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Provide mechanical and molecular definitions of work and heat.
Explain the difference between the change in internal energy and the change in enthalpy accompanying a chemical or physical process.
Explain the significance of the Joule and Joule- Thomson experiments. What would Joule observe in a more sensitive apparatus?
In many experimental thermo grams, such as that shown in Fig. 2.16, the baseline below TI is at a different level from that above T2• Explain this observation.
Calculate the work needed for a bird of mass 120 g to fly to a height of 50 m from the surface of the Earth.
A chemical reaction takes place in a container of cross-sectional area 50.0 cm/. As a result of the reaction, a piston is pushed out through 15 cm against an external pressure of 121 kPa. Calculate the work done by the system.
A sample consisting of 2.00 mol He is expanded isothermally at 22°C from 22.8 dm to 31. 7 dm 3
(a) Reversibly,
(b) Against a constant external pressure equal to the final pressure of the gas, and
(c) Freely (against zero external pressure). For the three processes calculate q, w, ∆U, and ∆H.
A sample consisting of 2.00 mol of perfect gas molecules, for which CV, m= 5/2 R, initially at PI = 111 kPa and TI = 277 K, is heated reversibly to 356 K at constant volume. Calculate the final pressure, ∆U, q, and w.
A sample of argon of mass 6.56 g occupies 18.5 dm3 at 305 K.
(a) Calculate the work done when the gas expands isothermally against a constant external pressure of7.7 kPa until its volume has increased by 2.5 dm3.
(b) Calculate the work that would be done if the same expansion occurred reversibly.
A sample of2.00 mol CH30H (g) is condensed isothermally and reversibly to liquid at 64oC. The standard enthalpy of vaporization of methanol at 64°C is 35.3 kJ mol-1. Find w, q, ∆U, and ∆H for this process.
A piece of zinc of mass 5.0 g is dropped into a beaker of dilute hydrochloric acid. Calculate the work done by the system as a result of the reaction. The atmospheric pressure is 1.1 atm and the temperature 23°e.
The constant-pressure heat capacity of a sample of a perfect gas was found to vary with temperature according to the expression Cp/ (J K-1) = 20.17 + 0.4001(T/K). Calculate q, w, ∆U, and ∆H when the temperature is raised from 25°C to 100°C
(a) At constant pressure,
(b) At constant volume.
Calculate the final temperature of a sample of carbon dioxide of mass 16.0 g that is expanded reversibly and adiabatically from 500 dm3 at 298.15 K to 2.00 dm3.
A sample of nitrogen of mass 3.12g at 23.0°C is allowed to expand reversibly and adiabatically from 400 cm3 to 2.00 dm3, what is the work done by the gas?
Calculate the final pressure of a sample of water vapour that expands reversibly and adiabatically from 87.3 Torr and 500 dm3 to a final volume of 3.0 dm3. Take Y = 1.3
When 178J of energy is supplied as heat to 1.9 mol of gas molecules, the temperature of the sample increases by 1.78 K. Calculate the molar heat capacities at constant volume and constant pressure of the gas.
When 2.0 mol CO2 is heated at a constant pressure of 1.25 atm, its temperature increases from 250 K to 277 K. Given that the molar heat capacity of CO2 at constant pressure is 37.11 J K-1 mol-1, calculate q, ∆H, and ∆U.
A sample of 5.0 mol CO2 is originally confined in 15 dm ' at 280 K and then undergoes adiabatic expansion against a constant pressure of 78.5 kPa until the volume has increased by a factor of 4.0. Calculate q, w, ∆T, ∆U, and MI.
(The final pressure of the gas is not necessarily 78.5 kPa.)
A sample consisting of 1.5 mol of perfect gas molecules with Cpm = 20.8) K-1 mol-1 is initially at 230 kPa and 315 K. It undergoes reversible adiabatic expansion until its pressure reaches 170 kPa. Calculate the final volume and temperature and the work done
A certain liquid has ∆vapHo=32.0 k] mol-1. Calculate q, w, ∆H, and ∆U when 0.75 mol is vaporized at 260 K and 765 Torr.
The standard enthalpy of formation of phenol is -165.0 k) mol-I. Calculate its standard enthalpy of combustion.
From the following data, determine ∆f Ho for diborane, B2H6 (g), at 298 K:
(I) B2H6 (g) + 3 O2 (g) → B2O3(s) + 3 H20 (g) ∆t Ho=-1941 kJ mol-1
(2) 2 B(s) + t Oh) → B2O3(S)
∆t, Ho = -2368 kJ mol-1
(3) H2 (g) + + 02(g) → H2O (g)
∆t, Ho = -241.8 kJ mol-1
When 2.25 mg of anthracene, CI4HlO(s), was burned in a bomb calorimeter the temperature raised by 1.35 K. Calculate the calorimeter constant. By how much will the temperature rise when 135 mg of phenol, C6HsOH(s), is burned in the calorimeter under the same conditions? (∆.c H (C14H1O, s) =-7061 k) mol-1)
Calculate the standard enthalpy of solution of AgBr(s) in water from the enthalpies of formation of the solid and the aqueous ions.
Given that the standard enthalpy of combustion of graphite is -393.51 kJ mol-1 and that of diamond is -395.41 kJ mol-1, calculate the enthalpy of the graphite-to-diamond transition.
Given the reactions (1) and (2) below, determine
(a) ∆Ho and ∆Uo for reaction (3),
(b) -∆Ho for both HI (g) and H20 (g) all at 298 K.
(1) H2 (g) + I2(s) → 2 HI (g)
∆, H" = +52.96 kJ mol-1
(2) 2 H2 (g) + 02(g) → 2 2 H20 (g)
∆, H= -483.64 k] mol-1
(3) 4 HI (g) + 02(g) → 2 I2(s) + 2 H2O (g)
For the reaction 2 C6HsCOOH(s) + 13 02(g) → 12 CO2 (g) + 6 H20 (g), -∆Uo= -772.7 k) mol-1 at 298 K. Calculate -∆1Ho.
Calculate the standard enthalpy of formation of NOCI (g) from the enthalpy of formation of NO given in Table 2.5, together with the following information:
2 NOCl (g) → 2 NO (g) + Clz (g)
∆1 Ho = + ∆Uo= +75.5 kJ mol-1
Use the information in Table 2.5 to predict the standard reaction enthalpy of2 H2 (g) + 02(g) → 2 H2O (1) at 100°C from its value at 25°C.
Calculate ∆tHo and ∆tUo at 298 K and ∆Ho at 348 K for the hydrogenation of ethyne (acetylene) to ethene (ethylene) from the enthalpyof combustion and heat capacity data in Tables 2.5 and 2.7. Assume the heat capacities to be constant over the temperature range involved.
Calculate ∆tHo for the reaction NaCl (aq) + AgN03 (aq) → AgCI(s) + NaN03 (aq) from the information in Table 2.7 in the Data section.
Set up a thermodynamic cycle for determining the enthalpy of hydration of Ca2+ ions using the following data: enthalpy of sublimation of Ca (s), + 178.2 k] mol-1, first and second ionization enthalpies of Ca (g), 589.7 k] mol-1 and 1145 k] mol-1: enthalpy of vaporization of bromine, +30.91 kJ mol-1; dissociation enthalpy of Br2(g), + 192.9 k] mol-1; electron gain enthalpy of Br (g), -331.0 k] mol-1: enthalpy of solution of CaBr2(s), -103.1 k] mol-1: enthalpy of hydration of Br- (g), -337 k] mol -1.
A vapour at 22 atm and 5°C was allowed to expand adiabatically to a final pressure of 1:00 atm; the temperature fell by 10 K. Calculate the Joule- Thomson coefficient, u, at 5°C, assuming it remains constant over this temperature range.
Repeat Exercise 2.30(a) for argon, from an initial volume of 1.00 dm3 to 22.1 dm3 at 298 K.
The volume of a certain liquid varies with temperature as V= V'{0.77 + 3.7 x 1O-4(T/K) + 1.52 X lO-6(T/K) 2}
The isothermal compressibility of lead at 293 K is 2.21 X 10-6 atm-1, Calculate the pressure that must be applied in order to increase its density by 0.08 per cent.
Given that μ = 1.11 K atm-I for carbon dioxide, calculate the value of its isothermal Joule- Thomson coefficient. Calculate the energy that must be supplied as heat to maintain constant temperature when 12.0 mol CO2 flows through a throttle in an isothermal Joule-Thomson experiment and the pressure drop is 55 atm.
A sample consisting of 1 mol of perfect gas atoms (for which CV•m = 3/2 R) is taken through the cycle shown in Fig. 2.34.
(a) Determine the temperature at the points 1, 2, and 3.
(b) Calculate q, w, ∆U, and ∆H for each step and for the overall cycle. If a numerical answer cannot be obtained from the information given, then write in +, -, 0, or? As appropriate
A sample consisting of2.0 mol CO2 occupies a fixed volume of 15.0 dm3 at 300 K. When it is supplied with 2.35 kJ of energy as heat its temperature increases to 341 K. Assume that CO2, is described by the van der Waals equation of state, and calculate w, ∆U, and ∆H
A sample of 1.00 mol perfect gas molecules with Cp,m = 7/2 R is put through the following cycle:
(a) Constant-volume heating to twice its initial volume,
(b) Reversible, adiabatic expansion back to its initial temperature,
(c) Reversible isothermal compression back to 1.00 atm. Calculate q, w, ∆U, and ∆H for each step and overall.
The molar heat capacity of ethane is represented in the temperature range 298 K to 400 K by the empirical expression Cp,m/ (J K-1 mol-1) = 14.73 + 0.1272(T/K). The corresponding expressions for C(s) and H2 (g) are given in Table 2.2. Calculate the standard enthalpy of formation of ethane at 350 K from its value at 298 K.
The standard enthalpy of formation of the metallocene bis (benzene) chromium was measured in a calorimeter. It was found for the reaction Cr (C6H6)2(s) →Cr(s) + 2 C6H6 (g) that ∆Uo (583 K) = +8.0 kJ mol-1. Find the corresponding reaction enthalpy and estimate the standard enthalpy of formation of the compound at 583 K. The constant-pressure molar heat capacity of benzene is 136.1 J K-1 mol-1 in its liquid range and 81.67 J K-I mol-1 as a gas.
It is possible to investigate the thermo chemical properties of hydrocarbons with molecular modeling methods.
(a) Use electronic structure software to predict ∆cHo values for the alkane’s methane through pentane. To calculate ∆cHo values, estimate the standard enthalpy of formation of CnH2 (n+l) (g) by performing semi-empirical calculations (for example, AMI or PM3 methods) and use experimental standard enthalpy of formation values for CO2 (g) and H20 (I).
(b) Compare your estimated values with the experimental values of ∆cHo (Table 2.5) and comment on the reliability of the molecular modeling method.
(c) Test the extent to which the relation ∆cHo= k {(M/ (g mol-1)} n holds and find the numerical values for k and n.
Since their discovery in 1985, fullerenes have received the attention of many chemical researchers. Kolesov et al. reported the standard enthalpy of combustion and of formation of crystalline C60 based on calorimetric measurements (V.P. Kolesov, S.M. Pirnenova, V.K. Pavlovich, N.B. Tamm, and A.A. Kurskaya,J. Chem. Thermodynamics 28, 1121 (1996)). In one of their runs, they found the standard specific internal energy of combustion to be -36.0334 kJ g-1 at 298.15 K Compute ∆cHo and ∆fHo of C60
Silylene (SiH2) is a key intermediate in the thermal decomposition of silicon hydrides such as silane (SiH4) and disilane (Si2H6). Moffat et al. (H.K.
Moffat, K.F. Jensen, and R.W. Carr, J. Phys. Chem. 95,145 (1991)) report ∆fHo SiH2) = +274 kJ mol-1. If ∆rHo (SiH4) = +34.3 k] mol-1 and ∆fHo(Si1H6)= +80.3 k] mol-1: (CRC Handbook (2004)), compute the standard enthalpies of the following reactions:
(a) SiH4 (g) →7 SiH2 (g) + H2 (g)
(b) Si2H6 (g) ---7 SiH2) + SiH4 (g)
The constant -volume heat capacity of a gas can be measured by observing the decrease in temperature when it expands adiabatically and reversibly. If the decrease in pressure is also measured, we can use it to infer the value of y= Cp/Cv and hence, by combining the two values, deduce the constant-pressure heat capacity. A fluorocarbon gas was allowed to expand reversibly and adiabatically to twice its volume; as a result, the temperature fell from 298.15 K to 248.44 K and its pressure fell from 202.94 kPa to 81.840 kPa. Evaluate Cp'
Take nitrogen to be a van der Waals gas with a = 1.352 dm6 atm mol-2 and b = 0.0387 dm3 mol-1, and calculate ∆Hm when the pressure on the gas is decreased from 500 atm to 1.00 atm at 300 K. For a van der Waals gas, .u= {(2a/RD - b}/Cp,m Assume Cp•m = 7/2 R.
(a) What is the total differential of z = x2 + 2y2 - 2xy+ 2x- 4y - 8?
(b) Show that ∂2z/∂y∂x = ∂2z/∂x∂y for this function.
(c) Let z= xy- y + in x + 2. Find dz and show that it is exact.
(a) Derive the relation Cv= - (∂U/∂V)T (∂V/∂T)u from the expression for the total differential of U(T, V) and
(b) Starting from the expression for the total differential of H(T,p), express (∂H/∂p)T in terms of Cp and the Joule- Thomson coefficient, μ.
(a) By direct differentiation of H = U + P V, obtain a relation between (∂H/∂U)p and (∂U/∂V)p
(b) Confirm that (∂H/∂U)p = I + p(∂V/∂U)p by expressing (∂H/∂U)p as the ratio of two derivatives with respect to volume and then using the definition of enthalpy.
Calculate the work done during the isothermal reversible expansion of a gas that satisfies the virial equation of state, eqn 1.19. Evaluate
(a) The work for 1.0 mol Ar at 273 K (for data, see Table 1.3) and
(b) The same amount of a perfect gas. Let the expansion be from 500 em-1 to 1000 em-1 in each case.
A gas obeying the equation of state p(V-nb) = nRT is subjected to a Joule- Thomson expansion. Will the temperature increase, decrease, or remain the same?
Rearrange the van der Waals equation of state to give an expression for T as a function of p and V (with n constant). Calculate (∂T/∂p)v and confirm that (∂T/∂p)v= l/(∂p/∂D")v. Go on to confirm Euler's chain relation.
On a cold, dry morning after a frost, the temperature was -5°C and the partial pressure of water in the atmosphere fell to 0.30 kPa. Will the frost sublime? What partial pressure of water would ensure that the frost remained?
Given that μCp = T(∂V/∂T)p - V, derive an expression for .u in terms of the van der Waals parameters a and b, and express it in terms of reduced variables. Evaluate u at 25°C and 1.0 atm, when the molar volume of the gas is 24.6 dm3 mol-1 use the expression obtained to derive a formula for the inversion temperature of a van der Waals gas in terms of reduced variables, and evaluate it for the xenon sample.
The normal boiling point of hexane is 69.0°C. Estimate
(a) Its enthalpy of vaporization and
(b) Its vapour pressure at 25°C and 60°C.
Calculate the melting point of ice under a pressure of 10 MPa. Assume that the density of ice under these conditions is approximately 0.915 g cm-1 and that of liquid water is 0.998 g cm-1.
Show that for a van der Waals gas, Cp,m – Cv,m = λR 1/λ = 1 (3Vt – 1)2/4V3tTt and evaluate the difference for xenon at 25°C and 10.0 atm.
A gas obeys the equation of state Vm = RT/p + aT2 and its constant pressure heat capacity is given by Cp,m = A + BT + Cp, where a, A, B, and Care constants independent of T and p. Obtain expressions for
(a) The Joule-Thomson coefficient and
(b) Its constant-volume heat capacity.
What fraction of the enthalpy of vaporization of ethanol is spent on expanding its vapour?
There are no dietary recommendations for consumption of carbohydrates. Some nutritionists recommend diets that are largely devoid of carbohydrates, with most of the energy needs being met by fats. However, the most common recommendation is that at least 65 per cent of our food calories should come from carbohydrates. A i-cup serving of pasta contains 40 g of carbohydrates.
What percentage of the daily calorie requirement for a person on a 2200 Calorie diet (1 Cal = 1 kcal) does this serving represent?
The temperature dependence of the vapour pressure of solid sulfur dioxide can be approximately represented by the relation log (p/Torr) = 10.5916 - 1871.2/ (T/K) and that of liquid sulfur dioxide by log (p/Torr) = 8.3186 - 1425.7 /(T/K). Estimate the temperature and pressure of the triple point of sulfur dioxide.
Glucose and fructose are simple sugars with the molecular formula C6HI206• Sucrose, or table sugar, is a complex sugar with molecular formula C12H220I1 that consists of a glucose unit covalently bound to a fructose unit (a water molecule is given off as a result of the reaction between glucose and fructose to form sucrose).
(a) Calculate the energy released as heat when a typical table sugar cube of mass 1.5 g is burned in air.
(b) To what height could you climb on the energy a table sugar cube provides assuming 25 per cent of the energy is available for work?
(c) The mass of a typical glucose tablet is 2.5 g. Calculate the energy released as heat when a glucose tablet is burned in air.
(d) To what height could you climb on the energy a cube provides assuming 25 per cent of the energy is available for work?
You have at your disposal a sample of pure polymer P and a sample of P that has just been synthesized in a large chemical reactor and that may contain impurities. Describe how you would use differential scanning calorimetry to determine the mole percentage composition of P in the allegedly impure sample.
The enthalpy of vaporization of a certain liquid is found to be 14.4 k] mol' at 180 K, its normal boiling point. The molar volumes of the liquid and the vapour at the boiling point are 115 cm3 mol-1 and 14.5 dm3 mol-1 respectively.
(a) Estimate dp/dTfrom the Clapeyron equation and
(b) The percentage error in its value if the Clausius-Clapeyron equation is used instead.
In 1995, the Intergovernmental Panel on Climate Change (IPCe) considered a global average temperature rise of 1.0-3.5°C likely by the year 2100, with 2.0°C its best estimate. Predict the average rise in sea level due to thermal expansion of sea water based on temperature rises of 1.0°C, 2.0°C, and 3.5°C given that the volume of the Earth's oceans is 1.37 x 109 km3 and their surface area is 361 X 106 km/, and state the approximations that go into the estimates.
Calculate the difference in slope of the chemical potential against pressure on either side of
(a) The normal freezing point of water and
(b) The normal boiling point of water. The densities of ice and water at O°Care 0.917 g cm-3 and 1.000 g cm3, and those of water and water vapour at 100°C are 0.958 g cm3 and 0.598 g dm-1, respectively. By how much does the chemical potential of water vapour exceed that of liquid water at 1.2 atm and 100°C?
Another alternative refrigerant (see preceding problem) is 1,1,1,2- tetrafluoroethane (refrigerant HFC-134a). Tillner-Roth and Baehr published a compendium of thermo physical properties of this substance (R. Tillner-Roth and H.D. Baehr,]. Phys. Chem. Ref Data 23,657 (1994)), from which properties such as the Joule- Thomson coefficient μ can be computed.
(a) Compute μ at 0.100 MPa and 300 K from the following data (all referring to 300 K):
P/MPa 0.080 0.100 0.12
Specific enthalpy/Ikl kg-1) 426.48 426.12 425.76
(The specific constant-pressure heat capacity is 0.7649 kl K-I kg-I)
(b) Compute μ at 1.00 MPa and 350 K from the following data (all referring to 350 K):
P/MPa 0.80 1.00 1.2
Specific enthalpy/Ikl kg-1) 461.93 459.12 456.15
(The specific constant-pressure heat capacity is 1.0392 k] K-1 kg-1)
The evolution of life requires the organization of a very large number of molecules into biological cells. Does the formation of living organisms violate the Second Law of thermodynamics? State your conclusion clearly and present detailed arguments to support it.
50.0 dm3 of dry air was slowly bubbled through a thermally insulated beaker containing 250 g of water initially at 25°C. Calculate the final temperature. (The vapour pressure of water is approximately constant at 3.17 kPa throughout, and its heat capacity is 75.5 J K-i mol-1. Assume that the air is not heated or cooled and that water vapour is a perfect gas.)
The following expressions have been used to establish criteria for spontaneous change: ∆Stot > 0, dSu,v > 0 and d Us,v < 0, dAT,V <: 0, and dGT,P <: O. Discuss the origin, significance, and applicability of each criterion.
The vapour pressure of the ketone carvone (M = 150.2 g mol-1), a component of oil of spearmint, is as follows:
θ/’C 57.4 100.4 133.0 157.3 203.5 227.5
P/Torr 1.00 10.0 40.0 100 400 760
What are?
(a) The normal boiling point and
(b) The enthalpy of vaporization of carvone?
Discuss the physical interpretation of anyone Maxwell relation.
Suggest a physical interpretation of the dependence of the Gibbs energy on the pressure.
Calculate the change in entropy when 50 k] of energy is transferred reversibly and isothermally as heat to a large block of copper at
(a) O°C,
(b) 70°e
Calculate the molar entropy of a constant-volume sample of argon at 250 K given that it is 154.84 J K-I mol-1 at 298 K.
Calculate ∆S (for the system) when the state of2.00 mol diatomic perfect gas molecules, for which Cp,m = 7/2 R, is changed from 25°C and 1.50 atm to 135°C and 7.00 atm. How do you rationalize the sign of ∆S
A sample consisting of2.00 mol of diatomic perfect gas molecules at 250 K is compressed reversibly and adiabatically until its temperature reaches 300 K. Given that CV,m = 27.5 J K-I mol-1, calculate q, w, ∆U, ∆H, and ∆S.
In an investigation of thermophysicai p∆I' erties of toluene (R.D Goodwin], phys. Chem. Ref Data 18, 1565 (1989)) pr.,-ented expressions for two coexistence curves (phase boundaries) the solid-liquid coexistence curve is given by plbar =pibar+ 1000 x (5.60 + 11.727x) x where x = ∆T} - 1 and the triple point pressure and temperature are P3 = 0.4362 ubar and T3 = 178.15 K. The liquid-vapour curve is given by: In (p/bar) = -1O.418/y + 21.157 - 15.996y + 14.015yz - 5.0120y3 + 4.7224(1- y) 1.70 where y = T/Te = TI (593.95 K).
(a) Plot the solid-liquid and liquid-vapour phase boundaries.
(b) Estimate the standard melting point of toluene.
(c) Estimate the standard boiling point of toluene.
(d) Compute the standard enthalpy of vaporization of toluene, given that the molar volumes of the liquid and vapour at the normal boiling point are 0.12 dm3 mol-l and 30.3 dm3 mol-1, respectively.
Calculate LVI and i1S'OIwhen two iron blocks, each of mass 1.00 kg, one at 200°C and the other at 25°C, are placed in contact in an isolated container.
The specific heat capacity of iron is 0.449 J K-I g-l and may be assumed constant over the temperature range involved.
Show that, for a transition between two incompressible solid phases, ∆1Gis independent of the pressure.
Consider a system consisting of 1.5 mol CO2 (g), initially at 15°C and 9.0 atm and confined to a cylinder of cross-section 100.0 cm2, The sample is allowed to expand adiabatically against an external pressure of 1.5 atm until the piston has moved outwards through 15 cm. Assume that carbon dioxide may be considered a perfect gas with CV,m = 28.8 J K-l mol-1, and calculate
(a) q,
(b) w,
(c) ∆U,
(d) ∆T,
(e) ∆S.
In the 'gas saturation method' for the measurement of vapour pressure, a volume V of gas (as measured at a temperature T and a pressure p) is bnbbled slowly through the liquid that is maintained at the temperature T, and a mass loss m is measured. Show that the vapour pressure, p, of the liquid is related to its molar mass, M, by P =AmPI (1 + Am), where A = RTIMPV. The vapour pressure of geraniol (M = 154.2 g mol-1), which is a component of oil of roses, was measured at 110°C. It was found that, when 5.00 dm3 of nitrogen at 760 Torr was passed slowly through the heated liquid, the loss of mass was 0.32 g. Calculate the vapour pressure of geraniol.
The enthalpy of vaporization of methanol is 35.27 k] mol-I at its normal boiling point of 64.1oC. Calculate
(a) The entropy of vaporization of methanol at this temperature and
(b) The entropy change of the surroundings.
Calculate the standard reaction entropy at 298 K of
(a) Zn(s) + Cu2+ (aq) → 7 Zn2+ (aq) + Cu(s)
(b) C12H220ll(s) + 12 02(g) → 12 CO2 (g) + 11 H2 (1)
Combine the reaction entropies calculated in Exercise 3.8b with the reaction enthalpies, and calculate the standard reaction Gibbs energies at 298 K.
Figure 4.9 gives a schematic representation of how the chemical potentials of the solid, liquid, and gaseous phases of a substance vary with temperature. All have a negative slope, but it is unlikely that they are truly straight lines as indicated in the illustration. Derive an expression for the curvatures (specifically, the second derivatives with respect to temperature) of these lines. Is there a restriction on the curvature of these lines? Which state of matter shows the greatest curvature?
Use standard Gibbs energies of formation to calculate the standard reaction Gibbs energies at 298 K of the reactions in Exercise 3.8b.
Calculate the standard Gibbs energy of the reaction CO (g) + CH3H (I) →CH3COOH (I) at 298 K, from the standard entropies and enthalpies of formation given in the Data section.
The standard enthalpy of combustion of solid urea (CO (NH2)2) is -632 kl mol-1 at 298 K and its standard molar entropy is 104.60 J K-1 mol-1, Calculate the standard Gibbs energy of formation of urea at 298 K.
Calculate the change in the entropies of the system and the surroundings, and the total change in entropy, when the volume of a sample of argon gas of mass 21 gat 298 K and 1.50 bar increases from 1.20 dm3 to 4.60 dm3 in
(a) An isothermal reversible expansion,
(b) An isothermal irreversible expansion against Pex = 0, and
(c) An adiabatic reversible expansion.
The use of supercritical fluids as mobile phases in SFC depends on their properties as non polar solvents. The solubility parameter, ∂, is defined as (∆Ucohesive/Vm)1/2, where ∆Ucohesive is the cohesive energy of the solvent,
the energy per mole needed to increase the volume isothermally to an infinite value. Diethyl ether, carbon tetrachloride, and dioxane have solubility parameter ranges of7-8, 8-9, and 10-11, respectively. (a) Derive a practical equation for the computation of the isotherms for the reduced internal energy change, ∆U (TV, vt,) defined as
∆Ut (TtVt) = Ut (TvVt) – Ut (Tvoo)/PcVc
(b) Draw a graph of U against p, .for the isotherms T, = 1, 1.2, and 1.5 in the reduced pressure range for which 0.7 < V, < 2.
(c) Draw a graph of ∂ against P, for the carbon dioxide isotherms T, = 1 and 1.5 in the reduced pressure range for which 1 < V, < 3. In what pressure range at Tf= I will carbon dioxide have solvent properties similar to those of liquid carbon tetrachloride? Hint. Use mathematical software or a spreadsheet.
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 propane at 298 K.
A certain heat engine operates between 1000 K and 500 K.
(a) What is the maximum efficiency of the engine?
(b) Calculate the maximum work that can be done by for each 1.0 k] of heat supplied by the hot source.
(c) How much heat is discharged into the cold sink in a reversible process for each 1.0 k] supplied by the hot source?
Suppose that 2.5 mmol Ar (g) occupies 72 dm3 at 298 K and expands to 100 dm3, Calculate ∆G for the process.
Diamond, an allotrope of carbon, is the hardest substance and the best conductor of heat yet characterized. For these reasons, diamond is used widely in industrial applications that require a strong abrasive. Unfortunately, it is difficult to synthesize diamond from the more readily available allotropes of carbon, such as graphite. To illustrate this point,
calculate the pressure required to convert graphite into diamond at 25°C. The following data apply to 25°C and 100 kPa. Assume the specific volume; Vs' and KT are constant with respect to pressure changes.
Graphite Diamond
∆tGo/(kJ mol-1) 0 +2.8678
Vc/(cm3 g-I) 0.444 0.284
KT/kPa 3.04x10-4 0.187x10-4
The change in the Gibbs energy of a certain constant-pressure process was found to fit the expression ∆G/T =-73.1 + 42.8(T/K). Calculate the value of ∆S for the process.
State and justify the thermodynamic criterion for solution-vapour equilibrium.
Calculate the change in Gibbs energyof25 g of methanol (mass density 0.791 g cm-3) when the pressure is increased isothermally from 100 kPa to 100 MPa.
Calculate the change in chemical potential of a perfect gas when its pressure is increased isothermally from 92.0 kPa to 252.0 kPa at 50°C.
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