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Questions and Answers of Physical Chemistry

Explain why the oscillations in the two-phase coexistence region using the Redlich€“Kwong and van der Waals equations of state (see Figure 7.4) do not correspond to reality.Figure 7.4 140
A bottle at 325 K contains an ideal gas at a pressure of 162.5 × 103 Pa. The rubber stopper closing the bottle is removed. The gas expands adiabatically against P external = 120.0 × 103 Pa, and
A gas is slightly above its Boyle temperature. Do you expect z to increase or decrease as P increases?
Calculate ΔS surroundings and ΔS total for part (c) of Problem P5.6. Is the process spontaneous? The state of the surroundings is T = 310.K, P = 0.333 bar.
A 1.25 mole sample of an ideal gas is expanded from 320. K and an initial pressure of 3.10 bar to a final pressure of 1.00 bar, and CP,m = 5/2R. Calculate w for the following two cases:a. The
Is the ratio of fugacity to pressure greater to or less than one if the attractive part of the interaction potential between gas molecules dominates?
A system consisting of 82.5 g of liquid water at 300. K is heated using an immersion heater at a constant pressure of 1.00 bar. If a current of 1.75 A passes through the 25.0 ohm resistor for 100. s,
What can you conclude about the ratio of fugacity to pressure for N2,H2, and NH3at 500 bar using the data in Figure 7.10?Figure 7.10 1.5 H2, 1.4 N2 1.3 1.2 1.1 1.0 100 200 300 400 500 600 700
For a given set of conditions, the fugacity of a gas is greater than the pressure. What does this tell you about the interaction between the molecules of the gas?
In the reversible adiabatic expansion of 1.75 mol of an ideal gas from an initial temperature of 27.0°C, the work done on the surroundings is 1300. J. If CV ,m = 3/2R, calculate q, w, ΔU, and ΔH.
Given the data in Table 4.1 (Appendix B, Data Tables) and the following information, calculate the single bond enthalpies and energies for Si€”F, Si€”Cl, C€”F,
A van der Waals gas undergoes an isothermal reversible expansion under conditions such that z > 1. Is the work done more or less than if the gas followed the ideal gas law?
Calculate the pressure exerted by Ar for a molar volume of 1.31 L mol–1 at 426 K using the van der Waals equation of state. The van der Waals parameters a and b for Ar are 1.355 bar dm6 mol–2 and
Explain the significance of the Boyle temperature.
A compressed cylinder of gas contains 2.74 × 103 g of N2 gas at a pressure of 3.75 × 107 Pa and a temperature of 18.7°C. What volume of gas has been released into the atmosphere if the final
Why is the standard state of fugacity, f °, equal to the standard state of pressure, P°?
Between 0°C and 100°C, the heat capacity of Hg(l) is given byCalculate Î”H and Î”S if 2.25 moles of Hg(l) is raised in temperature from 0.00° to 88.0°C at
Consider the comparison made between accurate results and those based on calculations using the van der Waals and Redlich€“Kwong equations of state in Figures 7.1 and 7.5. Is it clear that
We return to the 60. kg hiker of P4.34, who is climbing the 828 m tall Burj Khalifa in Dubai. If the efficiency of converting the energy content of the bars into the work of climbing is 25%, the
Using the concept of the intermolecular potential, explain why two gases in corresponding states can be expected to have the same value for z.
What is the point of having an outer water bath in a bomb calorimeter (see Figure 4.3), especially if its temperature is always equal to that of the inner water bath?Figure 4.3 - Thermometer Stirrer
Using your results from Problems P5.18 and P5.7, calculate Î”S, Î”Ssurroundings, and Î”Stotalfor each step in the cycle and for the total Carnot cycle described in
In calculating ΔHoR at 285.15 K, only the ΔHof of the compounds that take part in the reactions listed in Tables 4.1 and 4.2 (Appendix B, Data Tables) are needed. Is this statement also true if you
A cylindrical vessel with rigid adiabatic walls is separated into two parts by a frictionless adiabatic piston. Each part contains 45.0 L of an ideal monatomic gas with CV ,m = 3/2R. Initially, Ti =
From the following data, calculate Î”HoR,391.4 Kfor the reaction CH3COOH(g) + 2O2(g) †’ 2H2O(g) + 2CO2(g):Values for Î”HoR for the first two reactions are at
A refrigerator is operated by a 0.25-hp (1 hp = 746 watts) motor. If the interior is to be maintained at 4.50°C and the room temperature is 38°C, what is the maximum heat leak (in watts) that can
In order to get in shape for mountain climbing, an avid hiker with a mass of 60. kg ascends the stairs in the world’s tallest structure, the 828 m tall Burj Khalifa in Dubai, United Arab Emirates.
Show that (∂CV/∂V)T = 0. for an ideal and for a van der Waals gas.
Approximately how many oxygen molecules arrive each second at the mitochondrion of an active person with a mass of 84 kg? The following data are available: Oxygen consumption is about 40. mL of O2
A muscle fiber contracts by 3.5 cm and in doing so lifts a weight. Calculate the work performed by the fiber. Assume the muscle fiber obeys Hooke’s law F = −k x with a force constant, k, of 750.
Humans cool off through perspiration. How does the effectiveness of this process depend on the relative humidity?
Show that (∂CV/∂V)T = T(∂2 P/ ∂T2)V
Prove that C V = - (∂U/∂V)T (∂V/∂T)U.
Calculate ΔHof for NO(g), at 975 K, assuming that the heat capacities of reactants and products are constant over the temperature interval at their values at 298.15 K.
As shown in Example Problem 3.5, (∂Um/∂V)T a/V2m for a van der Waals gas. In this problem, you will compare the change in energy with temperature and volume for N2, treating it as a van der Waals
Calculate ΔS surroundings and ΔS total for the processes described in parts (a) and (b) of Problem P5.16. Which of the processes is a spontaneous process? The state of the surroundings for each
At 298 K and 1 bar pressure, the density of water is 0.9970 g cm−3, and CP,m = 75.3 J K-1 mol-1. The change in volume with temperature is given by ΔV = Vi βΔT, where β, the coefficient of
Use the equation CP,m − CV ,m = TVmβ2 /κ and the Data Tables to determine CV ,m for H2O(l) at 298 K. Calculate (Cp,m − CV,m)/CP,m.
Calculate the pressure exerted by benzene for a molar volume of 2.00 L at 595 K using the Redlich€“Kwong equation of state:The Redlich€“Kwong parameters a and b for benzene are
Explain why attractive interactions between molecules in gas make the pressure less than that predicted by the ideal gas equation of state.
Calculate ΔHoR at 675 K for the reaction 4NH3(g) + 6NO(g) → 5N2(g) + 6H2O(g) using the temperature dependence of the heat capacities from the data tables. Compare your result with ΔHoR
The mass of a He atom is less than that of an Ar atom. Does that mean that because of its larger mass, Argon exerts a higher pressure on the container walls than He at the same molar density, volume,
If the wall depicted in Figure 1.2 were a movable piston, under what conditions would it move as a result of the molecular collisions?Figure 1.2 mvx mvx х
Consider the equilibrium 3O2(g) ⇋ 2O3(g).a. Using the Data tables, calculate KP at 298 K.b. Assuming that the extent of reaction at equilibrium ξ eq is much less than 1, show that the
Calculate w for the adiabatic expansion of 2.50 mol of an ideal gas at an initial pressure of 2.25 bar from an initial temperature of 450. K to a final temperature of 300. K. Write an expression for
Rewrite the van der Waals equation using the molar volume rather than V and n.
A mixture of 2.10 × 10−3 g of O2, 3.88 × 10-3 mol of N2, and 5.25 × 1020 molecules of CO are placed into a vessel of volume 5.25 L at 12.5°C.a. Calculate the total pressure in the vessel.b.
Why do the z and y components of the velocity not change in the collision depicted in Figure 1.2?Figure 1.2 mvx mvx х
Which of the following systems are isolated?a) A bottle of wineb) A tightly sealed, perfectly insulated thermos bottlec) A tube of toothpasted) our solar system. Explain your answers.
Under anaerobic conditions, glucose is broken down in muscle tissue to form lactic acid according to the reaction: C6H12O6(s) †’ 2CH3CHOHCOOH(aq). Thermodynamic data at T = 298 K
Is ΔH for breaking the first C—H bond in methane equal to the average C—H bond enthalpy in this molecule? Explain your answer.
Assume the internal energy of an elastic fiber under tension (see Problem 6.16) is given by. dU = T dS – P dV – F dl. Obtain an expression for, (∂g/∂L)P,T and calculate the maximum
For an ideal gas, (∂U/∂V)T and (∂h/∂P)T = 0. Prove that CV is independent of volume and CP is independent of pressure.
Calculate q, w, ΔU, and ΔH if 2.25 mol of an ideal gas with Cv,m = 3/2 R undergoes a reversible adiabatic expansion from an initial volume Vi = 5.50 m3 to a final volume. Vf =25.0 m3 .The initial
The following heat capacity data have been reported for L-alanine:By a graphical treatment, obtain the molar entropy of L-alanine at T = 300.K.You can perform the integration numerically using either
Calculate ΔS, ΔS surroundings , and ΔS universe per day for the air conditioned house described in Problem 5.4. Assume that the interior temperature is 65°F and the exterior temperature is 99°F.
Which of the following systems are open? a) A dog,b) An incandescent light bulbc) A tomato plantd) a can of tomatoes. Explain your answers.
Consider the reaction TiO2(s) + 2 C(graphite) + 2 Cl2(g) †’ 2 CO(g) + TiCl4(l) for which Î”HoR ,298 K= €“80. kJ mol€“1. Given the following
Derive the equation (∂H/∂T)V = CV + Vβ/κ from basic equations and definitions.
A 1.50 mole sample of an ideal gas at 28.5°C expands isothermally from an initial volume of 22.5 dm3 to a final volume of 75.5 dm3. Calculate w for this process a. For expansion against a
Give an example of two systems separated by a wall that are in thermal but not chemical equilibrium.
If 3.365 g of ethanol, C2H5OH(l), is burned completely in a bomb calorimeter at 298.15 K, the heat produced is 99.472 kJ.a. Calculate ΔHo combustion for ethanol at 298.15 K.b. Calculate ΔHof of
Count Rumford observed that using cannon boring machinery a single horse could heat 11.6 kg of ice water (T = 273 K) to T = 355 K in 2.5 hours. Assuming the same rate of work, how high could a horse
If the reaction Fe2N(s) + 3/2H2(g) ⇋ 2Fe(s) + NH3(g) comes to equilibrium at a total pressure of 1 bar, analysis of the gas shows that at 700. and 800. K, PNH3 /PH2 = 2.165 and 1.083,
Derive the equation (∂P/∂V)T = −1/(κV ) from basic equations and definitions.
A hiker caught in a thunderstorm loses heat when her clothing becomes wet. She is packing emergency rations which if completely metabolized will release 35 kJ of heat per gram of rations consumed.
Using the chain rule for differentiation, show that the isobaric expansion coefficient expressed in terms of density is given by β = −(1/ρ)(∂p/∂T)P.
At sufficiently high temperatures, the van der Waals equation has the form P ‰ˆ L RT>(Vm- b). Note that the attractive part of the potential has no influence in this expression. Justify
Regard the enthalpy as a function of T and P. Use the cyclic rule to obtain the expression Әт не, ан Cp ӘР, ӘР
A 2.50 mole sample of an ideal gas, for which CV ,m = 3/2 R, is subjected to two successive changes in state: a) From 25.0°C and 125. × 103 Pa, the gas is expanded isothermally against a
The temperature of 1.75 moles of an ideal gas increases from 10.2°C to 48.6°C as the gas is compressed adiabatically. Calculate q, w, ΔU, and ΔH for this process assuming that CV ,m = 3/2 R.
An athlete at high performance inhales ~3.75 L of air at 1.0 atm and 298 K at a respiration rate of 32 breaths per minute. If the exhaled and inhaled air contain 15.3 and 20.9% by volume of oxygen,
One mole of H2O(l) is super cooled to −3.75°C at 1 bar pressure. The freezing temperature of water at this pressure is 0.00°C. The transformation H2O(l) → H2O(s) is suddenly observed
This problem will give you practice in using the cyclic rule. Use the ideal gas law to obtain the three functions P = f (V, T),V = g(P, T), and T = h(P,V ). Show that the cyclic rule (∂P/∂V)T
Aerobic cells metabolize glucose in the respiratory system. This reaction proceeds according to the overall reaction6O2(g) + C6H12O6(s) → 6CO2(g) + 6H2O(l)Calculate the volume of oxygen required at
Give an example of two systems that are in equilibrium with respect to only one of two state variables.
N2O3 dissociates according to the equilibrium N2O3(g) ⇋ NO2(g) + NO(g). At 298 K and one bar pressure, the degree of dissociation defined as the ratio of moles of NO(g) or NO2(g) to the
Starting with β = (1/V )(∂V /∂T)P, show that β = −(1/ρ )( ∂ρ /∂T)P, where ρ is the density.
The location of the boundary between the system and the surroundings is a choice that must be made by the thermodynamicist. Consider a beaker of boiling water in an airtight room. Is the system open
Use the following data at 298.15 K to complete this problem:Calculate Î”HoR fora. OH(g) †’ H(g) + O(g)b. H2O(g) †’ 2H(g) + O(g)c.
Dogs cool off in hot weather by panting. Write a chemical equation to describe this process and calculate ΔHoR.
Make a drawing indicating the four-step process d of Figure 8.4 in Figure 8.13.Figure 8.4Figure 8.13 Critical- point Liquid Solid Triple point Gas т Tm Temperature Ть Pressure/bar Critical point
The following data are a DSC scan of a solution of a T4 lysozyme mutant. From the data determine Tm. Determine also the excess heat capacity Î”CPat T = 308 K. Determine also the
For the equation of state Vm= RT /P + B(T), show that а' в(т) = -T- dт? аСри т ӘР
Is the following statement correct? Because dry ice sublimes, carbon dioxide has no liquid phase. Explain your answer.
A 3.75 mole sample of an ideal gas with CV ,m = 3/2 R initially at a temperature Ti = 298 K and Pi = 1.00 bar is enclosed in an adiabatic piston and cylinder assembly. The gas is compressed by
The amino acid glycine dimerizes to form the dipeptide glycylglycine according to the reaction2Glycine(s): †’ Glycylglycine(s) + H2O(l)Calculate Î”S, Î”Ssurr, and
Use the relationthe cyclic rule and the van der Waals equation of state, to derive an equation for CP,m ˆ’ CV,m in terms of Vm, T, and the gas constants R, a, and b. aV Әт. ӘР Cr m = T
Yeast and other organisms can convert glucose (C6H12O6) to ethanol (CH3CH2OH) by a process called alcoholic fermentation. The net reaction isC6H12O6(s) → 2C2H5OH(l) + 2CO2(g)Calculate the
The amino acid glycine dimerizes to form the dipeptide glycylglycine according to the reaction2Glycine(s) †’ Glycylglycine(s) + H2O(l)Calculate Î”S,
Because V is a state function, (∂(∂V/∂T)P/∂P)T = (∂ (∂V/∂P)T /∂T)P. Using this relationship, show that the isothermal compressibility and isobaric expansion coefficient are related by
What is the difference between a quasi-static process and a reversible process?
Devise a temperature scale, abbreviated G, for which the magnitude of the ideal gas constant is 5.52 J G−1 mol−1.
What can you say about ΔH vaporization of a liquid as the temperature approaches the critical temperature?
For a gas that obeys the equation of state Vm= Rt/P + B(T) derive the result dB(T) = B(T) – Tª ән т dт ӘР
Explain why CP,m is a function of temperature for ethane, but not for argon in a temperature range in which electronic excitations do not occur.
Show that dρ/ρ = −β/dT + κ/dP, where ρ is the density ρ = m/V. Assume that the mass, m, is constant.
Explain why ethene has a higher value for CV ,m at 800. K than CO.
Make a graph of the densities of a liquid and its gas as a function of the temperature from low temperatures up to the critical point. Explain the behavior at the critical point.
A differential dz = f (x, y) dx + g(x, y) dy is exact if the integral ∫ f (x, y) dx + ∫ g(x, y) dy is independent of the path. Demonstrate that the differential dz = 2xy dx + x2 dy is exact by

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