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chemistry
physical chemistry

Physical Chemistry 7th Edition Peter Atkins - Solutions

The heat capacity of anhydrous potassium hexacyanoferrate (II) varies with temperature as follows: TIK Cp,m/J K-I mol-I) TIK Cp,m/JK-I
Estimate the coefficients a and b in the Dieterici equation of state from the critical constants of xenon. Calculate the pressure exerted by 1.0 mol Xe when it is confined to 1.0 dm3 at 25°C.
Given that Som = 29.79 J K-I mol-1 for bismuth at 100 K and the following tabulated heat capacities data (D.G. Archer,]. Chem. Eng. Data 40, 1015 (1995)), compute the standard molar entropy of bismuth at 200 K T/K 100 120 140 150 160 180 200 Cp, m/JK-I
Estimate the standard reaction Gibbs energy of N2 (g) + 3 H2 (g) –t 2 NH3 (g) at (a) 500 K, (b) 1000 K from their values at 298 K.
Represent the Carnot cycle on a temperature-entropy diagram and show that the area enclosed by the cycle is equal to the work done.
Prove that the perfect gas temperature scale and the thermodynamic temperature scale based on the Second Law of thermodynamics differ from each other by at most a constant numerical factor.
Evaluate (ClS/ClV)]' for (a) A van der Waals gas, (b) A Dieterici gas (Table 1.7). For an isothermal expansion, for which kind of gas (and a perfect gas) will /).5be greatest? Explain your conclusion.
Two of the four Maxwell relations were derived in the text, but two were not. Complete their derivation by showing that (∂S/∂V)T = (∂p/∂T)V (∂T/∂P)s = (∂V/∂S)p
Use the Maxwell relations to show that the entropy of a perfect gas depends on the volume as 5 = R In V.
Show that if B (T) is the second virial coefficient of a gas, and ∆B = B (T") – B (T), /)'T= T' - T, and T is the mean of T' and T, then πT= RT2t ∆BIV~,/)'T. Estimate IT]' for argon given that B(250 K) = -28.0 cm3 mol-1 and B(300 K) = -15.6 cm3 mol-1 at 275 K at (a) 1.0 atm,
Evaluate πT for a Dieterici gas (Table 1.7). Justify physically the form of the expression obtained.
Suppose that S is regarded as a function of P and T. Show that TdS= CpdT- aTVdp. Hence, show that the energy transferred as heat when the pressure on an incompressible liquid or solid is increased by ∆p is equal to -aTV∆p. Evaluate q when the pressure acting on 100 cm3 of mercury at
Find an expression for the fugacity coefficient of a gas that obeys the equation of state pVm = RT(1 +B/Vm + C/V-1). Use the resulting expression to estimate the fugacity of argon at 1.00 am3 and 100 K using B = -21.13 cm? mol-1 and C = 1054 em3 mol-1.
At 298 K the standard enthalpy of combustion of sucrose is -5797 k] mol-I and the standard Gibbs energy of the reaction is -6333 k] mol ". Estimate the additional non-expansion work that may be obtained by raising the temperature to blood temperature, 37aC.
In 1995, the Intergovernmental Panel on Climate Change (IPCC) considered a global average temperature rise of 1.0-3SC likely by the year 2100, with 2.0°C its best estimate. Because water vapour is itself a greenhouse gas, the increase in water vapour content of the atmosphere is of some concern to
J. Gao and J. H. Weiner in their study of the origin of stress on the atomic level in dense polymer systems (Science 266,748 (1994)), observe that the tensile force required to maintain the length, I, of a long linear chain of N freely jointed links each of length a, can be interpreted as arising
The cycle involved in the operation of an internal combustion engine is called the Otto cycle. Air can be considered to be the working substance and can be assumed to be a perfect gas. The cycle consists of the following steps: (l) reversible adiabatic compression from A to B, (2) reversible
The expressions that apply to the treatment of refrigerators also describe the behaviour of heat pumps, where warmth is obtained from the back of a refrigerator while its front is being used to cool the outside world. Heat pumps are popular home heating devices because they are very
Define the following terms: phase, constituent, component, and degree of freedom.
Draw phase diagrams for the following types of systems. Label the regions and intersections of the diagrams, stating what materials (possibly compounds or azeotropes) are present and whether they are solid liquid or gas. (a) One component, pressure-temperature diagram, liquid density greater than
Label the regions of the phase diagram in Fig. 6.3 7. State what substances (if compounds give their formulas) exist in each region. Label each substance in each region as solid, liquid, or gas.
The emf of the cell Bi|Bi2S3(s) IBi2S3(aq) IBi is -0.96 V at 25°e. Calculate (a) The solubility product ofBi2S3 and (b) Its solubility. at310K?
At 90°C, the vapour pressure of I, 2-dimethylbenzene is 20 kPa and that of 1,3-dimethylbenzene is 18 kPa. What is the composition of a liquid mixture that boils at 90°C when the pressure is 19 kPa? What is the composition of the vapour produced?
The vapour pressure of pure liquid A at 293 K is 68.8 kPa and that of pure liquid B is 82.1 kPa. These two compounds form ideal liquid and gaseous mixtures. Consider the equilibrium composition of a mixture in which the mole fraction of A in the vapour is 0.612. Calculate the total pressure of the
It is found that the boiling point of a binary solution of A and B with xA = 0.4217 is 96°C. At this temperature the vapour pressures of pure A and B are l lu.I kPa and 76.5 kPa, respectively.(a) Is this solution ideal?(b) What is the initial composition of the vapor above the solution?
Benzene and toluene form nearly ideal solutions. Consider an equimolar solution of benzene and toluene. At 20°C the vapour pressures of pure benzene and toluene are 9.9 kPa and 2.9 kPa, respectively. The solution is boiled by reducing the external pressure below the vapour pressure. Calculate
The following temperature/composition data were obtained for a mixture of two liquids A and B at 1.00 atm, where x is the mole fraction in the liquid and Y the mole fraction in the vapour at equilibrium. Ere 125 130 135 140 145 150 XA 0.91 0.65 0045 0.30 0.18 0.098 YA 0.99 0.91
State the number of components for a system in which AlCI, is dissolved in water, noting that hydrolysis and precipitation of AI (OH), occur.
Ammonium chloride, NH4Cl, decomposes when it is heated. (a) How many components and phases are present when the salt is heated in an otherwise empty container? (b) Now suppose that additional ammonia is also present. How many components and phases are present?
Suppose that the solution referred to in Exercise 6.8a is not saturated. (a) How many phases and components are present? (b) What is the variance (the number of degrees of freedom) of the system? Identify the independent variables.
Sketch the phase diagram of the system NH3/NzH. given that the two substances do not form a compound with each other, that NH3 freezes at -78°C and N2H. freezes at +2°C, and that a eutectic is formed when the mole fraction ofN2H. is 0.07 and that the eutectic melts at -SO°e.
Figure 6.40 is the phase diagram for silver and tin. Label the regions, and describe what will be observed when liquids of compositions a and bare cooled to 200 K.
Indicate on the phase diagram in Fig. 6.42 the feature that denotes incongruent melting. What is the composition of the eutectic mixture and at what temperature does it melt?
Sketch the cooling curves for the isopleths a and b in Fig. 6.42
Use the phase diagram in Fig. 6.41 to state (a) The solubility of B in A at 500°C and (b) The solubility of AB2 in A at 390°C, (c) The solubility of ABz in Bat 300°e.
Uranium tetra fluoride and zirconium tetra fluoride melt at 1035°C and 912°C, respectively. They form a continuous series of solid solutions with a minimum melting temperature of 765°C and composition x (ZrF.) = 0.77. At 900°C, the liquid solution of composition x(ZrF.) = 0.28 is in equilibrium
Describe the phase changes that take place when a liquid mixture of 4.0 mol B2H6 (melting point 131 K) and 1.0 mol CH30CH3 (melting point 135 K) is cooled from 140 K to 90 K. These substances form a compound (CH3), OB2H6 that melts congruently at 133 K. The system exhibits one eutectic at x (B2H6)
Refer to the information in Exercise 6.15(a) and sketch the cooling curves for liquid mixtures in which x(CF4) is(a) 0.10,(b) 0.30,(c) 0.50,(d) 0.80,(e) 0.95.
Two liquids, A and B, show partial miscibility below 52.4°C. The critical concentration at the upper critical temperature is x = 0.459, where x is the mole fraction of A. At 40.0°C the two solutions in equilibrium have x = 0.22 and x = 0.60, respectively, and at 42.5°C the mole fractions are
I-Butanol and chlorobenzene form a minimum-boiling azeotropic system. The mole fraction of I-butanol in the liquid (x) and vapour (y) phases at 1.000 atm is given below for a variety of boiling temperatures (H. Artigas, C. Lafuente, P. Cea, F.M. Royo, and J.S. Urieta,J. Chem. Eng. Data 42,132
The following data have been obtained for the liquid-vapour equilibrium compositions of mixtures of nitrogen and oxygen at 100 kPa. T/K 77.3 78 80 82 84 86 88 90.2 X (O2) 0 10 34 54 70 82 92 100 y(O2) 0 2 11 22 35 52 73 100 P(O2)/torr 154 171 225 294 377 479 601 760 Plot the data on a
The table below gives the break and halt temperatures found in the cooling curves of two metals A and B. Construct a phase diagram consistent with the data of these curves. Label the regions of the diagram, stating what phases and substances are present. Give the probable formulas of any compounds
Sketch the phase diagram for the Mg/Cu system using the following information: Br(Mg) = 648°C, Br(Cu) = 1085°C; two intermetallic compounds are formed with Br(MgCu2) = 800°C and Br(Mg2Cu) = 580°C; eutectics of mass percentage Mg composition and melting points la per cent (690°C), 33 per cent
The temperature-composition diagram for the Ca/Si binary system is shown in Fig. 6.46. (a) Identify eutectics, congruent melting compounds, and incongruent melting compounds. (b) If a 20 per cent by atom composition melt of silicon at 1500°C is cooled to 1000°C, what phases (and phase
Show that two phases are in thermal equilibrium only if their temperatures are the same.
The unfolding, or denaturation, of a biological macromolecule may be brought about by treatment with substances, called denaturants that disrupt the intermolecular interactions responsible for the native three-dimensional conformation of the polymer. For example, urea, CO (NH2)2' competes for NH
The compound p-azoxyanisole forms a liquid crystal. 5.0 g of the solid was placed in a tube, which was then evacuated and sealed. Use the phase rule to prove that the solid will melt at a definite temperature and that the liquid crystal phase will make a transition to a normal liquid phase at a
Use a phase diagram like that shown in Fig. 6.36 to indicate how zone leveling may be described.
Magnesium oxide and nickel oxide withstand high temperatures. However, they do melt when the temperature is high enough and the behaviour of mixtures of the two is of considerable interest to the ceramics industry. Draw the temperature-composition diagram for the system using the data below, where
Carbon dioxide at high pressure is used to separate various compounds in citrus oil. The mole fraction of CO, in the liquid (x) and vapour (y) at 323.2 K is given below for a variety of pressures (Y. Iwai, T. Morotomi, K.Sakamoto, Y. Koga, and Y. Arai,J. Chem. Eng. Data 41,951 (1996)).PlMPa
Explain how the mixing of reactants and products affects the position of chemical equilibrium.
Account for Le Chatelier's principle in terms of thermodynamic quantities.
(a) How may an Ellingham diagram be used to decide whether one metal may be used to reduce the oxide of another metal?(b) Use the Ellingham
Describe the contributions to the emf of cells formed by combining the electrodes specified in Table 7.1.
Devise a method for the determination of the pH of an aqueous solution.
For the equilibrium, NP4 (g); =‘02N02 (g), the degree of dissociation, a" at 298 K is 0.201 at 1.00 bar total pressure. Calculate(a) ∆G,(b) K,(c) ∆G at 298 K.
Molecular bromine is 24 per cent dissociated at 1600 K and 1.00 bar in the equilibrium Br2 (g) = o 2 Br (g). Calculate(a) Kat 25°C,(b) ∆p3,(c) Kat 2000°C given that L3.,H3= + 112 k] mol-lover the temperature range.
From information in the Data section, calculate the standard Gibbs energy and the equilibrium constant at(a) 25°C(b) 50°C for the reaction CH4(g) + 3 C12(g) ='0CHC13(l) + 3 HCl(g). Assume that the reaction enthalpy is independent of temperature.
In the gas-phase reaction A + B ;:='0C + 2 D, it was found that, when 2.00 mol A, 1.00 mol B, and 3.00 mol D were mixed and allowed to come to equilibrium at 25°C, the resulting mixture contained 0.79 mol C at a total pressure of 1.00 bar. Calculate(a) The mole fractions of each species at
The standard enthalpy of a certain reaction is approximately constant at + 125 k] mol-l from 800 K up to 1500 K. The standard reaction Gibbs energy is +22 kJ mol-1 at 1120 K. Estimate the temperature at which the equilibrium constant becomes greater than 1.
The equilibrium constant of a reaction is found to fit the expression In K =A + BIT+ CIT3 between 400 K and 500 K with A = -2.04, B =-1176 K, and C = 2.1 X 107 K3 Calculate the standard reaction enthalpy and standard reaction entropy at 450 K.
The equilibrium pressure of H, over solid uranium and uranium hydride, UH3' at 500 K is 139 Pa. Calculate the standard Gibbs energy of formation ofUH3 (s) at 500 K.
Calculate the percentage change in K; for the reaction CH30H (g) + NOCl(g) ;:='0HCl(g) + CH3N02(g) when the total pressure is increased from 1.0 bar to 2.0 bar at constant temperature.
The equilibrium constant for the reaction N2 (g) + O,(g) ;:='02NO(g) is 1.69 x 10-3 at 2300 K. A mixture consisting of 5.0 g of nitrogen and 2.0 g of oxygen in a container of volume 1.0 dm3 is heated to 2300 K and allowed to come to equilibrium. Calculate the mole fraction of NO at equilibrium.
What is the standard enthalpy of a reaction for which the equilibrium constant is (a) doubled, (b) halved when the temperature is increased by 15 K
The dissociation vapour pressure ofNH4Cl at 427°C is 608 kPa but at 459°C it has risen to 1115 kPa. Calculate (a) The equilibrium constant, (b) The standard reaction Gibbs energy, (c) The standard enthalpy, (d) The standard entropy of dissociation, all at 427°C. Assume that the vapour
Estimate the temperature at which CuS045H,O undergoes dehydration.
For PbI2(s) = 0Pb+(aq) + 2 r(aq), K = 1.4 X 10-8 at 25°C and the standard Gibbs energy of formation ofPbI2(s) is -173.64 k] mol ". Calculate the standard Gibbs energy of formation of PbI2 (aq).
Write the cell reaction and electrode half-reactions and calculate the standard emf of each the following cells: (a) Ptl C12 (g) I HCl (aq) 11 K, Cr04 (aq) IAg, Cr04(s) IAg (b) Pt 1 Fe3+(aq),Fe2+(aq) 11 Sn4+(aq),Sn2+(aq) 1 Pt (c) Cu 1 Cu2+ (aq) 11 Mn2+ (aq), W (aq) 1 MnO, (s) 1 Pt
Devise cells in which the following are the reactions and calculate the standard emf in each case: (a) 2 Na(s) + 2 H20 (l) --7 2 NaOH (aq) + H2 (g) (b) H2 (g) + I2 (g) --72 HI (aq) (c) H30+ (aq) + OW (aq) --72 HzO (l)
Consider the cell Pt |H2 (g, po) | HC| (aq) AgCI(s) Ag, for which the cell reaction is 2 AgCl(s) + H2 (g) --72 Ag(s) + 2 HCl (aq). At 25°C and a molality of HCl of 0.010 mol kg, E = +0.4658 V. (a) Write the Nernst equation for the cell reaction. (b) Calculate ∆G for the cell reaction.
Calculate the equilibrium constants of the following reactions at 25°C from standard potential data: (a) Sn(s) + CuS04 (aq) ~ Cu(s) + SnS04 (aq) (b) Cu2+(aq) + Cu(s) ~ 2 Cu+{aq)
The equilibrium constant for the reaction, 12(s) + Br2 (g) 2 IB r (g) is 0.164 at 25°C. (a) Calculate ∆rG° for this reaction. (b) Bromine gas is introduced into a container with excess solid iodine. The pressure and temperature are held at 0.164 atm and 25°C, respectively. Find the
The equilibrium pressure ofH2 over U(s) and UH3(s) between 450 K and 715 K fits the expression in (p/Pa) =A + B/T + C ln (T/K), with A = 69.32, B = -1.464 X 104K, and C = -5.65. Find an expression for the standard enthalpy of formation ofUH3(s) and from it calculate ∆rCp
The standard reaction enthalpy for the decomposition of CaCI2•NH3(s) into CaCl2 (s) and NH3 (g) is nearly constant at +78 k] rnol-1 between 350 K and 470 K. The equilibrium pressure of NH3 in the presence ofCaCI2•NH3 is 1.71 kPa at 400 K. Find an expression for the temperature dependence of
Acetic acid was evaporated in container of volume 21.45 cm3 at 437 K and at an external pressure of 101.9 kPa, and the container was then sealed. The mass of acid present in the sealed container was 0.0519 g. The experiment was repeated with the same container but at 471 K, and it was found that
The dissociation of I, can be monitored by measuring the total pressure, and three sets of results are as follows: T/K 973 1073 1173 100p/atm 6.244 7.500 9.181 104nj 2.4709 2.4555 2.4366 Where n1 is the amount of I atoms per mole of I, molecules in the mixture, which occupied
The 1980s saw reports of ∆fHΘ (SiH2) ranging from 243 to 289 k] mol-1. For example, the lower value was cited in the review article by R. Walsh (Ace. Chem. Res. 14,246 (1981)); Walsh later leant towards the upper end of the range (H.M. Frey, R. Walsh, and LM. Watts, J Chem. Soc., Chem.
Given that ∆tGΘ = -212.7 kJ mol-1 for the reaction in the Daniell cell at 25°C, and b (CuS04) = 1.0 x 10-3 mol kg-i and b (ZnS04) = 3.0 x 10-3 mol kg-I, calculate (a) The ionic strengths of the solutions, (b) The mean ionic activity coefficients in the compartments, (c) The
Although the hydrogen electrode may be conceptually the simplest electrode and is the basis for our reference state of electrical potential in electrochemical systems, it is cumbersome to use. Therefore, several substitutes for it have been devised. One of these alternatives is the quinhydrone
The emf of the cell Pt | H2 (g, pΘ) | HCI (aq, b) | Hg2Cl2 (s) | Hg (l) has been measured with high precision (G.]. Hills and D].G. Ives, J. Chem. Soc., 311 (1951)) with the following results at 25°C: B/(mmolkg-1) 1.6077 3.0769 5.0403 7.6938 10.9474 E/V
Measurements of the emf of cells of the type Ag |AgX (s)| IMX (bl) | Mx Hg | MX (b2) AgX(s) Ag, where Mz Hg denotes an amalgam and the electrolyte is an alkali metal halide dissolved in ethylene glycol, have been reported (U. Sen, J Chem. Sac. Faraday Trans. I69, 2006 (1973)) and some values for
(a) Derive a general relation for (∂E/∂P)T,n for electrochemical cells employing reactants in any state of matter.(b) E, Cohen and K. Piepenbroek (2. Physik Chem. 167A, 365 (1933)) calculated the change in volume for the reaction TICI(s) + CNS-(aq) → TICNS(s) + Cl-(aq) at 30°C from density
Super heavy elements are now of considerable interest, particularly because signs of stability are starting to emerge with element 114, which has recently been made. Shortly before it was (falsely) believed that the first super heavy element had been discovered, an attempt was made to predict the
Express the equilibrium constant of a gas-phase reaction A + 3 B ~ 2 C in terms of the equilibrium value of the extent of reaction, ~, given that initially A and B were present in stoichiometric proportions. Find an expression for ~ as a function of the total pressure, p, of the reaction mixture
Show that, if the ionic strength of a solution of the sparingly soluble salt MX and the freely soluble salt NX is dominated by the concentration C of the latter, and if it is valid to use the Debye--Huckel limiting law, the solubility S' in the mixed solution is given by S = Kse4.606Ac/2 when K, is
To get a sense of the effect of cellular conditions on the ability of ATP to drive biochemical processes, compare the standard Gibbs energy of hydrolysis of ATP to ADP with the reaction Gibbs energy in an environment at 37°C in which pH = 7.0 and the ATP, ADP, and Pi concentrations are all 1.0
In anaerobic bacteria, the source of carbon may be a molecule other than glucose and the final electron acceptor is some molecule other than 02 Could a bacterium evolve to use the ethanol nitrate pair instead of the glucose/O, pair as a source of metabolic energy?
The standard potentials of proteins are not commonly measured by the methods described in this chapter because proteins often lose their native structure and function when they react on the surfaces of electrodes. In an alternative method, the oxidized protein is allowed to react with an
Nitric acid hydrates have received much attention as possible catalysts for heterogeneous reactions that bring about the Antarctic ozone hole. Worsnop et al. investigated the thermodynamic stability of these hydrates under conditions typical of the polar winter stratosphere (D.R. Worsnop, 1oE. Fox,
Given that p*(HzO) = 0.02308 atm and p (HzO) = 0.02239 atm in a solution in which 0.122 kg of a non-volatile solute (M = 241 g mol-1) is dissolved in 0.920 kg water at 293 K, calculate the activity and activity coefficient of water in the solution. Discuss.
Explain why Einstein's introduction of quantization accounted for the properties of heat capacities at low temperatures.
Account for the uncertainty relation between position and linear momentum in terms of the shape of the wave function.
To what speed must a proton be accelerated for it to have a wavelength of3.0 cm?
Calculate the linear momentum of photons of wavelength 350 nm. What speed does a hydrogen molecule need to travel to have the same linear momentum?
The speed of a certain electron is 995 km S-I. If the uncertainty in its momentum is to be reduced to 0.0010 per cent, what uncertainty in its location must be tolerated?
Calculate the energy per photon and the energy per mole of photons for radiation of wavelength (a) 200 nm (ultraviolet), (b) 150 pm (X-ray), (c) 1.00 cm (microwave)
Calculate the speed to which a stationary 4He atom (mass 4.0026 u) would be accelerated if it absorbed each of the photons used in Exercise S.4b
A photon-powered spacecraft of mass 10.0 kg emits radiation of wavelength 225 nm with a power of 1.50 kW entirely in the backward direction. To what speed will it have accelerated after 10.0 y if released into free space?
A laser used to read CDs emits red light of wavelength 700 nm. How many photons does it emit each second if its power is? (a) 0.10 W, (b) LOW?

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