M, can give rise to the following reaction sequence:Suppose that the absorbed light intensity is so weak that! «k4 [Cr (CO) 5M]. Find
Many enzyme-catalyzed reactions are consistent with a modified version of the Michaelis-Menten mechanism in which the second step is also reversible.(a) For this mechanism show that the rate of
Enzyme-catalyzed reactions are sometimes analyzed by use of the Eadie-Hofstee plot, in which v is plotted against v/[S]o (a) Using the simple Michaelis-Menten mechanism, derive a relation between
The enzyme carboxypeptidase€™s catalyses the hydrolysis of polypeptides and here we consider its inhibition. The following results were obtained when the rate of the enzymolysis of
In light-harvesting complexes, the fluorescence of a chlorophyll molecule is quenched by nearby chlorophyll molecules. Given that for a pair of chlorophyll a molecules Ra = 5.6 nm, by what distance
The emission spectrum of a porphyry in dissolved in O,-saturated water shows a strong band at 650 nm and a weak band at 1270 nm. In separate experiments, it was observed that the electronic
Use the Chapman model to explore the behaviour of a model atmosphere consisting of pure 0, at 10 Torr and 298 K that is exposed to measurable frequencies and intensities of UV radiation. (a) Look up
Because of its importance in atmospheric chemistry, the thermal decomposition of nitric oxide, 2 NO (g) -7 N,(g) + O,(g), has been amongst the most thoroughly studied of gas-phase reactions. The
Describe the essential features of the harpoon mechanism.
Describe the formulation of the Eyring equation.
Describe how the following techniques are used in the study of chemical dynamics: infrared chemiluminescence’s laser-induced fluorescence, multi-photon ionization, resonant multi-photon ionization,
A method for directing the outcome of a chemical reaction consists of using molecular beams to control the relative orientations of reactants during a collision. Consider the reaction Rb + CH3I
Calculate the collision frequency, z, and the collision density, Z, in carbon monoxide, R = 180 pm at 25°C and 100 kPa. What is the percentage increase when the temperature is raised by 10 K at
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= 15 k] mol-1, (b) Ea = 150 k]
Calculate the percentage increase in the fractions in Exercise 24.2b when the temperature is raised by 10 K.
Use the collision theory of gas-phase reactions to calculate the theoretical value of the second-order rate constant for the reaction D2 (g) + Br2 (g) →2 DBr (g) at 450 K, assuming that it is
Suppose that the typical diffusion coefficient for a reactant in aqueous solution at 25°C is 4.2 x 10-9 m2 S-I. If the critical reaction distance is 0.50 nm, what value is expected for the
Calculate the magnitude of the diffusion-controlled rate constant at 298 K for a species in (a) Decylbenzene, (b) Concentrated sulfuric acid. The viscosities are 3.36 cP and 27 cP, respectively.
Calculate the magnitude of the diffusion-controlled rate constant at 298 K for the recombination of two atoms in benzene, for which 17 = 0.601 cP. Assuming the concentration of the reacting species
For the gaseous reaction A + B --7 P, the reactive cross-section obtained from the experimental value of the pre-exponential factor is 8.7 X 10-22 nm. The collision cross-sections of A and B
Two neutral species, A and B, with diameters 442 pm and 885 pm, respectively, undergo the diffusion-controlled reaction A + B --7 P in a solvent of viscosity 1.27 cP at20°C. Calculate the initial
The reaction A- + H+ --7 P has a rate constant given by the empirical expression k2 = (8.72 x 1012)e-(6134KI/T dm-3 mol-1 s-1 Evaluate the energy and entropy of activation at 25°C.
A rate constant is found to fit the expression k2 = (6.45 X 1013) e-(5375K)/T dm3 mol-3 s-1 near 25°C. Calculate G for the reaction at 25°C.
A gas-phase recombination reaction is first-order in each of the reactants. The energy of activation for the reaction is 49.6 kJ mol-1 at 55°C the rate constant is 0.23 m' S-I. Calculate the entropy

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