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physical chemistry

Questions and Answers of Physical Chemistry

Express the work of isothermal reversible expansion of a van der Waals gas in reduced variables and find a definition of reduced work that makes the overall expression independent of the identity of
When a certain freon used in refrigeration was expanded adiabatically from an initial pressure of 32 atm and 0°C to a final pressure of 1.00 atm, the temperature fell by 22 K. Calculate the
For a van der Waals gas, πT = a/V2m. Calculate ∆Um for the isothermal expansion of nitrogen gas from an initial volume of 1.00 dm3 to 24.8 dm3 at 298 K. What are the values of q and w?
The isothermal compressibility of copper at 293 K is 7.35 × 10−7 atm−1. Calculate the pressure that must be applied in order to increase its density by 0.08 per cent.
Calculate the isothermal compressibility and the expansion coefficient of a van der Waals gas. Show, using Euler’s chain relation, that κTR = α(Vm − b).
Given that µ = 0.25 K atm−1 for nitrogen, calculate the value of its isothermal Joule–Thomson coefficient. Calculate the energy that must be supplied as heat to maintain constant temperature
The thermodynamic equation of state (∂U/∂V)T = T(∂p/∂T)V − p was quoted in the chapter. Derive its partnerfrom it and the general relations between partial differentials.
An average human produces about 10 MJ of heat each day through metabolic activity. If a human body were an isolated system of mass 65 kg with the heat capacity of water, what temperature rise would
You received an unsolicited proposal from a self-declared inventor who is seeking investors for the development of his latest idea: a device that uses heat extracted from the ground by a heat pump to
Calculate the molar entropy of a constant-volume sample of neon at 500 K given that it is 146.22 J K−1 mol−1 at 298 K.
The following expressions have been used to establish criteria for reversibility: dAT,V = 0 and dGT,p = 0. Discuss the origin, significance, and applicability of each criterion.
A sample consisting of 3.00 mol of diatomic perfect gas molecules at 200 K is compressed reversibly and adiabatically until its temperature reaches 250 K. Given that CV,m = 27.5 J K−1 mol−1,
Calculate ∆H and ∆Stot when two copper blocks, each of mass 10.0 kg, one at 100°C and the other at 0°C, are placed in contact in an isolated container. The specific heat capacity of copper is
1.00 mol of perfect gas molecules at 27°C is expanded isothermally from an initial pressure of 3.00 atm to a final pressure of 1.00 atm in two ways:(a) Reversibly, and(b) Against a constant external
Account for the dependence of πT of a van der Waals gas in terms of the significance of the parameters a and b.
Consider a system consisting of 2.0 mol CO2(g), initially at 25°C and 10 atm and confined to a cylinder of cross-section 10.0 cm2. It is allowed to expand adiabatically against an external pressure
The enthalpy of vaporization of chloroform (CHCl3) is 29.4 kJ mol−1 at its normal boiling point of 334.88 K. Calculate(a) The entropy of vaporization of chloroform at this temperature and(b) The
Suggest a physical interpretation of the dependence of the Gibbs energy on the temperature.
Calculate the standard Gibbs energy of the reaction 4 HCl(g) + O2(g) → 2 Cl2(g) + 2 H2O(l) at 298 K, from the standard entropies and enthalpies of formation given in the Data section.
From standard enthalpies of formation, standard entropies, and standard heat capacities available from tables in the Data section, calculate the standard enthalpies and entropies at 298 K and 398 K
The standard enthalpy of combustion of solid phenol (C6H5OH) is −3054 kJ mol−1 at 298 K and its standard molar entropy is 144.0 J K−1 mol−1. Calculate the standard Gibbs energy of formation
Calculate the change in the entropies of the system and the surroundings, and the total change in entropy, when a sample of nitrogen gas of mass 14 g at 298 K and 1.00 bar doubles its volume in(a) An
Calculate the maximum non-expansion work per mole that may be obtained from a fuel cell in which the chemical reaction is the combustion of methane at 298 K.
(a) Calculate the Carnot efficiency of a primitive steam engine operating on steam at 100°C and discharging at 60°C. (b) Repeat the calculation for a modern steam turbine that operates with
At 200 K, the compression factor of oxygen varies with pressure as shown below. Evaluate the fugacity of oxygen at this temperature and 100 atm. platm 1.0000 4.00000 7.00000 Z 10.0000
The change in the Gibbs energy of a certain constant-pressure process was found to fit the expression ∆G/J = −85.40 + 36.5(T/K). Calculate the value of ∆S for the process.
Calculate the change in Gibbs energy of 35 g of ethanol (mass density 0.789 g cm−3) when the pressure is increased isothermally from 1 atm to 3000 atm.
Calculate the change in chemical potential of a perfect gas when its pressure is increased isothermally from 1.8 atm to 29.5 atm at 40°C.
Prove that two reversible adiabatic paths can never cross. Assume that the energy of the system under consideration is a function of temperature only.
The fugacity coefficient of a certain gas at 200 K and 50 bar is 0.72. Calculate the difference of its molar Gibbs energy from that of a perfect gas in the same state.
Estimate the change in the Gibbs energy of 1.0 dm3 of benzene when the pressure acting on it is increased from 1.0 atm to 100 atm.
Calculate the change in the molar Gibbs energy of hydrogen gas when its pressure is increased isothermally from 1.0 atm to 100.0 atm at 298 K.
The Joule coefficient, µJ , is defined as µJ = (∂T/∂V)U. Show that µJ CV = p − αT/κT.
Suppose that(a) The attractive interactions between gas particles can be neglected.(b) The attractive interaction is dominant in a van der Waals gas, and the pressure is low enough to make the
Suppose that an internal combustion engine runs on octane, for which the enthalpy of combustion is −5512 kJ mol−1 and take the mass of 1 gallon of fuel as 3 kg. What is the maximum height,
The vapour pressure of dichloromethane at 24.1°C is 53.3 kPa and its enthalpy of vaporization is 28.7 kJ mol−1. Estimate the temperature at which its vapour pressure is 70.0 kPa.
The molar volume of a certain solid is 161.0 cm3 mol−1 at 1.00 atm and 350.75 K, its melting temperature. The molar volume of the liquid at this temperature and pressure is 163.3 cm3 mol−1. At
Prior to the discovery that freon-12 (CF2Cl2) was harmful to the Earth’s ozone layer, it was frequently used as the dispersing agent in spray cans for hair spray, etc. Its enthalpy of vaporization
The vapour pressure of a liquid in the temperature range 200 K to 260 K was found to fit the expression ln(p/Torr) = 16.255 – 2501.8/(T/K). Calculate the enthalpy of vaporization of the liquid.
The vapour pressure of benzene between 10°C and 30°C fits the expression log(p/Torr) = 7.960 – 1780/(T/K). Calculate(a) The enthalpy of vaporization and(b) The normal boiling point of benzene.
When benzene freezes at 5.5°C its density changes from 0.879 g cm−3 to 0.891 g cm−3. Its enthalpy of fusion is 10.59 kJ mol−1. Estimate the freezing point of benzene at 1000 atm.
Explain the significance of the Clapeyron equation and of the Clausius–Clapeyron equation.
In July in Los Angeles, the incident sunlight at ground level has a power density of 1.2 kW m−2 at noon. A swimming pool of area 50 m2 is directly exposed to the sun. What is the maximum rate of
The enthalpy of fusion of mercury is 2.292 kJ mol−1, and its normal freezing point is 234.3 K with a change in molar volume of +0.517 cm−3 mol−1 on melting. At what temperature will the bottom
Naphthalene, C10H8, melts at 80.2°C. If the vapour pressure of the liquid is 1.3 kPa at 85.8°C and 5.3 kPa at 119.3°C, use the Clausius–Clapeyron equation to calculate(a) The enthalpy of
Calculate the melting point of ice under a pressure of 50 bar. Assume that the density of ice under these conditions is approximately 0.92 g cm−3 and that of liquid water is 1.00 g cm−3.
What fraction of the enthalpy of vaporization of water is spent on expanding the water vapour?
Construct the phase diagram for benzene near its triple point at 36 Torr and 5.50°C using the following data: ∆fusH = 10.6 kJ mol−1, ∆vapH = 30.8 kJ mol−1, ρ(s) = 0.891 g cm−3, ρ(l) =
The change in enthalpy is given by dH = CpdT + Vdp. The Clapeyron equation relates dp and dT at equilibrium, and so in combination the two equations can be used to find how the enthalpy changes along
A kettle containing 3.00 liters of water at a temperature of 18°C is placed on an electric stove and begins to boil in three minutes.(a) Write an energy balance on the water and determine an
A gas that contains CO2 is contacted with liquid water in an agitated batch absorber. The equilibrium solubility of CO2 in water is given by Henry’s law (Section 6.4b)CA = pA/HAwhere CA(mol/cm3) =
Phosgene (COCl2) is formed by CO and Cl2 reacting in the presence of activated charcoal:At T = 303:8 K the rate of formation of phosgene in the presence of 1 gram of charcoal iswhere C denotes
In an enzyme-catalyzed reaction with stoichiometry A → B, A is consumed at a rate given by an expression of the Michaelis–Menten form:where CA(mol/L) is the reactant concentration, and k1 and k2
The demand for biopharmaceutical products in the form of complex proteins is growing. These proteins are most often produced by cells genetically engineered to produce the protein of interest, known
A tracer is used to characterize the degree of mixing in a continuous stirred tank. Water enters and leaves the mixer at a rate of V̇ (m3/min). Scale has built up on the inside walls of the tank, so
A stirred tank contains 1500 lbm of pure water at 70°F. At time t = 0, two streams begin to flow into the tank and one is withdrawn. One input stream is a 20.0 wt% aqueous solution of NaCl at 85°F
Ninety kilograms of sodium nitrate is dissolved in 110 kg of water. When the dissolution is complete (at time t = 0), pure water is fed to the tank at a constant rate ṁ(kg/min), and solution is
Methane is generated via the anaerobic decomposition (biological degradation in the absence of oxygen) of solid waste in landfills. Collecting the methane for use as a fuel rather than allowing it to
Purification of proteins for use as biopharmaceuticals is often accomplished by ion exchange chromatography, in which a process fluid passes through a column packed with small resin beads whose ionic
The flow rate of a process stream has tended to fluctuate considerably, creating problems in the process unit to which the stream is flowing. A horizontal surge drum has been inserted in the line to
A 7.35 million gallon tank used for storing liquefied natural gas (LNG, which may be taken to be pure methane) must be taken out of service and inspected. All the liquid that can be pumped from the
The wastewater treatment plant at the Ossabaw Paper Company paper mill generates about 24 tonnes of sludge per day. The consistency of the sludge is 35%, meaning that the sludge contains 35 wt%
Acetylene is produced by pyrolyzing—decomposing at high temperature—natural gas (predominantly methane):The heat required to sustain this endothermic reaction is provided by feeding oxygen to the
Natural gas that contains methane, ethane, and propane is to be burned with humid air. The adiabatic flame temperature is to be calculated from specified values of the following quantities:(a)
In Problem 9.79, the synthesis of methanol from carbon monoxide and hydrogen was described.Further analysis, however, reveals that three reactions can take place:(a) Show that only two of these
A methanol-synthesis reactor is fed with a gas stream at 220°C consisting of 5.0 mole% methane, 25.0% CO, 5.0% CO2, and the remainder hydrogen. The reactor and feed stream are at 7.5 MPa. The
Methane and 30% excess air are to be fed to a combustion reactor. An inexperienced technician mistakes his instructions and charges the gases together in the required proportion into an evacuated
Methane is burned with 25% excess air in a continuous adiabatic reactor. The methane enters the reactor at 25°C and 1.10 atm at a rate of 550 L/s, and the entering air is at 150°C and 1.1
A city with a population of 200,000 people operates a 20:0 × 106 gal/day wastewater treatment plant.For every million gallons of wastewater treated, 1875 lbm of solids are generated, with 75% of the
A gaseous fuel containing methane and ethane is burned with excess air. The fuel enters the furnace at 25°C and 1 atm, and the air enters at 200°C and 1 atm. The stack gas leaves the furnace at
The heating value of a fuel oil is to be measured in a constant-volume bomb calorimeter. The bomb is charged with oxygen and 0:00215 lbm of the fuel and is then sealed and immersed in an insulated
A fuel gas is known to contain methane, ethane, and carbon monoxide. A sample of the gas is charged into an initially evacuated 2.000-liter vessel at 25°C and 2323mm Hg absolute. The vessel is
A natural gas is analyzed and found to consist of 85.5% v/v (volume percent) methane, 8.5% ethane, 2.5% propane, and 3.5% N2 (noncombustible).(a) Calculate the higher and lower heating values of this
Various uses for nitric acid are given in Problem 6.43, along with information about how this important chemical is synthesized industrially. The key reactions are oxidations of ammonia to nitric
Citric acid (C6H8O7) is used in the preparation of many foods, pharmaceuticals, soft drinks, and personal-care products. Although it can be recovered by concentration and crystallization from citrus
Calcium chloride is a salt used in a number of food and medicinal applications and in brine for refrigeration systems. Its most distinctive property is its affinity for water: in its anhydrous form
Five cubic meters of a 1.00-molar aqueous sulfuric acid solution (SG = 1:064) is stored at 25°C. Use data in Tables B.1 and B.11 to calculate the standard heat of formation of the solution in kJ/mol
Five cubic meters of a 1.00-molar aqueous sulfuric acid solution (SG = 1:064) is stored at 25°C. Use data in Tables B.1 and B.11 to calculate the standard heat of formation of the solution in kJ/mol
Hydrogen is produced in the steam reforming of propane:The water–gas shift reaction also takes place in the reactor, leading to the formation of additional hydrogen:The reaction is carried out over
You are checking the performance of a reactor in which acetylene is produced from methane in the reactionAn undesired side reaction is the decomposition of acetylene:Methane is fed to the reactor at
You are checking the performance of a reactor in which acetylene is produced from methane in the reactionAn undesired side reaction is the decomposition of acetylene:Methane is fed to the reactor at
Carbon disulfide, a key component in the manufacture of rayon fibers, is produced in the reaction between methane and sulfur vapor over a metal oxide catalyst:Methane and molten sulfur, each at
The synthesis of methanol from carbon monoxide and hydrogen is carried out in a continuous vaporphase reactor at 5.00 atm absolute. The feed contains CO and H2 in stoichiometric proportion and enters
Solid oxide fuel cells (SOFC) have been proposed as an alternative energy technology for use in large stationary power applications (1 to 10MWof electrical power). These devices have an ion
Biodiesel fuel—a sustainable alternative to petroleum diesel as a transportation fuel—is produced via the transesterification of triglyceride molecules derived from vegetable oils or animal fats.
The synthesis of ethyl chloride is accomplished by reacting ethylene with hydrogen chloride in the presence of an aluminum chloride catalyst:Process data and a simplified schematic flowchart are
Formaldehyde is produced by decomposing methanol over a silver catalyst:To provide heat for this endothermic reaction, some oxygen is included in the feed to the reactor,leading to the partial
Ethylbenzene is converted to styrene in the catalytic dehydrogenation reactionA flowchart of a simplified version of the commercial process is shown here.Fresh and recycled liquid ethylbenzene
Cumene (C6H5C3H7) is produced by reacting benzene with propylene [ΔHr (77°F) = -39;520 Btu].A liquid feed containing 75 mole% propylene and 25% n-butane and a second liquid stream containing
Ethylene oxide is produced by the catalytic oxidation of ethylene:An undesired competing reaction is the combustion of ethylene to CO2.The feed to a reactor contains 2mol C2H4/mol O2. The conversion
In respiration, air is inhaled into the lungs, which provide a large surface area for transport of oxygen, carbon dioxide, and water to or from the blood. The transported oxygen is delivered to body
Benzaldehyde is produced from toluene in the catalytic reactionDry air and toluene vapor are mixed and fed to the reactor at 350°F and 1 atm. Air is supplied in 100% excess. Of the toluene fed to
Formaldehyde is produced commercially by the catalytic oxidation of methanol. In a side reaction, methanol is oxidized to CO2.A mixture containing 55.6 mole% methanol and the balance oxygen enters a
Synthetically produced ethanol is an important industrial commodity used for various purposes, including as a solvent (especially for substances intended for human contact or consumption); in
As described in Problem 9.21, the manufacture of ethanol from corn starch involves fermentation using a yeast that converts sugars from the starch to ethanol and carbon dioxide in a complicated
Ethyl alcohol (ethanol) can be produced by the fermentation of sugars derived from agricultural products such as sugarcane and corn. Some countries without large petroleum and natural gas
Metallic iron is produced in the reaction between ferrous oxide and carbon monoxide:The flowchart shown below depicts this process for a basis of 1 mol FeO fed at 298 K.(a) We wish to explore the
Fuel cells have been proposed as an alternative energy technology for use in stationary and transportation applications. A fuel cell is an electrochemical device in which hydrogen reacts with oxygen
The thermal decomposition of dimethyl etheris to be carried out in an isothermal 2.00-liter laboratory reactor at 600°C. The reactor is charged with pure dimethyl ether at a pressure of 350 torr.
Normal heptane is dehydrocyclicized to toluene and hydrogen in a continuous vapor-phase reaction:Pure heptane at 400°C is fed to the reactor. The reactor operates isothermally at 400°C and the

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