Sihangli/scibench-rl huggingface dataset:
Problem: 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:  -1368 $\mathrm{~kJ} \mathrm{~mol}^{-1}$
Numeric value: -1368
Problem: 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:  0  
Numeric value: 0
Problem: 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:  169  $\mathrm{g} \mathrm{mol}^{-1}$
Numeric value: 169
Problem: 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: $-167$ $\mathrm{J}$
Numeric value: -167
Problem: 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: $-1.5$ $\text{kJ}$ 
Numeric value: -1.5
Problem: 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:  131 $\mathrm{J} \mathrm{mol}^{-1}$
Numeric value: 131
Problem: 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:  +3.60 $\text{kJ}$ 
Numeric value: +3.60
Problem: 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:  152.67 $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
Numeric value: 152.67
Problem: 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: 131  $\mathrm{K}$
Numeric value: 131
Problem: 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:  92 $\mathrm{J} \mathrm{K}^{-1}$
Numeric value: 92
Problem: 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:  +3.03 $\text{kJ}$
Numeric value: +3.03
Problem: 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:  29.9 $\mathrm{K} \mathrm{MPa}^{-1}$
Numeric value: 29.9
Problem: 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:  1.2 $\mathrm{dm}^3 \mathrm{~mol}^{-1}$ 
Numeric value: 1.2
Problem: 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:  6.2 $\text{kg}$ 
Numeric value: 6.2
Problem: 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: 41.40 $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
Numeric value: 41.40
Problem: 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: 7 $\mathrm{mol}^{-1}$
Numeric value: 7
Problem: 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:  +87.8 $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
Numeric value: +87.8
Problem: 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).

(1) $\mathrm{H}_2(\mathrm{g})+\mathrm{Cl}_2(\mathrm{g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})$, $\Delta_{\mathrm{r}} H^{\ominus}=-184.62 \mathrm{~kJ} \mathrm{~mol}^{-1}$

(2) $2 \mathrm{H}_2(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$, $\Delta_{\mathrm{r}} H^\ominus=-483.64 \mathrm{~kJ} \mathrm{~mol}^{-1}$

(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:  -114.40 $\mathrm{KJ} \mathrm{mol}^{-1}$
Numeric value: -114.40
Problem: 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:  +37 $\text{K}$ 
Numeric value: +37
Problem: 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:  0.118 $\mathrm{nm}$ 
Numeric value: 0.118
Problem: 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:  -87.8 $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
Numeric value: -87.8
Problem: 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:  -233 $^{\circ} \mathrm{N}$
Numeric value: -233
Problem: 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: 0.88   
Numeric value: 0.88
Problem: 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:  -3.8  $\text{J}$
Numeric value: -3.8
Problem: 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:  3.0 $\mathrm{atm}$ 
Numeric value: 3.0
Problem: 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:  0  
Numeric value: 0
Problem: 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:  -2.99 $\mathrm{K}$
Numeric value: -2.99
Problem: 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:  0.38  
Numeric value: 0.38
Problem: 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:  0.011  
Numeric value: 0.011
Problem: 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:  -20 $\text{J}$ 
Numeric value: -20
Problem: 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:  0.71 $\mathrm{K} \mathrm{atm}^{-1}$
Numeric value: 0.71
Problem: 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
$$
V=V^{\prime}\left\{0.75+3.9 \times 10^{-4}(T / \mathrm{K})+1.48 \times 10^{-6}(T / \mathrm{K})^2\right\}
$$
where $V^{\prime}$ is its volume at $300 \mathrm{~K}$. Calculate its expansion coefficient, $\alpha$, at $320 \mathrm{~K}$.
Answer: $1.31 \times 10^{-3}$ $\mathrm{~K}^{-1}$
Numeric value: 0.00131
Problem: 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:  +116.0 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: +116.0
Problem: 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: 30 $\mathrm{lb} \mathrm{in}^{-2}$
Numeric value: 30
Problem: 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:  35.2 $\mathrm{atm}$ 
Numeric value: 35.2
Problem: 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:  0.139 $\mathrm{nm}$ 
Numeric value: 0.139
Problem: 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:  +4.1 $\text{kJ}$ 
Numeric value: +4.1
Problem: 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:  8.3147 $\mathrm{JK}^{-1} \mathrm{~mol}^{-1}$
Numeric value: 8.3147
Problem: 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:  -50 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: -50
Problem: 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:  -20 $\text{J}$ 
Numeric value: -20
Problem: 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:  102 $\mathrm{kPa}$
Numeric value: 102
Problem: 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: $+17.7$ $\mathrm{~kJ} \mathrm{~mol}^{-1}$ 
Numeric value: +17.7
Problem: 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:  0.11  
Numeric value: 0.11
Problem: 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:  140 $\text{atm}$
Numeric value: 140
Problem: 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.
Silylene $\left(\mathrm{SiH}_2\right)$ 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:
$\mathrm{SiH}_4 (\mathrm{g}) \rightarrow \mathrm{SiH}_2(\mathrm{g})+\mathrm{H}_2(\mathrm{g})$
Answer:  240 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: 240
Problem: 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
$3.3 \mathrm{dm}^3$.
Answer: $-88$ $\mathrm{J}$ 
Numeric value: -88
Problem: 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:  $1.7 \times 10^{-5}$  
Numeric value: 0.00017
Problem: 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:  0.1353 $\mathrm{dm}^3 \mathrm{~mol}^{-1}$
Numeric value: 0.1353