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physical chemistry
Questions and Answers of
Physical Chemistry
Calculate ΔS° for the reaction 3H2(g) + N2(g) → 2NH3(g) at 725 K. Omit terms in the temperature-dependent heat capacities higher than T2 /K2.
Calculate ΔS for the isothermal compression of 1.75 mol of Cu(s) from 2.15 bar to 1250. bar at 298 K. β = 0.492 × 10−4 K−1, κ = 0.78 × 10−6 bar−1, and the density is 8.92 g cm−3.
1.10 moles of N2at 20.5°C and 6.20 bar undergoes a transformation to the state described by 215°C and 1.75 bar. Calculate ÎS if Сри Jmol-1 к-1 + 2.3968 x 10- г? -1.0176 х
2.25 moles of an ideal gas with CV ,m = 5/2 R is transformed from an initial state T 680. K and P = 1.15 bar to a final state T = 298.K and P = 4.75 bar. Calculate ΔU, ΔH, and ΔS for this process.
The maximum theoretical efficiency of an internal combustion engine is achieved in a reversible Carnot cycle. Assume that the engine is operating in the Otto cycle and that CV ,m = 5/2 R for the
Calculate ΔS, ΔS total , and ΔS surroundings when the volume of 150. g of CO initially at 273 K and 1.00 bar increases by a factor of two in a. An adiabatic reversible expansionb. An
The average heat evolved by the oxidation of foodstuffs in an average adult per hour per kilogram of body weight is 7.20 kJ kg−1 hr−1. Assume the weight of an average adult is 62.0 kg. Suppose
Consider the reversible Carnot cycle shown in Figure 5.2 with 1.25 mol of an ideal gas with CV= 5/2R as the working substance. The initial isothermal expansion occurs at the hot reservoir temperature
2.25 moles of an ideal gas with CV ,m = 3/2 R undergoes the transformations described in the following list from an initial state described by T = 310.K. and P = 1.00 bar. Calculate q, w, ΔU, ΔH,
One mole of H2O(l) is compressed from a state described by P = 1.00 bar and T = 350.K to a state described by P = 590. bar and T = 750.K. In addition, β = 2.07 × 10−4 K−1, and the density can
An air conditioner is a refrigerator with the inside of the house acting as the cold reservoir and the outside atmosphere acting as the hot reservoir. Assume that an air conditioner consumes 1.70 ×
An electrical motor is used to operate a Carnot refrigerator with an interior temperature of 0.00°C. Liquid water at 0.00°C is placed into the refrigerator and transformed to ice at 0.00°C. If the
The Chalk Point, Maryland, generating station supplies electrical power to the Washington, D.C., area. Units 1 and 2 have a gross generating capacity of 710. MW (megawatt). The steam pressure is 25
Consider the formation of glucose from carbon dioxide and water, that is, the reaction of the photosynthetic process:6CO2(g) + 6H2O(l) C6H12O6(s) + 6O2(g).The following table
Can incandescent lighting be regarded as an example of cogeneration during the heating season? In a season where air conditioning is required?
Solid methanol in thermal contact with the surroundings is reversibly melted at the normal melting point at a pressure of 1 atm. Are ΔS, ΔS surroundings , and ΔS total positive, negative, or zero?
Without using equations, explain why ΔS for a liquid or solid is dominated by the temperature dependence of S as both P and T change.
Two vessels of equal volume, pressure, and temperature both containing Ar are connected by a valve. What is the change in entropy when the valve is opened, allowing mixing of the two volumes? Is ΔS
Why is the efficiency of a Carnot heat engine the upper bound to the efficiency of an internal combustion engine?
Is the equationvalid for an ideal gas? Tf PV; -V;) T; Cy dT Lav = C, n2v, -v) %3D AS = т
An ideal gas in a piston and cylinder assembly with adiabatic walls undergoes an expansion against a constant external pressure. Are ΔS, ΔS surroundings , and ΔS total positive, negative, or zero?
A system undergoes a change from one state to another along two different pathways, one of which is reversible and the other of which is irreversible. What can you say about the relative magnitudes
If the ΔHof for the chemical compounds involved in a reaction are available at a given temperature, how can ΔHoR be calculated at another temperature?
When a saturated solution of a salt is cooled, a precipitate crystallizes out. Is the entropy of the crystalline precipitate greater or less than the dissolved solute? Explain why this process is
An ideal gas undergoes an adiabatic expansion into a vacuum. Are ΔS, ΔS surroundings , and ΔS total positive, negative, or zero? Explain your reasoning.
Your roommate decides to cool the kitchen by opening the refrigerator. Will this strategy work? Explain your reasoning.
One joule of work is done on a system, raising its temperature by one degree centigrade. Can this increase in temperature be harnessed to do one joule of work? Explain.
Which of the following processes is spontaneous?a. The reversible isothermal expansion of an ideal gas.b. The vaporization of superheated water at 102°C and 1 bar.c. The constant pressure
Is the following statement true of false? If it is false, rephrase it so that it is true. The entropy of a system cannot increase in an adiabatic process.
Under what conditions does the equality ΔS = ΔH/T hold?
You are told that ΔS = 0 for a process in which the system is coupled to its surroundings. Can you conclude that the process is reversible? Justify your answer.
A process involving an ideal gas is carried out in which the temperature changes at constant volume. For a fixed value of ΔT, the mass of the gas is doubled. The process is repeated with the same
The amplitude of a pendulum consisting of a mass on a long wire is initially adjusted to have a very small value. The amplitude is found to decrease slowly with time. Is this process reversible?
An ideal gas in thermal contact with the surroundings is cooled in an irreversible process at constant pressure. Are ΔS, ΔS surroundings , and ΔS total positive, negative, or zero? Explain your
Why are ΔS fusion and ΔS vaporization always positive?
Under what conditions is ΔS < 0 for a spontaneous process?
The standard entropy of Pb(s) at 298.15 K is 64.80 J K-1mol-1. Assume that the heat capacity of Pb(s) is given byThe melting point is 327.4°C and the heat of fusion under these conditions is 4770. J
For protein denaturation, the excess entropy of denaturation is defined asis thetransition excess heat capacity. The way in which δC trs P can be extracted from differential scanning
An ideal gas sample containing 1.75 moles for which CV ,m = 5/2R undergoes the following reversible cyclical process from an initial state characterized by T = 275 K and P = 1.00 bar:a. It is
The mean solar flux at the Earth’s surface is ~2.00 J cm–2 min–1. In a non-focusing solar collector, the temperature reaches a value of 79.5°C. A heat engine is operated using the collector as
Using your result from Problem 5.31, extrapolate the absolute entropy of L-alanine to physiological conditions, T = 310.K. Assume the heat capacity is constant between T = 300. K and T = 310. K.
At 1000.K, ΔHoR = –123.77 kJ mol–1 for the reaction N2(g) + 3H2(g) → 2NH3(g), with CP,m = 3.502R, 3.466 R, and 4.217 R for N2(g), H2(g), and NH3(g), respectively. Calculate
Calculate ΔHoR and ΔUoR at 298.15 K for the following reactions:a. 4NH3(g) + 6NO(g) → 5N2(g) + 6H2O(g)b. 2NO(g) + O2(g) → 2NO2(g)c. TiCl4 (l) + 2H2O(l) → TiO2
A camper stranded in snowy weather loses heat by wind convection. The camper is packing emergency rations consisting of 58% sucrose, 31% fat, and 11% protein by weight. Using the data provided in
From the following data at 298.15 K calculate the standard enthalpy of formation of FeO(s) and of Fe2O3(s): AĦ¿(kJ mol) Fe,0;(s) + 3C(graphite) → 2Fe(s) + 3cO(g) FeO(s) + C(graphite) →
Compare the heat evolved at constant pressure per mole of oxygen in the combustion of sucrose (C12H22O11) and palmitic acid (C16H32O2) with the combustion of a typical protein, for which the
Is the following statement correct? If not, rewrite it so that it is correct. Because the enthalpy of formations of elements is zero, ΔHof (O(g)) = 0.
Given the data in Table 4.3 and the data tables, calculate the bond enthalpy and energy of the following:a. The CH bond in CH4b. The CC single bond in C2H6c. The C£C
You wish to measure the heat of solution of NaCl in water. Would the calorimetric technique of choice be at constant pressure or constant volume? Why?
What is the advantage of a differential scanning calorimeter over a bomb calorimeter in determining the enthalpy of fusion of a series of samples?
The reactants in the reaction 2NO(g) + O2(g) → 2NO2(g) are initially at 298 K. Why is the reaction enthalpy the same if (a) the reaction is constantly kept at 298 K or (b) if the reaction
The total surface area of Asia consisting of forest, cultivated land, grass land, and desert is 4.46 × 107 km2. Every year, the mass of carbon fixed by photosynthesis by vegetation covering this
Is the following statement correct? If not rewrite it so that it is correct. Because the reaction H2(g) + O2(g) → H2O(l) is exothermic, the products are at a higher temperature than the
Calculate ΔH for the process in which Cl2(g) initially at 298.15 K at 1 bar is heated to 690.K at 1 bar. Use the temperature-dependent heat capacities in the data tables. How large is the relative
Nitrogen is a vital component of proteins and nucleic acids, and thus is necessary for life. The atmosphere is composed of roughly 80% N2, but most organisms cannot directly utilize N2for
In a calorimetric study, the temperature of the system rises to 325 K before returning to its initial temperature of 298 K. Why doesn’t this temperature rise affect your measurement of ΔHoR at 298
Derive the following expression for calculating the isothermal change in the constant volume heat capacity:(∂CV/∂V)T = T (∂2P/∂T2)V.
Use the tabulated values of the enthalpy of combustion of benzene and the enthalpies of formation of CO2(g) and H2O(l) to determine ΔHof for benzene.
Calculate the standard enthalpy of formation of FeS2(s) at 600. °C from the following data at 298.15 K. Assume that the heat capacities are independent of temperature.You are also given that for
Why is it valid to add the enthalpies of any sequence of reactions to obtain the enthalpy of the reaction that is the sum of the individual reactions?
Is the following statement correct? If not rewrite it so that it is correct. The superscript zero in ΔHof means that the reactions conditions are 298.15 K.
Given the following heat capacity data, calculate ÎHofof CO2(g) at 525 K. C(graphite) co:(g) 0:(g) Substance CP.m/J mol-K-1 8.52 28.8 37.1
Several reactions and their standard reaction enthalpies at 298.15 K are given here:The standard enthalpies of combustion of graphite and C2H2(g) are 393.51 and 1299.58 kJ
Why are heat capacities of reactants and products required for calculations of ΔHoR at elevated temperatures?
Use the average bond energies in Table 4.3 to estimate ÎU for the reaction C2H4(g) + H2(g) C2H6(g). Also calculate ÎUoRfrom the tabulated values of
Using the protein DSC data in Problem P4.10, calculate the enthalpy change between the T = 288 K and T = 318 K. Give your answer in units of kJ per mole. Assume the molecular weight of the protein is
Why are elements included in the sum in Equation (4.20) when they are not included in calculating ΔHoR at 298 K?
The total surface area of the Earth covered by ocean is 3.35 × 108 km2. Carbon is fixed in the oceans via hotosynthesis performed by marine plants according to the reaction 6CO2(g) +
An 75.0g piece of gold at 650.K is dropped into 180. g of H2O(l) at 310.K in an insulated container at 1 bar pressure. Calculate the temperature of the system once equilibrium has been reached.
Because (∂H/∂P)T = -CP μ J −T , the change in enthalpy of a gas expanded at constant temperature can be calculated. To do so, the functional dependence of μ J −T on P must be known.
A mass of 32.0 g of H2O(g) at 373 K is flowed into 295 g of H2O(l) at 310.K and 1 atm. Calculate the final temperature of the system once equilibrium has been reached. Assume that CP,m for H2O(l) is
Integrate the expression β = 1/V (∂V /∂T)P assuming that β is independent of pressure. By doing so, obtain an expression for V as a function of T and β at constant P.
A vessel is filled completely with liquid water and sealed at 13.56°C and a pressure of 1.00 bar. What is the pressure if the temperature of the system is raised to 82.0°C? Under these conditions,
A mass of 34.05 g of H2O(s) at 273 K is dropped into 185 g of H2O(l) at 310.K in an insulated container at 1 bar of pressure. Calculate the temperature of the system once equilibrium has been
Use the relation (∂U/∂V )T = T(∂P/∂T)V − P and the cyclic rule to obtain an expression for the internal pressure, (0U/0V )T , in terms of P, β , T, and κ .
The molar heat capacity CP,mof SO2(g) is described by the following equation over the range 300 K < T < 1700 K:In this equation, T is the absolute temperature in kelvin. The ratios
Use the result of Problem P3.10 to show that (∂CV /∂V)T for the van der Waals gas is zero.
Obtain an expression for the isothermal compressibility κ = −1/V (∂V /∂P)T for a van der Waals gas.
Is the expressiononly valid for an ideal gas if V is constant? T, AUr = [ CydT = n[ Cy,maT
Why was the following qualification made in Section 3.7? Note that Equation (3.47) is only applicable to a process in which there is no change in the phase of the system, such as vaporization or
The molar volume of H2O(l) decreases with increasing temperature near 4°C. Can you explain this behavior using a molecular level model?
Is the following statement always, never, or sometimes valid? Explain your reasoning: q = 0 for a cyclic process.
Is the following statement always, never, or sometimes valid? Explain your reasoning: A thermodynamic process is completely defined by the initial and final states of the system.
Is the following statement always, never, or sometimes valid? Explain your reasoning: ΔH is only defined for a constant pressure process.
What is the relationship between a state function and an exact differential?
Why is the equation
Why are q and w not state functions?
Classify the following variables and functions as intensive or extensive: T, P, V, q, w, U, H.
Why is qV = ΔU only for a constant volume process? Is this formula valid if work other than P − V work is possible?
Can a gas be liquefied through an isenthalpic expansion if μ J −T = 0?
Refer to Figure 1.10 and explain why (U/V)Tis generally small for a real gas.Figure 1.10 Ideal gas Real gas Tranlaition rv-0 (4)A
Why is it reasonable to write dH ≈ CPdT + VdP for a liquid or solid sample?
Explain without using equations why (∂H /∂P)T 0H 0P is generally small for a real gas.
Why can qV be equated with a state function if q is not a state function?
Why does the relation CP > CV always hold for a gas? Can CP < CV be valid for a liquid?
Why didn’t Joule change his experiment to make C surroundings /C system approx = 0.001 to increase the sensitivity of the apparatus?
What is the physical basis for the experimental result that U is a function of V at constant T for a real gas? Under what conditions will U decrease as V increases?
The heat capacity CP,m is less than CV ,m for H2O(l) near 4°C. Explain this result.
In the experiment shown in Figure 2.4b, the weight drops in a very short time. How will the temperature of the water change with time?Figure 2.4b Electrical generator Mass Heating - coil (b)
Explain the relationship between the terms exact differential and state function.
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