Sihangli/scibench-rl huggingface dataset:
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 $q$.
Answer:  0  
Numeric value: 0
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 $\Delta S$.
Answer:  0  
Numeric value: 0
Problem: 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:  0.9974 $\text{atm}$ 
Numeric value: 0.9974
Problem: 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:  817.90 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: 817.90
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:
$\mathrm{Si}_2 \mathrm{H}_6(\mathrm{g}) \rightarrow \mathrm{SiH}_2(\mathrm{g})+\mathrm{SiH}_4(\mathrm{g})$
Answer:  228 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: 228
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 $\Delta S$.
Answer:  +0.60 $\mathrm{J} \mathrm{K}^{-1}$
Numeric value: +0.60
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 compression factor from the virial expansion of the van der Waals equation.
Answer:  0.7158  
Numeric value: 0.7158
Problem: Express the van der Waals parameters $a=0.751 \mathrm{~atm} \mathrm{dm}^6 \mathrm{~mol}^{-2}$ in SI base units.
Answer: $7.61 \times 10^{-2}$ $\mathrm{kg} \mathrm{~m}^5 \mathrm{~s}^{-2} \mathrm{~mol}^{-2}$
Numeric value: 0.0761
Problem: 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:  +10 $\text{kJ}$ 
Numeric value: +10
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 compression factor from the data.
Answer:  0.6957  
Numeric value: 0.6957
Problem: 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:  12 $\text{kJ}$ 
Numeric value: 12
Problem: 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:  -273 $^{\circ} \mathrm{C}$ 
Numeric value: -273
Problem: 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:  0.66  
Numeric value: 0.66
Problem: 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:  21 $\mathrm{atm}$ 
Numeric value: 21
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 isothermal reversible expansion.
Answer:  0  
Numeric value: 0
Problem: 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:  0  
Numeric value: 0
Problem: 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:  3.38 $\mathrm{atm}$ 
Numeric value: 3.38
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 isothermal irreversible expansion against $p_{\mathrm{ex}}=0$.
Answer:  +2.9 $\mathrm{J} \mathrm{K}^{-1}$
Numeric value: +2.9
Problem: 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:  +11 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: +11
Problem: 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:  3.42 $ \mathrm{bar}$
Numeric value: 3.42
Problem: 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:  -22.1 $\mathrm{J} \mathrm{K}^{-1}$
Numeric value: -22.1
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 $\Delta H$.
Answer:  +5.4 $\text{kJ}$ 
Numeric value: +5.4
Problem: 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: $4.20 \times 10^{-2}$  $\text{atm}$
Numeric value: 0.042
Problem: 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: $-1.0 \times 10^2$ $\mathrm{J}$
Numeric value: -100
Problem: Use the van der Waals parameters for chlorine to calculate approximate values of the Boyle temperature of chlorine.
Answer: $1.41 \times 10^3$  $\mathrm{K}$
Numeric value: 1410
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 $\Delta T$.
Answer:  -0.347 $\text{K}$ 
Numeric value: -0.347
Problem: 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:  +107 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: +107
Problem: 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:  24 $\mathrm{atm}$
Numeric value: 24
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 external atmospheric pressure at a typical cruising altitude of an aircraft (11 km) when the pressure at ground level is 1.0 atm.
Answer:  0.72  
Numeric value: 0.72
Problem: 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:  9.14 $\mathrm{kPa}$ 
Numeric value: 9.14
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. 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:  4.09 $\text{kg}$ 
Numeric value: 4.09
Problem: 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:  0.0245 $\mathrm{kPa}$ 
Numeric value: 0.0245
Problem: 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:  22 $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
Numeric value: 22
Problem: Express the van der Waals parameters $b=0.0226 \mathrm{dm}^3 \mathrm{~mol}^{-1}$ in SI base units.
Answer:  2.26 \times 10^{-5}   $\mathrm{~m}^3 \mathrm{~mol}^{-1}$
Numeric value: 0.0000226
Problem: 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:  0.5 $\text{m}^3$ 
Numeric value: 0.5
Problem: 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:  -36.5 $\mathrm{J} \mathrm{K}^{-1}$
Numeric value: -36.5
Problem: 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 $-6333 \mathrm{~kJ} \mathrm{~mol}^{-1}$.
Estimate the additional non-expansion work that may be obtained by raising the temperature to blood temperature, $37^{\circ} \mathrm{C}$.
Answer:  -21 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: -21
Problem: 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: 0.0029  $\mathrm{atm}$ 
Numeric value: 0.0029
Problem: 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:  +93.4 $\mathrm{J} \mathrm{K}^{-1}$
Numeric value: +93.4
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 $\Delta U$.
Answer: +2.35 $\text{kJ}$
Numeric value: +2.35
Problem: 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:  -4564.7  $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: -4564.7
Problem: 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: $-383$ $\mathrm{kJ} \mathrm{~mol}^{-1}$ 
Numeric value: -383
Problem: 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:   -194 $\mathrm{~J}$
Numeric value:  -194
Problem: 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: $2.6 \times 10^3$ $\mathrm{J}$
Numeric value: 2600
Problem: 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:  22 $\mathrm{atm}$ 
Numeric value: 22
Problem: 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:  0.0245 $\mathrm{kPa}$ 
Numeric value: 0.0245
Problem: 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: $4.2 \times 10^2$  $\mathrm{J}$
Numeric value: 420
Problem: 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:  205 $\text{K}$ 
Numeric value: 205
Problem: 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:  22 $\text{kPA}$
Numeric value: 22
Problem: 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:  30 $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$
Numeric value: 30
Problem: 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:  -0.55 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: -0.55
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 $\Delta_{\mathrm{r}} U^{\ominus}$ 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:  -111.92 $\mathrm{kJ} \mathrm{mol}^{-1}$
Numeric value: -111.92
Problem: A fluid has density $870 \mathrm{~kg} / \mathrm{m}^3$ and flows with velocity $\mathbf{v}=z \mathbf{i}+y^2 \mathbf{j}+x^2 \mathbf{k}$, where $x, y$, and $z$ are measured in meters and the components of $\mathbf{v}$ in meters per second. Find the rate of flow outward through the cylinder $x^2+y^2=4$, $0 \leqslant z \leqslant 1$.

Answer:  0  $\mathrm{kg}/\mathrm{s}$
Numeric value: 0
Problem: Suppose that $2 \mathrm{~J}$ of work is needed to stretch a spring from its natural length of $30 \mathrm{~cm}$ to a length of $42 \mathrm{~cm}$. How far beyond its natural length will a force of $30 \mathrm{~N}$ keep the spring stretched?
Answer:  10.8  $\mathrm{cm}$
Numeric value: 10.8
Problem: Find the work done by a force $\mathbf{F}=8 \mathbf{i}-6 \mathbf{j}+9 \mathbf{k}$ that moves an object from the point $(0,10,8)$ to the point $(6,12,20)$ along a straight line. The distance is measured in meters and the force in newtons.
Answer:  144  $\mathrm{J}$
Numeric value: 144
Problem: A ball is thrown at an angle of $45^{\circ}$ to the ground. If the ball lands $90 \mathrm{~m}$ away, what was the initial speed of the ball?

Answer:  30  $\mathrm{m}/\mathrm{s}$
Numeric value: 30
Problem: Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it. A leaky 10-kg bucket is lifted from the ground to a height of $12 \mathrm{~m}$ at a constant speed with a rope that weighs $0.8 \mathrm{~kg} / \mathrm{m}$. Initially the bucket contains $36 \mathrm{~kg}$ of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 12-m level. How much work is done?

Answer:  3857  $\mathrm{J}$
Numeric value: 3857
Problem: Find the volume of the described solid $S$. The base of $S$ is an elliptical region with boundary curve $9 x^2+4 y^2=36$. Cross-sections perpendicular to the $x$-axis are isosceles right triangles with hypotenuse in the base.
Answer:  24  
Numeric value: 24
Problem: A swimming pool is circular with a $40-\mathrm{ft}$ diameter. The depth is constant along east-west lines and increases linearly from $2 \mathrm{ft}$ at the south end to $7 \mathrm{ft}$ at the north end. Find the volume of water in the pool.
Answer:  $1800\pi$  $\mathrm{ft}^3$
Numeric value: 5654.86677646
Problem: The orbit of Halley's comet, last seen in 1986 and due to return in 2062, is an ellipse with eccentricity 0.97 and one focus at the sun. The length of its major axis is $36.18 \mathrm{AU}$. [An astronomical unit (AU) is the mean distance between the earth and the sun, about 93 million miles.] By finding a polar equation for the orbit of Halley's comet, what is the maximum distance from the comet to the sun?
Answer:  35.64  $\mathrm{AU}$
Numeric value: 35.64