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[{"problem_text": "Suppose that $10.0 \\mathrm{~mol} \\mathrm{C}_2 \\mathrm{H}_6(\\mathrm{~g})$ is confined to $4.860 \\mathrm{dm}^3$ at $27^{\\circ} \\mathrm{C}$. Predict the pressure exerted by the ethane from the perfect gas.", "answer_latex": " 50.7", "answer_number": "50.7", "unit": "$\\mathrm{atm}$ ", "source": "atkins", "problemid": " e1.17(a)(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Calculate the standard enthalpy of solution of $\\mathrm{AgCl}(\\mathrm{s})$ in water from the enthalpies of formation of the solid and the aqueous ions.", "answer_latex": " +65.49", "answer_number": "+65.49", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": "e2.21(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in chemical potential of a perfect gas when its pressure is increased isothermally from $1.8 \\mathrm{~atm}$ to $29.5 \\mathrm{~atm}$ at $40^{\\circ} \\mathrm{C}$.", "answer_latex": " +7.3", "answer_number": "+7.3", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": " e3.19(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in entropy when $25 \\mathrm{~kJ}$ of energy is transferred reversibly and isothermally as heat to a large block of iron at $100^{\\circ} \\mathrm{C}$.", "answer_latex": " 67", "answer_number": "67", "unit": "$\\mathrm{J} \\mathrm{K}^{-1}$ ", "source": "atkins", "problemid": " e3.1(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. A sample consisting of $3.00 \\mathrm{~mol}$ of diatomic perfect gas molecules at $200 \\mathrm{~K}$ is compressed reversibly and adiabatically until its temperature reaches $250 \\mathrm{~K}$. Given that $C_{V, \\mathrm{~m}}=27.5 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$, calculate $q$.", "answer_latex": "0 ", "answer_number": "0", "unit": " ", "source": "atkins", "problemid": " e3.4(a)(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. For the reaction $\\mathrm{C}_2 \\mathrm{H}_5 \\mathrm{OH}(\\mathrm{l})+3 \\mathrm{O}_2(\\mathrm{~g}) \\rightarrow 2 \\mathrm{CO}_2(\\mathrm{~g})+3 \\mathrm{H}_2 \\mathrm{O}(\\mathrm{g})$, $\\Delta_{\\mathrm{r}} U^\\ominus=-1373 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$ at $298 \\mathrm{~K}$, calculate $\\Delta_{\\mathrm{r}} H^{\\ominus}$.", "answer_latex": " -1368", "answer_number": "-1368", "unit": "$\\mathrm{~kJ} \\mathrm{~mol}^{-1}$", "source": "atkins", "problemid": "e2.24(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. A sample consisting of $2.0 \\mathrm{~mol} \\mathrm{CO}_2$ occupies a fixed volume of $15.0 \\mathrm{dm}^3$ at $300 \\mathrm{~K}$. When it is supplied with $2.35 \\mathrm{~kJ}$ of energy as heat its temperature increases to $341 \\mathrm{~K}$. Assume that $\\mathrm{CO}_2$ is described by the van der Waals equation of state, and calculate $w$.", "answer_latex": " 0", "answer_number": "0", "unit": " ", "source": "atkins", "problemid": "p2.3(a) ", "comment": " ", "solution": ""}, {"problem_text": "The density of a gaseous compound was found to be $1.23 \\mathrm{kg} \\mathrm{m}^{-3}$ at $330 \\mathrm{K}$ and $20 \\mathrm{kPa}$. What is the molar mass of the compound?", "answer_latex": " 169", "answer_number": "169", "unit": " $\\mathrm{g} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": " e1.11(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A sample of $4.50 \\mathrm{~g}$ of methane occupies $12.7 \\mathrm{dm}^3$ at $310 \\mathrm{~K}$. Calculate the work that would be done if the same expansion occurred reversibly.", "answer_latex": "$-167$", "answer_number": "-167", "unit": "$\\mathrm{J}$", "source": "atkins", "problemid": " e2.5(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A strip of magnesium of mass $15 \\mathrm{~g}$ is placed in a beaker of dilute hydrochloric acid. Calculate the work done by the system as a result of the reaction. The atmospheric pressure is 1.0 atm and the temperature $25^{\\circ} \\mathrm{C}$.", "answer_latex": "$-1.5$", "answer_number": "-1.5", "unit": "$\\text{kJ}$ ", "source": "atkins", "problemid": " e2.7(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. For a van der Waals gas, $\\pi_T=a / V_{\\mathrm{m}}^2$. Calculate $\\Delta U_{\\mathrm{m}}$ for the isothermal expansion of nitrogen gas from an initial volume of $1.00 \\mathrm{dm}^3$ to $24.8 \\mathrm{dm}^3$ at $298 \\mathrm{~K}$.", "answer_latex": " 131", "answer_number": "131", "unit": "$\\mathrm{J} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": " e2.31(a)(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.01325 bar. Unless otherwise stated, thermochemical data are for 298.15 K. Take nitrogen to be a van der Waals gas with $a=1.352 \\mathrm{dm}^6 \\mathrm{~atm} \\mathrm{\\textrm {mol } ^ { - 2 }}$ and $b=0.0387 \\mathrm{dm}^3 \\mathrm{~mol}^{-1}$, and calculate $\\Delta H_{\\mathrm{m}}$ when the pressure on the gas is decreased from $500 \\mathrm{~atm}$ to $1.00 \\mathrm{~atm}$ at $300 \\mathrm{~K}$. For a van der Waals gas, $\\mu=\\{(2 a / R T)-b\\} / C_{p, \\mathrm{~m}}$. Assume $C_{p, \\mathrm{~m}}=\\frac{7}{2} R$.", "answer_latex": " +3.60", "answer_number": "+3.60", "unit": "$\\text{kJ}$ ", "source": "atkins", "problemid": "p2.21", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the molar entropy of a constant-volume sample of neon at $500 \\mathrm{~K}$ given that it is $146.22 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$ at $298 \\mathrm{~K}$.", "answer_latex": " 152.67", "answer_number": "152.67", "unit": "$\\mathrm{J} \\mathrm{K}^{-1} \\mathrm{~mol}^{-1}$", "source": "atkins", "problemid": " e3.2(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Calculate the final temperature of a sample of argon of mass $12.0 \\mathrm{~g}$ that is expanded reversibly and adiabatically from $1.0 \\mathrm{dm}^3$ at $273.15 \\mathrm{~K}$ to $3.0 \\mathrm{dm}^3$.", "answer_latex": "131", "answer_number": "131", "unit": " $\\mathrm{K}$", "source": "atkins", "problemid": " e2.9(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in entropy when $25 \\mathrm{~kJ}$ of energy is transferred reversibly and isothermally as heat to a large block of iron at $0^{\\circ} \\mathrm{C}$.", "answer_latex": " 92", "answer_number": "92", "unit": "$\\mathrm{J} \\mathrm{K}^{-1}$", "source": "atkins", "problemid": "e3.1(a)(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. A sample consisting of $2.0 \\mathrm{~mol} \\mathrm{CO}_2$ occupies a fixed volume of $15.0 \\mathrm{dm}^3$ at $300 \\mathrm{~K}$. When it is supplied with $2.35 \\mathrm{~kJ}$ of energy as heat its temperature increases to $341 \\mathrm{~K}$. Assume that $\\mathrm{CO}_2$ is described by the van der Waals equation of state, and calculate $\\Delta H$.", "answer_latex": " +3.03", "answer_number": "+3.03", "unit": "$\\text{kJ}$", "source": "atkins", "problemid": " p2.3(c)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. Concerns over the harmful effects of chlorofluorocarbons on stratospheric ozone have motivated a search for new refrigerants. One such alternative is 2,2-dichloro-1,1,1-trifluoroethane (refrigerant 123). Younglove and McLinden published a compendium of thermophysical properties of this substance (J. Phys. Chem. Ref. Data 23, 7 (1994)), from which properties such as the Joule-Thomson coefficient $\\mu$ can be computed. Compute $\\mu$ at 1.00 bar and $50^{\\circ} \\mathrm{C}$ given that $(\\partial H / \\partial p)_T=-3.29 \\times 10^3 \\mathrm{~J} \\mathrm{MPa}^{-1} \\mathrm{~mol}^{-1}$ and $C_{p, \\mathrm{~m}}=110.0 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$.", "answer_latex": " 29.9", "answer_number": "29.9", "unit": "$\\mathrm{K} \\mathrm{MPa}^{-1}$", "source": "atkins", "problemid": " p2.45(a)", "comment": " ", "solution": ""}, {"problem_text": "A gas at $250 \\mathrm{~K}$ and $15 \\mathrm{~atm}$ has a molar volume 12 per cent smaller than that calculated from the perfect gas law. Calculate the molar volume of the gas.", "answer_latex": " 1.2", "answer_number": "1.2", "unit": "$\\mathrm{dm}^3 \\mathrm{~mol}^{-1}$ ", "source": "atkins", "problemid": " e1.15(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Calculate the mass of water vapour present in a room of volume $400 \\mathrm{m}^3$ that contains air at $27^{\\circ} \\mathrm{C}$ on a day when the relative humidity is 60 percent.'", "answer_latex": " 6.2", "answer_number": "6.2", "unit": "$\\text{kg}$ ", "source": "atkins", "problemid": " e1.9(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. 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 $\\gamma=C_p / C_V$ 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 $298.15 \\mathrm{~K}$ to $248.44 \\mathrm{~K}$ and its pressure fell from $202.94 \\mathrm{kPa}$ to $81.840 \\mathrm{kPa}$. Evaluate $C_p$.", "answer_latex": "41.40", "answer_number": "41.40", "unit": "$\\mathrm{J} \\mathrm{K}^{-1} \\mathrm{~mol}^{-1}$", "source": "atkins", "problemid": " p2.19", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298 K unless otherwise stated. Estimate the standard reaction Gibbs energy of $\\mathrm{N}_2(\\mathrm{g})+3 \\mathrm{H}_2(\\mathrm{g}) \\rightarrow$ $2 \\mathrm{NH}_3$ (g) at $500 \\mathrm{~K}$.", "answer_latex": "7", "answer_number": "7", "unit": "$\\mathrm{mol}^{-1}$", "source": "atkins", "problemid": "p3.17(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The enthalpy of vaporization of chloroform $\\left(\\mathrm{CHCl}_3\\right)$ is $29.4 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$ at its normal boiling point of $334.88 \\mathrm{~K}$. Calculate the entropy of vaporization of chloroform at this temperature.", "answer_latex": " +87.8", "answer_number": "+87.8", "unit": "$\\mathrm{J} \\mathrm{K}^{-1} \\mathrm{~mol}^{-1}$", "source": "atkins", "problemid": " e3.7(a)(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Given the reactions (1) and (2) below, determine $\\Delta_{\\mathrm{r}} H^{\\ominus}$ for reaction (3).\r\n\r\n(1) $\\mathrm{H}_2(\\mathrm{g})+\\mathrm{Cl}_2(\\mathrm{g}) \\rightarrow 2 \\mathrm{HCl}(\\mathrm{g})$, $\\Delta_{\\mathrm{r}} H^{\\ominus}=-184.62 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$\r\n\r\n(2) $2 \\mathrm{H}_2(\\mathrm{g})+\\mathrm{O}_2(\\mathrm{g}) \\rightarrow 2 \\mathrm{H}_2 \\mathrm{O}(\\mathrm{g})$, $\\Delta_{\\mathrm{r}} H^\\ominus=-483.64 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$\r\n\r\n(3) $4 \\mathrm{HCl}(\\mathrm{g})+\\mathrm{O}_2(\\mathrm{g}) \\rightarrow 2 \\mathrm{Cl}_2(\\mathrm{g})+2 \\mathrm{H}_2 \\mathrm{O}(\\mathrm{g})$", "answer_latex": " -114.40", "answer_number": "-114.40", "unit": "$\\mathrm{KJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": " e2.23(a)(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. An average human produces about $10 \\mathrm{MJ}$ of heat each day through metabolic activity. If a human body were an isolated system of mass $65 \\mathrm{~kg}$ with the heat capacity of water, what temperature rise would the body experience?", "answer_latex": " +37", "answer_number": "+37", "unit": "$\\text{K}$ ", "source": "atkins", "problemid": "p2.11(a) ", "comment": " ", "solution": ""}, {"problem_text": "The critical constants of methane are $p_{\\mathrm{c}}=45.6 \\mathrm{~atm}, V_{\\mathrm{c}}=98.7 \\mathrm{~cm}^3 \\mathrm{~mol}^{-1}$, and $T_{\\mathrm{c}}=190.6 \\mathrm{~K}$. Estimate the radius of the molecules.", "answer_latex": " 0.118", "answer_number": "0.118", "unit": "$\\mathrm{nm}$ ", "source": "atkins", "problemid": " e1.19(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The enthalpy of vaporization of chloroform $\\left(\\mathrm{CHCl}_3\\right)$ is $29.4 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$ at its normal boiling point of $334.88 \\mathrm{~K}$. Calculate the entropy change of the surroundings.", "answer_latex": " -87.8", "answer_number": "-87.8", "unit": "$\\mathrm{J} \\mathrm{K}^{-1} \\mathrm{~mol}^{-1}$", "source": "atkins", "problemid": " e3.7(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Recent communication with the inhabitants of Neptune has revealed that they have a Celsius-type temperature scale, but based on the melting point $(0^{\\circ} \\mathrm{N})$ and boiling point $(100^{\\circ} \\mathrm{N})$ of their most common substance, hydrogen. Further communications have revealed that the Neptunians know about perfect gas behaviour and they find that, in the limit of zero pressure, the value of $p V$ is $28 \\mathrm{dm}^3$ atm at $0^{\\circ} \\mathrm{N}$ and $40 \\mathrm{dm}^3$ atm at $100^{\\circ} \\mathrm{N}$. What is the value of the absolute zero of temperature on their temperature scale?", "answer_latex": " -233", "answer_number": "-233", "unit": "$^{\\circ} \\mathrm{N}$", "source": "atkins", "problemid": " p1.1", "comment": " ", "solution": ""}, {"problem_text": "A gas at $250 \\mathrm{~K}$ and $15 \\mathrm{~atm}$ has a molar volume 12 per cent smaller than that calculated from the perfect gas law. Calculate the compression factor under these conditions.", "answer_latex": "0.88 ", "answer_number": "0.88", "unit": " ", "source": "atkins", "problemid": "e1.15(a)(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Suppose that $3.0 \\mathrm{mmol} \\mathrm{N}_2$ (g) occupies $36 \\mathrm{~cm}^3$ at $300 \\mathrm{~K}$ and expands to $60 \\mathrm{~cm}^3$. Calculate $\\Delta G$ for the process.", "answer_latex": " -3.8", "answer_number": "-3.8", "unit": " $\\text{J}$", "source": "atkins", "problemid": "e3.16(a) ", "comment": " ", "solution": ""}, {"problem_text": "A vessel of volume $22.4 \\mathrm{dm}^3$ contains $2.0 \\mathrm{~mol} \\mathrm{H}_2$ and $1.0 \\mathrm{~mol} \\mathrm{~N}_2$ at $273.15 \\mathrm{~K}$. Calculate their total pressure.", "answer_latex": " 3.0", "answer_number": "3.0", "unit": "$\\mathrm{atm}$ ", "source": "atkins", "problemid": " e1.18(a)(c)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the total change in entropy, when a sample of nitrogen gas of mass $14 \\mathrm{~g}$ at $298 \\mathrm{~K}$ and $1.00 \\mathrm{bar}$ doubles its volume in an adiabatic reversible expansion.", "answer_latex": " 0", "answer_number": "0", "unit": " ", "source": "atkins", "problemid": "e3.13(a)(c) ", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. Concerns over the harmful effects of chlorofluorocarbons on stratospheric ozone have motivated a search for new refrigerants. One such alternative is 2,2-dichloro-1,1,1-trifluoroethane (refrigerant 123). Younglove and McLinden published a compendium of thermophysical properties of this substance (J. Phys. Chem. Ref. Data 23, 7 (1994)), from which properties such as the Joule-Thomson coefficient $\\mu$ can be computed. Compute the temperature change that would accompany adiabatic expansion of $2.0 \\mathrm{~mol}$ of this refrigerant from $1.5 \\mathrm{bar}$ to 0.5 bar at $50^{\\circ} \\mathrm{C}$.", "answer_latex": " -2.99", "answer_number": "-2.99", "unit": "$\\mathrm{K}$", "source": "atkins", "problemid": " p2.45(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the Carnot efficiency of a modern steam turbine that operates with steam at $300^{\\circ} \\mathrm{C}$ and discharges at $80^{\\circ} \\mathrm{C}$.", "answer_latex": " 0.38", "answer_number": "0.38", "unit": " ", "source": "atkins", "problemid": " e3.15(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "The discovery of the element argon by Lord Rayleigh and Sir William Ramsay had its origins in Rayleigh's measurements of the density of nitrogen with an eye toward accurate determination of its molar mass. Rayleigh prepared some samples of nitrogen by chemical reaction of nitrogencontaining compounds; under his standard conditions, a glass globe filled with this 'chemical nitrogen' had a mass of $2.2990 \\mathrm{~g}$. He prepared other samples by removing oxygen, carbon dioxide, and water vapour from atmospheric air; under the same conditions, this 'atmospheric nitrogen' had a mass of $2.3102 \\mathrm{~g}$ (Lord Rayleigh, Royal Institution Proceedings 14, 524 (1895)). With the hindsight of knowing accurate values for the molar masses of nitrogen and argon, compute the mole fraction of argon in the latter sample on the assumption that the former was pure nitrogen and the latter a mixture of nitrogen and argon.", "answer_latex": " 0.011", "answer_number": "0.011", "unit": " ", "source": "atkins", "problemid": " p1.23", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Consider a system consisting of $2.0 \\mathrm{~mol} \\mathrm{CO}_2(\\mathrm{~g})$, initially at $25^{\\circ} \\mathrm{C}$ and $10 \\mathrm{~atm}$ and confined to a cylinder of cross-section $10.0 \\mathrm{~cm}^2$. It is allowed to expand adiabatically against an external pressure of 1.0 atm until the piston has moved outwards through $20 \\mathrm{~cm}$. Assume that carbon dioxide may be considered a perfect gas with $C_{V, \\mathrm{~m}}=28.8 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$ and calculate $w$.", "answer_latex": " -20", "answer_number": "-20", "unit": "$\\text{J}$ ", "source": "atkins", "problemid": "e3.6(a)(b) ", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. When a certain freon used in refrigeration was expanded adiabatically from an initial pressure of $32 \\mathrm{~atm}$ and $0^{\\circ} \\mathrm{C}$ to a final pressure of $1.00 \\mathrm{~atm}$, the temperature fell by $22 \\mathrm{~K}$. Calculate the Joule-Thomson coefficient, $\\mu$, at $0^{\\circ} \\mathrm{C}$, assuming it remains constant over this temperature range.", "answer_latex": " 0.71", "answer_number": "0.71", "unit": "$\\mathrm{K} \\mathrm{atm}^{-1}$", "source": "atkins", "problemid": " e2.30(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. The volume of a certain liquid varies with temperature as\r\n$$\r\nV=V^{\\prime}\\left\\{0.75+3.9 \\times 10^{-4}(T / \\mathrm{K})+1.48 \\times 10^{-6}(T / \\mathrm{K})^2\\right\\}\r\n$$\r\nwhere $V^{\\prime}$ is its volume at $300 \\mathrm{~K}$. Calculate its expansion coefficient, $\\alpha$, at $320 \\mathrm{~K}$.", "answer_latex": "$1.31 \\times 10^{-3}$", "answer_number": "0.00131", "unit": "$\\mathrm{~K}^{-1}$", "source": "atkins", "problemid": "e2.32(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. The standard enthalpy of formation of the metallocene bis(benzene)chromium was measured in a calorimeter. It was found for the reaction $\\mathrm{Cr}\\left(\\mathrm{C}_6 \\mathrm{H}_6\\right)_2(\\mathrm{~s}) \\rightarrow \\mathrm{Cr}(\\mathrm{s})+2 \\mathrm{C}_6 \\mathrm{H}_6(\\mathrm{~g})$ that $\\Delta_{\\mathrm{r}} U^{\\bullet}(583 \\mathrm{~K})=+8.0 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$. Estimate the standard enthalpy of formation of the compound at $583 \\mathrm{~K}$. The constant-pressure molar heat capacity of benzene is $136.1 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$ in its liquid range and $81.67 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$ as a gas.", "answer_latex": " +116.0", "answer_number": "+116.0", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": " p2.9(b)", "comment": " ", "solution": ""}, {"problem_text": "A car tyre (i.e. an automobile tire) was inflated to a pressure of $24 \\mathrm{lb} \\mathrm{in}^{-2}$ $(1.00 \\mathrm{atm}=14.7 \\mathrm{lb} \\mathrm{in}^{-2})$ on a winter's day when the temperature was $-5^{\\circ} \\mathrm{C}$. What pressure will be found, assuming no leaks have occurred and that the volume is constant, on a subsequent summer's day when the temperature is $35^{\\circ} \\mathrm{C}$?", "answer_latex": "30", "answer_number": "30", "unit": "$\\mathrm{lb} \\mathrm{in}^{-2}$", "source": "atkins", "problemid": " e1.3(a)", "comment": " ", "solution": ""}, {"problem_text": "Suppose that $10.0 \\mathrm{~mol} \\mathrm{C}_2 \\mathrm{H}_6(\\mathrm{~g})$ is confined to $4.860 \\mathrm{dm}^3$ at $27^{\\circ} \\mathrm{C}$. Predict the pressure exerted by the ethane from the van der Waals equations of state.", "answer_latex": " 35.2", "answer_number": "35.2", "unit": "$\\mathrm{atm}$ ", "source": "atkins", "problemid": " e1.17(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Use the van der Waals parameters for chlorine to calculate approximate values of the radius of a $\\mathrm{Cl}_2$ molecule regarded as a sphere.", "answer_latex": " 0.139", "answer_number": "0.139", "unit": "$\\mathrm{nm}$ ", "source": "atkins", "problemid": " e1.20(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. A sample consisting of $3.00 \\mathrm{~mol}$ of diatomic perfect gas molecules at $200 \\mathrm{~K}$ is compressed reversibly and adiabatically until its temperature reaches $250 \\mathrm{~K}$. Given that $C_{V, \\mathrm{~m}}=27.5 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$, calculate $\\Delta U$.", "answer_latex": " +4.1", "answer_number": "+4.1", "unit": "$\\text{kJ}$ ", "source": "atkins", "problemid": "e3.4(a)(c) ", "comment": " ", "solution": ""}, {"problem_text": "In an attempt to determine an accurate value of the gas constant, $R$, a student heated a container of volume $20.000 \\mathrm{dm}^3$ filled with $0.25132 \\mathrm{g}$ of helium gas to $500^{\\circ} \\mathrm{C}$ and measured the pressure as $206.402 \\mathrm{cm}$ of water in a manometer at $25^{\\circ} \\mathrm{C}$. Calculate the value of $R$ from these data. (The density of water at $25^{\\circ} \\mathrm{C}$ is $0.99707 \\mathrm{g} \\mathrm{cm}^{-3}$; a manometer consists of a U-shaped tube containing a liquid. One side is connected to the apparatus and the other is open to the atmosphere. The pressure inside the apparatus is then determined from the difference in heights of the liquid.)", "answer_latex": " 8.3147", "answer_number": "8.3147", "unit": "$\\mathrm{JK}^{-1} \\mathrm{~mol}^{-1}$", "source": "atkins", "problemid": " e1.7(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The standard enthalpy of combustion of solid phenol $\\left(\\mathrm{C}_6 \\mathrm{H}_5 \\mathrm{OH}\\right)$ is $-3054 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$ at $298 \\mathrm{~K}_{\\text {and }}$ its standard molar entropy is $144.0 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$. Calculate the standard Gibbs energy of formation of phenol at $298 \\mathrm{~K}$.", "answer_latex": " -50", "answer_number": "-50", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": "e3.12(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Consider a system consisting of $2.0 \\mathrm{~mol} \\mathrm{CO}_2(\\mathrm{~g})$, initially at $25^{\\circ} \\mathrm{C}$ and $10 \\mathrm{~atm}$ and confined to a cylinder of cross-section $10.0 \\mathrm{~cm}^2$. It is allowed to expand adiabatically against an external pressure of 1.0 atm until the piston has moved outwards through $20 \\mathrm{~cm}$. Assume that carbon dioxide may be considered a perfect gas with $C_{V, \\mathrm{~m}}=28.8 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$ and calculate $\\Delta U$.", "answer_latex": " -20", "answer_number": "-20", "unit": "$\\text{J}$ ", "source": "atkins", "problemid": "e3.6(a)(c) ", "comment": " ", "solution": ""}, {"problem_text": "A manometer consists of a U-shaped tube containing a liquid. One side is connected to the apparatus and the other is open to the atmosphere. The pressure inside the apparatus is then determined from the difference in heights of the liquid. Suppose the liquid is water, the external pressure is 770 Torr, and the open side is $10.0 \\mathrm{cm}$ lower than the side connected to the apparatus. What is the pressure in the apparatus? (The density of water at $25^{\\circ} \\mathrm{C}$ is $0.99707 \\mathrm{g} \\mathrm{cm}^{-3}$.)", "answer_latex": " 102", "answer_number": "102", "unit": "$\\mathrm{kPa}$", "source": "atkins", "problemid": " e1.6(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. The standard enthalpy of formation of the metallocene bis(benzene)chromium was measured in a calorimeter. It was found for the reaction $\\mathrm{Cr}\\left(\\mathrm{C}_6 \\mathrm{H}_6\\right)_2(\\mathrm{~s}) \\rightarrow \\mathrm{Cr}(\\mathrm{s})+2 \\mathrm{C}_6 \\mathrm{H}_6(\\mathrm{~g})$ that $\\Delta_{\\mathrm{r}} U^{\\bullet}(583 \\mathrm{~K})=+8.0 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$. Find the corresponding reaction enthalpy and estimate the standard enthalpy of formation of the compound at $583 \\mathrm{~K}$. The constant-pressure molar heat capacity of benzene is $136.1 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$ in its liquid range and $81.67 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$ as a gas.", "answer_latex": "$+17.7$", "answer_number": "+17.7", "unit": "$\\mathrm{~kJ} \\mathrm{~mol}^{-1}$ ", "source": "atkins", "problemid": " p2.9(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the Carnot efficiency of a primitive steam engine operating on steam at $100^{\\circ} \\mathrm{C}$ and discharging at $60^{\\circ} \\mathrm{C}$.", "answer_latex": " 0.11", "answer_number": "0.11", "unit": " ", "source": "atkins", "problemid": "e3.15(a)(a) ", "comment": " ", "solution": ""}, {"problem_text": "In an industrial process, nitrogen is heated to $500 \\mathrm{~K}$ at a constant volume of $1.000 \\mathrm{~m}^3$. The gas enters the container at $300 \\mathrm{~K}$ and $100 \\mathrm{~atm}$. The mass of the gas is $92.4 \\mathrm{~kg}$. Use the van der Waals equation to determine the approximate pressure of the gas at its working temperature of $500 \\mathrm{~K}$. For nitrogen, $a=1.352 \\mathrm{dm}^6 \\mathrm{~atm} \\mathrm{~mol}^{-2}, b=0.0387 \\mathrm{dm}^3 \\mathrm{~mol}^{-1}$.", "answer_latex": " 140", "answer_number": "140", "unit": "$\\text{atm}$", "source": "atkins", "problemid": " e1.16(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K.\r\nSilylene $\\left(\\mathrm{SiH}_2\\right)$ is a key intermediate in the thermal decomposition of silicon hydrides such as silane $\\left(\\mathrm{SiH}_4\\right)$ and disilane $\\left(\\mathrm{Si}_2 \\mathrm{H}_6\\right)$. Moffat et al. (J. Phys. Chem. 95, 145 (1991)) report $\\Delta_{\\mathrm{f}} H^{\\ominus}\\left(\\mathrm{SiH}_2\\right)=+274 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$. If $\\Delta_{\\mathrm{f}} H^{\\ominus}\\left(\\mathrm{SiH}_4\\right)=+34.3 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$ and $\\Delta_{\\mathrm{f}} H^{\\ominus}\\left(\\mathrm{Si}_2 \\mathrm{H}_6\\right)=+80.3 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$(CRC Handbook (2008)), compute the standard enthalpies of the following reaction:\r\n$\\mathrm{SiH}_4 (\\mathrm{g}) \\rightarrow \\mathrm{SiH}_2(\\mathrm{g})+\\mathrm{H}_2(\\mathrm{g})$", "answer_latex": " 240", "answer_number": "240", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": " p2.17(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A sample of $4.50 \\mathrm{~g}$ of methane occupies $12.7 \\mathrm{dm}^3$ at $310 \\mathrm{~K}$. Calculate the work done when the gas expands isothermally against a constant external pressure of 200 Torr until its volume has increased by\r\n$3.3 \\mathrm{dm}^3$.", "answer_latex": "$-88$", "answer_number": "-88", "unit": "$\\mathrm{J}$ ", "source": "atkins", "problemid": " e2.5(a)(a)", "comment": " ", "solution": ""}, {"problem_text": "The barometric formula relates the pressure of a gas of molar mass $M$ at an altitude $h$ to its pressure $p_0$ at sea level. Derive this relation by showing that the change in pressure $\\mathrm{d} p$ for an infinitesimal change in altitude $\\mathrm{d} h$ where the density is $\\rho$ is $\\mathrm{d} p=-\\rho g \\mathrm{~d} h$. Remember that $\\rho$ depends on the pressure. Evaluate the pressure difference between the top and bottom of a laboratory vessel of height 15 cm.", "answer_latex": " $1.7 \\times 10^{-5}$", "answer_number": "0.00017", "unit": " ", "source": "atkins", "problemid": " p1.27(a)", "comment": " ", "solution": ""}, {"problem_text": "The mass density of water vapour at $327.6 \\mathrm{~atm}$ and $776.4 \\mathrm{~K}$ is $133.2 \\mathrm{~kg} \\mathrm{~m}^{-3}$. Given that for water $T_{\\mathrm{c}}=647.4 \\mathrm{~K}, p_{\\mathrm{c}}=218.3 \\mathrm{~atm}, a=5.464 \\mathrm{dm}^6 \\mathrm{~atm} \\mathrm{~mol}^{-2}$, $b=0.03049 \\mathrm{dm}^3 \\mathrm{~mol}^{-1}$, and $M=18.02 \\mathrm{~g} \\mathrm{~mol}^{-1}$, calculate the molar volume.", "answer_latex": " 0.1353", "answer_number": "0.1353", "unit": "$\\mathrm{dm}^3 \\mathrm{~mol}^{-1}$", "source": "atkins", "problemid": " p1.11(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Consider a system consisting of $2.0 \\mathrm{~mol} \\mathrm{CO}_2(\\mathrm{~g})$, initially at $25^{\\circ} \\mathrm{C}$ and $10 \\mathrm{~atm}$ and confined to a cylinder of cross-section $10.0 \\mathrm{~cm}^2$. It is allowed to expand adiabatically against an external pressure of 1.0 atm until the piston has moved outwards through $20 \\mathrm{~cm}$. Assume that carbon dioxide may be considered a perfect gas with $C_{V, \\mathrm{~m}}=28.8 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$ and calculate $q$.", "answer_latex": " 0", "answer_number": "0", "unit": " ", "source": "atkins", "problemid": "e3.6(a)(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. A sample consisting of $3.00 \\mathrm{~mol}$ of diatomic perfect gas molecules at $200 \\mathrm{~K}$ is compressed reversibly and adiabatically until its temperature reaches $250 \\mathrm{~K}$. Given that $C_{V, \\mathrm{~m}}=27.5 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$, calculate $\\Delta S$.", "answer_latex": " 0", "answer_number": "0", "unit": " ", "source": "atkins", "problemid": "e3.4(a)(b) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298 K unless otherwise stated. Find an expression for the fugacity coefficient of a gas that obeys the equation of state $p V_{\\mathrm{m}}=R T\\left(1+B / V_{\\mathrm{m}}+C / V_{\\mathrm{m}}^2\\right)$. Use the resulting expression to estimate the fugacity of argon at 1.00 atm and $100 \\mathrm{~K}$ using $B=-21.13 \\mathrm{~cm}^3 \\mathrm{~mol}^{-1}$ and $C=1054 \\mathrm{~cm}^6 \\mathrm{~mol}^{-2}$.", "answer_latex": " 0.9974", "answer_number": "0.9974", "unit": "$\\text{atm}$ ", "source": "atkins", "problemid": "p3.35 ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. 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 $298 \\mathrm{~K}$.", "answer_latex": " 817.90", "answer_number": "817.90", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": "e3.14(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K.\r\nSilylene $\\left(\\mathrm{SiH}_2\\right)$ is a key intermediate in the thermal decomposition of silicon hydrides such as silane $\\left(\\mathrm{SiH}_4\\right)$ and disilane $\\left(\\mathrm{Si}_2 \\mathrm{H}_6\\right)$. Moffat et al. (J. Phys. Chem. 95, 145 (1991)) report $\\Delta_{\\mathrm{f}} H^{\\ominus}\\left(\\mathrm{SiH}_2\\right)=+274 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$. If $\\Delta_{\\mathrm{f}} H^{\\ominus}\\left(\\mathrm{SiH}_4\\right)=+34.3 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$ and $\\Delta_{\\mathrm{f}} H^{\\ominus}\\left(\\mathrm{Si}_2 \\mathrm{H}_6\\right)=+80.3 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$(CRC Handbook (2008)), compute the standard enthalpies of the following reaction:\r\n$\\mathrm{Si}_2 \\mathrm{H}_6(\\mathrm{g}) \\rightarrow \\mathrm{SiH}_2(\\mathrm{g})+\\mathrm{SiH}_4(\\mathrm{g})$", "answer_latex": " 228", "answer_number": "228", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": " p2.17(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Consider a system consisting of $2.0 \\mathrm{~mol} \\mathrm{CO}_2(\\mathrm{~g})$, initially at $25^{\\circ} \\mathrm{C}$ and $10 \\mathrm{~atm}$ and confined to a cylinder of cross-section $10.0 \\mathrm{~cm}^2$. It is allowed to expand adiabatically against an external pressure of 1.0 atm until the piston has moved outwards through $20 \\mathrm{~cm}$. Assume that carbon dioxide may be considered a perfect gas with $C_{V, \\mathrm{~m}}=28.8 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$ and calculate $\\Delta S$.", "answer_latex": " +0.60", "answer_number": "+0.60", "unit": "$\\mathrm{J} \\mathrm{K}^{-1}$", "source": "atkins", "problemid": " e3.6(a)(e)", "comment": " ", "solution": ""}, {"problem_text": "The mass density of water vapour at $327.6 \\mathrm{~atm}$ and $776.4 \\mathrm{~K}$ is $133.2 \\mathrm{~kg} \\mathrm{~m}^{-3}$. Given that for water $T_{\\mathrm{c}}=647.4 \\mathrm{~K}, p_{\\mathrm{c}}=218.3 \\mathrm{~atm}, a=5.464 \\mathrm{dm}^6 \\mathrm{~atm} \\mathrm{~mol}^{-2}$, $b=0.03049 \\mathrm{dm}^3 \\mathrm{~mol}^{-1}$, and $M=18.02 \\mathrm{~g} \\mathrm{~mol}^{-1}$, calculate the compression factor from the virial expansion of the van der Waals equation.", "answer_latex": " 0.7158", "answer_number": "0.7158", "unit": " ", "source": "atkins", "problemid": " p1.11(c)", "comment": " ", "solution": ""}, {"problem_text": "Express the van der Waals parameters $a=0.751 \\mathrm{~atm} \\mathrm{dm}^6 \\mathrm{~mol}^{-2}$ in SI base units.", "answer_latex": "$7.61 \\times 10^{-2}$", "answer_number": "0.0761", "unit": "$\\mathrm{kg} \\mathrm{~m}^5 \\mathrm{~s}^{-2} \\mathrm{~mol}^{-2}$", "source": "atkins", "problemid": " e1.14(a)(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Estimate the change in the Gibbs energy of $1.0 \\mathrm{dm}^3$ of benzene when the pressure acting on it is increased from $1.0 \\mathrm{~atm}$ to $100 \\mathrm{~atm}$.", "answer_latex": " +10", "answer_number": "+10", "unit": "$\\text{kJ}$ ", "source": "atkins", "problemid": "e3.21(a) ", "comment": " ", "solution": ""}, {"problem_text": "The mass density of water vapour at $327.6 \\mathrm{~atm}$ and $776.4 \\mathrm{~K}$ is $133.2 \\mathrm{~kg} \\mathrm{~m}^{-3}$. Given that for water $T_{\\mathrm{c}}=647.4 \\mathrm{~K}, p_{\\mathrm{c}}=218.3 \\mathrm{~atm}, a=5.464 \\mathrm{dm}^6 \\mathrm{~atm} \\mathrm{~mol}^{-2}$, $b=0.03049 \\mathrm{dm}^3 \\mathrm{~mol}^{-1}$, and $M=18.02 \\mathrm{~g} \\mathrm{~mol}^{-1}$, calculate the compression factor from the data.", "answer_latex": " 0.6957", "answer_number": "0.6957", "unit": " ", "source": "atkins", "problemid": "p1.11(b) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in Gibbs energy of $35 \\mathrm{~g}$ of ethanol (mass density $0.789 \\mathrm{~g} \\mathrm{~cm}^{-3}$ ) when the pressure is increased isothermally from $1 \\mathrm{~atm}$ to $3000 \\mathrm{~atm}$.", "answer_latex": " 12", "answer_number": "12", "unit": "$\\text{kJ}$ ", "source": "atkins", "problemid": "e3.18(a) ", "comment": " ", "solution": ""}, {"problem_text": "The densities of air at $-85^{\\circ} \\mathrm{C}, 0^{\\circ} \\mathrm{C}$, and $100^{\\circ} \\mathrm{C}$ are $1.877 \\mathrm{~g} \\mathrm{dm}^{-3}, 1.294 \\mathrm{~g}$ $\\mathrm{dm}^{-3}$, and $0.946 \\mathrm{~g} \\mathrm{dm}^{-3}$, respectively. From these data, and assuming that air obeys Charles's law, determine a value for the absolute zero of temperature in degrees Celsius.", "answer_latex": " -273", "answer_number": "-273", "unit": "$^{\\circ} \\mathrm{C}$ ", "source": "atkins", "problemid": " e1.12(a)", "comment": " ", "solution": ""}, {"problem_text": "A certain gas obeys the van der Waals equation with $a=0.50 \\mathrm{~m}^6 \\mathrm{~Pa}$ $\\mathrm{mol}^{-2}$. Its volume is found to be $5.00 \\times 10^{-4} \\mathrm{~m}^3 \\mathrm{~mol}^{-1}$ at $273 \\mathrm{~K}$ and $3.0 \\mathrm{MPa}$. From this information calculate the van der Waals constant $b$. What is the compression factor for this gas at the prevailing temperature and pressure?", "answer_latex": " 0.66", "answer_number": "0.66", "unit": " ", "source": "atkins", "problemid": "e1.22(a) ", "comment": " ", "solution": ""}, {"problem_text": "Calculate the pressure exerted by $1.0 \\mathrm{~mol} \\mathrm{Xe}$ when it is confined to $1.0 \\mathrm{dm}^3$ at $25^{\\circ} \\mathrm{C}$.", "answer_latex": " 21", "answer_number": "21", "unit": "$\\mathrm{atm}$ ", "source": "atkins", "problemid": " p1.13(c)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the total change in entropy, when a sample of nitrogen gas of mass $14 \\mathrm{~g}$ at $298 \\mathrm{~K}$ and $1.00 \\mathrm{bar}$ doubles its volume in an isothermal reversible expansion.", "answer_latex": " 0", "answer_number": "0", "unit": " ", "source": "atkins", "problemid": "e3.13(a)(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate $\\Delta H$ when two copper blocks, each of mass $10.0 \\mathrm{~kg}$, one at $100^{\\circ} \\mathrm{C}$ and the other at $0^{\\circ} \\mathrm{C}$, are placed in contact in an isolated container. The specific heat capacity of copper is $0.385 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~g}^{-1}$ and may be assumed constant over the temperature range involved.", "answer_latex": " 0", "answer_number": "0", "unit": " ", "source": "atkins", "problemid": "e3.5(a)(a) ", "comment": " ", "solution": ""}, {"problem_text": "A perfect gas undergoes isothermal compression, which reduces its volume by $2.20 \\mathrm{dm}^3$. The final pressure and volume of the gas are $5.04 \\mathrm{bar}$ and $4.65 \\mathrm{dm}^3$, respectively. Calculate the original pressure of the gas in atm.", "answer_latex": " 3.38", "answer_number": "3.38", "unit": "$\\mathrm{atm}$ ", "source": "atkins", "problemid": " e1.2(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the total change in entropy, when a sample of nitrogen gas of mass $14 \\mathrm{~g}$ at $298 \\mathrm{~K}$ and $1.00 \\mathrm{bar}$ doubles its volume in an isothermal irreversible expansion against $p_{\\mathrm{ex}}=0$.", "answer_latex": " +2.9", "answer_number": "+2.9", "unit": "$\\mathrm{J} \\mathrm{K}^{-1}$", "source": "atkins", "problemid": "e3.13(a)(b) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in the molar Gibbs energy of hydrogen gas when its pressure is increased isothermally from $1.0 \\mathrm{~atm}$ to 100.0 atm at $298 \\mathrm{~K}$.", "answer_latex": " +11", "answer_number": "+11", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": "e3.22(a) ", "comment": " ", "solution": ""}, {"problem_text": "A perfect gas undergoes isothermal compression, which reduces its volume by $2.20 \\mathrm{dm}^3$. The final pressure and volume of the gas are $5.04 \\mathrm{bar}$ and $4.65 \\mathrm{dm}^3$, respectively. Calculate the original pressure of the gas in bar.", "answer_latex": " 3.42", "answer_number": "3.42", "unit": "$ \\mathrm{bar}$", "source": "atkins", "problemid": " e1.2(a)(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate $\\Delta S$ (for the system) when the state of $3.00 \\mathrm{~mol}$ of perfect gas atoms, for which $C_{p, \\mathrm{~m}}=\\frac{5}{2} R$, is changed from $25^{\\circ} \\mathrm{C}$ and 1.00 atm to $125^{\\circ} \\mathrm{C}$ and $5.00 \\mathrm{~atm}$.", "answer_latex": " -22.1", "answer_number": "-22.1", "unit": "$\\mathrm{J} \\mathrm{K}^{-1}$", "source": "atkins", "problemid": "e3.3(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. A sample consisting of $3.00 \\mathrm{~mol}$ of diatomic perfect gas molecules at $200 \\mathrm{~K}$ is compressed reversibly and adiabatically until its temperature reaches $250 \\mathrm{~K}$. Given that $C_{V, \\mathrm{~m}}=27.5 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$, calculate $\\Delta H$.", "answer_latex": " +5.4", "answer_number": "+5.4", "unit": "$\\text{kJ}$ ", "source": "atkins", "problemid": " e3.4(a)(d)", "comment": " ", "solution": ""}, {"problem_text": "A sample of $255 \\mathrm{mg}$ of neon occupies $3.00 \\mathrm{dm}^3$ at $122 \\mathrm{K}$. Use the perfect gas law to calculate the pressure of the gas.", "answer_latex": "$4.20 \\times 10^{-2}$", "answer_number": "0.042", "unit": " $\\text{atm}$", "source": "atkins", "problemid": " e1.4(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A chemical reaction takes place in a container of cross-sectional area $100 \\mathrm{~cm}^2$. As a result of the reaction, a piston is pushed out through $10 \\mathrm{~cm}$ against an external pressure of $1.0 \\mathrm{~atm}$. Calculate the work done by the system.", "answer_latex": "$-1.0 \\times 10^2$", "answer_number": "-100", "unit": "$\\mathrm{J}$", "source": "atkins", "problemid": " e2.2(a)", "comment": " ", "solution": ""}, {"problem_text": "Use the van der Waals parameters for chlorine to calculate approximate values of the Boyle temperature of chlorine.", "answer_latex": "$1.41 \\times 10^3$", "answer_number": "1410", "unit": " $\\mathrm{K}$", "source": "atkins", "problemid": " e1.20(a)(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Consider a system consisting of $2.0 \\mathrm{~mol} \\mathrm{CO}_2(\\mathrm{~g})$, initially at $25^{\\circ} \\mathrm{C}$ and $10 \\mathrm{~atm}$ and confined to a cylinder of cross-section $10.0 \\mathrm{~cm}^2$. It is allowed to expand adiabatically against an external pressure of 1.0 atm until the piston has moved outwards through $20 \\mathrm{~cm}$. Assume that carbon dioxide may be considered a perfect gas with $C_{V, \\mathrm{~m}}=28.8 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~mol}^{-1}$ and calculate $\\Delta T$.", "answer_latex": " -0.347", "answer_number": "-0.347", "unit": "$\\text{K}$ ", "source": "atkins", "problemid": "e3.6(a)(d) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298 K unless otherwise stated. 3.17 Estimate the standard reaction Gibbs energy of $\\mathrm{N}_2(\\mathrm{~g})+3 \\mathrm{H}_2(\\mathrm{~g}) \\rightarrow$ $2 \\mathrm{NH}_3(\\mathrm{~g})$ at $1000 \\mathrm{~K}$ from their values at $298 \\mathrm{~K}$.", "answer_latex": " +107", "answer_number": "+107", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": " p3.17(b)", "comment": " ", "solution": ""}, {"problem_text": "What pressure would $131 \\mathrm{g}$ of xenon gas in a vessel of volume $1.0 \\mathrm{dm}^3$ exert at $25^{\\circ} \\mathrm{C}$ assume it behaved as a perfect gas?", "answer_latex": " 24", "answer_number": "24", "unit": "$\\mathrm{atm}$", "source": "atkins", "problemid": "e1.1(a)(a) ", "comment": " ", "solution": ""}, {"problem_text": "The barometric formula relates the pressure of a gas of molar mass $M$ at an altitude $h$ to its pressure $p_0$ at sea level. Derive this relation by showing that the change in pressure $\\mathrm{d} p$ for an infinitesimal change in altitude $\\mathrm{d} h$ where the density is $\\rho$ is $\\mathrm{d} p=-\\rho g \\mathrm{~d} h$. Remember that $\\rho$ depends on the pressure. Evaluate the external atmospheric pressure at a typical cruising altitude of an aircraft (11 km) when the pressure at ground level is 1.0 atm.", "answer_latex": " 0.72", "answer_number": "0.72", "unit": " ", "source": "atkins", "problemid": " p1.27(b)", "comment": " ", "solution": ""}, {"problem_text": "A constant-volume perfect gas thermometer indicates a pressure of $6.69 \\mathrm{kPa}$ at the triple point temperature of water (273.16 K). What pressure indicates a temperature of $100.00^{\\circ} \\mathrm{C}$?", "answer_latex": " 9.14", "answer_number": "9.14", "unit": "$\\mathrm{kPa}$ ", "source": "atkins", "problemid": " p1.5(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. An average human produces about $10 \\mathrm{MJ}$ of heat each day through metabolic activity. Human bodies are actually open systems, and the main mechanism of heat loss is through the evaporation of water. What mass of water should be evaporated each day to maintain constant temperature?", "answer_latex": " 4.09", "answer_number": "4.09", "unit": "$\\text{kg}$ ", "source": "atkins", "problemid": " p2.11(b)", "comment": " ", "solution": ""}, {"problem_text": "A constant-volume perfect gas thermometer indicates a pressure of $6.69 \\mathrm{kPa}$ at the triple point temperature of water (273.16 K). What change of pressure indicates a change of $1.00 \\mathrm{~K}$ at this temperature?", "answer_latex": " 0.0245", "answer_number": "0.0245", "unit": "$\\mathrm{kPa}$ ", "source": "atkins", "problemid": "p1.5(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. When $229 \\mathrm{~J}$ of energy is supplied as heat to $3.0 \\mathrm{~mol} \\mathrm{Ar}(\\mathrm{g})$ at constant pressure, the temperature of the sample increases by $2.55 \\mathrm{~K}$. Calculate the molar heat capacities at constant pressure of the gas.", "answer_latex": " 22", "answer_number": "22", "unit": "$\\mathrm{J} \\mathrm{K}^{-1} \\mathrm{~mol}^{-1}$", "source": "atkins", "problemid": " e2.12(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Express the van der Waals parameters $b=0.0226 \\mathrm{dm}^3 \\mathrm{~mol}^{-1}$ in SI base units.", "answer_latex": " 2.26 \\times 10^{-5} ", "answer_number": "0.0000226", "unit": " $\\mathrm{~m}^3 \\mathrm{~mol}^{-1}$", "source": "atkins", "problemid": " e1.14(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "A diving bell has an air space of $3.0 \\mathrm{m}^3$ when on the deck of a boat. What is the volume of the air space when the bell has been lowered to a depth of $50 \\mathrm{m}$? Take the mean density of sea water to be $1.025 \\mathrm{g} \\mathrm{cm}^{-3}$ and assume that the temperature is the same as on the surface.", "answer_latex": " 0.5", "answer_number": "0.5", "unit": "$\\text{m}^3$ ", "source": "atkins", "problemid": " e1.5(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The change in the Gibbs energy of a certain constant-pressure process was found to fit the expression $\\Delta G / \\text{J}=-85.40+36.5(T / \\text{K})$. Calculate the value of $\\Delta S$ for the process.", "answer_latex": " -36.5", "answer_number": "-36.5", "unit": "$\\mathrm{J} \\mathrm{K}^{-1}$", "source": "atkins", "problemid": "e3.17(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298 K unless otherwise stated. At $298 \\mathrm{~K}$ the standard enthalpy of combustion of sucrose is $-5797 \\mathrm{~kJ}$ $\\mathrm{mol}^{-1}$ and the standard Gibbs energy of the reaction is $-6333 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$.\r\nEstimate the additional non-expansion work that may be obtained by raising the temperature to blood temperature, $37^{\\circ} \\mathrm{C}$.", "answer_latex": " -21", "answer_number": "-21", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": "p3.37 ", "comment": " ", "solution": ""}, {"problem_text": "The composition of the atmosphere is approximately 80 per cent nitrogen and 20 per cent oxygen by mass. At what height above the surface of the Earth would the atmosphere become 90 per cent nitrogen and 10 per cent oxygen by mass? Assume that the temperature of the atmosphere is constant at $25^{\\circ} \\mathrm{C}$. What is the pressure of the atmosphere at that height?", "answer_latex": "0.0029 ", "answer_number": "0.0029", "unit": "$\\mathrm{atm}$ ", "source": "atkins", "problemid": "p1.31 ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate $\\Delta S_\\text{tot}$ when two copper blocks, each of mass $10.0 \\mathrm{~kg}$, one at $100^{\\circ} \\mathrm{C}$ and the other at $0^{\\circ} \\mathrm{C}$, are placed in contact in an isolated container. The specific heat capacity of copper is $0.385 \\mathrm{~J} \\mathrm{~K}^{-1} \\mathrm{~g}^{-1}$ and may be assumed constant over the temperature range involved.", "answer_latex": " +93.4", "answer_number": "+93.4", "unit": "$\\mathrm{J} \\mathrm{K}^{-1}$", "source": "atkins", "problemid": " e3.5(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Note that 1 atm = 1.013 25 bar. Unless otherwise stated, thermochemical data are for 298.15 K. A sample consisting of $2.0 \\mathrm{~mol} \\mathrm{CO}_2$ occupies a fixed volume of $15.0 \\mathrm{dm}^3$ at $300 \\mathrm{~K}$. When it is supplied with $2.35 \\mathrm{~kJ}$ of energy as heat its temperature increases to $341 \\mathrm{~K}$. Assume that $\\mathrm{CO}_2$ is described by the van der Waals equation of state, and calculate $\\Delta U$.", "answer_latex": "+2.35", "answer_number": "+2.35", "unit": "$\\text{kJ}$", "source": "atkins", "problemid": " p2.3(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. The standard enthalpy of formation of ethylbenzene is $-12.5 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$. Calculate its standard enthalpy of combustion.", "answer_latex": " -4564.7", "answer_number": "-4564.7", "unit": " $\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": " e2.18(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. The standard enthalpy of decomposition of the yellow complex $\\mathrm{H}_3 \\mathrm{NSO}_2$ into $\\mathrm{NH}_3$ and $\\mathrm{SO}_2$ is $+40 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$. Calculate the standard enthalpy of formation of $\\mathrm{H}_3 \\mathrm{NSO}_2$.", "answer_latex": "$-383$", "answer_number": "-383", "unit": "$\\mathrm{kJ} \\mathrm{~mol}^{-1}$ ", "source": "atkins", "problemid": " e2.22(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. A sample of carbon dioxide of mass $2.45 \\mathrm{~g}$ at $27.0^{\\circ} \\mathrm{C}$ is allowed to expand reversibly and adiabatically from $500 \\mathrm{~cm}^3$ to $3.00 \\mathrm{dm}^3$. What is the work done by the gas?", "answer_latex": " -194", "answer_number": " -194", "unit": "$\\mathrm{~J}$", "source": "atkins", "problemid": " e2.10(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Calculate the work needed for a $65 \\mathrm{~kg}$ person to climb through $4.0 \\mathrm{~m}$ on the surface of the Earth.", "answer_latex": "$2.6 \\times 10^3$", "answer_number": "2600", "unit": "$\\mathrm{J}$", "source": "atkins", "problemid": " e2.1(a)(a)", "comment": " ", "solution": ""}, {"problem_text": "What pressure would $131 \\mathrm{g}$ of xenon gas in a vessel of volume $1.0 \\mathrm{dm}^3$ exert at $25^{\\circ} \\mathrm{C}$ if it behaved as a van der Waals gas?", "answer_latex": " 22", "answer_number": "22", "unit": "$\\mathrm{atm}$ ", "source": "atkins", "problemid": " e1.1(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "A constant-volume perfect gas thermometer indicates a pressure of $6.69 \\mathrm{kPa}$ at the triple point temperature of water (273.16 K). What change of pressure indicates a change of $1.00 \\mathrm{~K}$ at the latter temperature?", "answer_latex": " 0.0245", "answer_number": "0.0245", "unit": "$\\mathrm{kPa}$ ", "source": "atkins", "problemid": " p1.5(c)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Calculate the work needed for a $65 \\mathrm{~kg}$ person to climb through $4.0 \\mathrm{~m}$ on the surface of the Moon $\\left(g=1.60 \\mathrm{~m} \\mathrm{~s}^{-2}\\right)$.", "answer_latex": "$4.2 \\times 10^2$", "answer_number": "420", "unit": " $\\mathrm{J}$", "source": "atkins", "problemid": "e2.1(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. When $120 \\mathrm{mg}$ of naphthalene, $\\mathrm{C}_{10} \\mathrm{H}_8(\\mathrm{~s})$, was burned in a bomb calorimeter the temperature rose by $3.05 \\mathrm{~K}$. By how much will the temperature rise when $10 \\mathrm{mg}$ of phenol, $\\mathrm{C}_6 \\mathrm{H}_5 \\mathrm{OH}(\\mathrm{s})$, is burned in the calorimeter under the same conditions?", "answer_latex": " 205", "answer_number": "205", "unit": "$\\text{K}$ ", "source": "atkins", "problemid": " e2.20(a)(b)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Calculate the final pressure of a sample of carbon dioxide that expands reversibly and adiabatically from $57.4 \\mathrm{kPa}$ and $1.0 \\mathrm{dm}^3$ to a final volume of $2.0 \\mathrm{dm}^3$. Take $\\gamma=1.4$.", "answer_latex": " 22", "answer_number": "22", "unit": "$\\text{kPA}$", "source": "atkins", "problemid": " e2.11(a)", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. When $229 \\mathrm{~J}$ of energy is supplied as heat to $3.0 \\mathrm{~mol} \\mathrm{Ar}(\\mathrm{g})$ at constant pressure, the temperature of the sample increases by $2.55 \\mathrm{~K}$. Calculate the molar heat capacities at constant volume.", "answer_latex": " 30", "answer_number": "30", "unit": "$\\mathrm{J} \\mathrm{K}^{-1} \\mathrm{~mol}^{-1}$", "source": "atkins", "problemid": "e2.12(a)(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. The fugacity coefficient of a certain gas at $200 \\mathrm{~K}$ and 50 bar is 0.72. Calculate the difference of its molar Gibbs energy from that of a perfect gas in the same state.", "answer_latex": " -0.55", "answer_number": "-0.55", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": "e3.20(a) ", "comment": " ", "solution": ""}, {"problem_text": "Assume all gases are perfect unless stated otherwise. Unless otherwise stated, thermodynamic data are for 298.15 K. Given the reactions (1) and (2) below, determine $\\Delta_{\\mathrm{r}} U^{\\ominus}$ for reaction (3).\r\n\r\n(1) $\\mathrm{H}_2(\\mathrm{g})+\\mathrm{Cl}_2(\\mathrm{g}) \\rightarrow 2 \\mathrm{HCl}(\\mathrm{g})$, $\\Delta_{\\mathrm{r}} H^{\\ominus}=-184.62 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$\r\n\r\n(2) $2 \\mathrm{H}_2(\\mathrm{g})+\\mathrm{O}_2(\\mathrm{g}) \\rightarrow 2 \\mathrm{H}_2 \\mathrm{O}(\\mathrm{g})$, $\\Delta_{\\mathrm{r}} H^\\ominus=-483.64 \\mathrm{~kJ} \\mathrm{~mol}^{-1}$\r\n\r\n(3) $4 \\mathrm{HCl}(\\mathrm{g})+\\mathrm{O}_2(\\mathrm{g}) \\rightarrow 2 \\mathrm{Cl}_2(\\mathrm{g})+2 \\mathrm{H}_2 \\mathrm{O}(\\mathrm{g})$", "answer_latex": " -111.92", "answer_number": "-111.92", "unit": "$\\mathrm{kJ} \\mathrm{mol}^{-1}$", "source": "atkins", "problemid": " e2.23(a)(b)", "comment": " ", "solution": ""}] |