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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 $500 \mathrm{~K}$. | Substance (state) ΔfG° ΔfG° Substance (state) (kJ/mol) (kcal/mol) NO(g) 87.6 20.9 NO2(g) 51.3 12.3 N2O(g) 103.7 24.78 H2O(g) −228.6 −54.64 H2O(l) −237.1 −56.67 CO2(g) −394.4 −94.26 CO(g) −137.2 −32.79 CH4(g) −50.5 −12.1 C2H6(g) −32.0 −7.65 C3H8(g) −23.4 −5.59 C6H6(g) 129.7 29.76 C6H6(l) 124.5 31.00 The standard Gibbs f... | 7 | 205 | 0.0245 | 9.73 | 58.2 | A |
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 ... | J/(mol K) Enthalpy of combustion –473.2 kJ/mol ΔcH ~~o~~ Heat capacity, cp 114.25 J/(mol K) Gas properties Std enthalpy change of formation, ΔfH ~~o~~ gas –103.18 kJ/mol Standard molar entropy, S ~~o~~ gas 295.6 J/(mol K) at 25 °C Heat capacity, cp 65.33 J/(mol K) at 25 °C van der Waals' constantsLange's Handbook of Ch... | 258.14 | +87.8 | 0.33333333 | -0.029 | 24 | B |
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) $\mathrm{H}_2(\mathrm{g})+\mathrm{Cl}_2(\mathrm{g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})$, $\De... | ==Critical point== ref Tc(K) Tc(°C) Pc(MPa) Pc(other) Vc(cm3/mol) ρc(g/cm3) 1 H hydrogen use 32.97 −240.18 1.293 CRC.a 32.97 −240.18 1.293 65 KAL 33.2 1.297 65.0 SMI −239.9 13.2 kgf/cm² 0.0310 1 H hydrogen (equilibrium) LNG −240.17 1.294 12.77 atm 65.4 0.0308 1 H hydrogen (normal) LNG −239.91 1.297 12.8 atm 65.0 0.0310... | 2.57 | 0.0761 | 0.8185 | -114.40 | 4.4 | D |
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 he... | The normal human body temperature is often stated as . Human body temperature varies. Normal human body temperature varies slightly from person to person and by the time of day. In humans, the average internal temperature is widely accepted to be 37 °C (98.6 °F), a "normal" temperature established in the 1800s. The nor... | 0.11 | 0.068 | 37.0 | 269 | 0.332 | C |
1.19(a) 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. | Methane has a boiling point of −161.5 °C at a pressure of one atmosphere. Methane's heat of combustion is 55.5 MJ/kg.Energy Content of some Combustibles (in MJ/kg) . Cooling methane at normal pressure results in the formation of methane I. However the authors stress "our findings are preliminary with regard to the meth... | 0.0408 | 0.05882352941 | 0.118 | 1260 | 22 | C |
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. | The entropy of vaporization of at its boiling point has the extraordinarily high value of 136.9 J/(K·mol). It is valid for many liquids; for instance, the entropy of vaporization of toluene is 87.30 J/(K·mol), that of benzene is 89.45 J/(K·mol), and that of chloroform is 87.92 J/(K·mol). The entropy of vaporization is ... | -87.8 | 0.139 | 1.7 | 1.775 | 6.0 | A |
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 ... | Below 0.9 kelvin at their saturated vapor pressure, a mixture of the two isotopes undergoes a phase separation into a normal fluid (mostly helium-3) that floats on a denser superfluid consisting mostly of helium-4. At these low temperatures, the melting pressure of helium-3 varies from about 2.9 MPa to nearly 4.0 MPa. ... | 135.36 | 4943 | 2283.63 | -233 | 47 | D |
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. | For an ideal gas the compressibility factor is Z=1 per definition. In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. The compressibility factor is defined in thermodynamics and engineering ... | 0.5117 | 10 | 0.88 | -6.04697 | 7.25 | C |
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. | The value of ΔL must however be taken from the relevant cartridge data information in the C.I.P. Tables. Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked file is 17 Meg) :R∗ = = . We... | 257 | 0.0761 | 0.082 | 13 | -3.8 | E |
1.18(a) 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. | With the "area" in the numerator and the "area" in the denominator canceling each other out, we are left with :\text{pressure} = \text{weight density} \times \text{depth}. The exact formula varies with the tank shape but depends on the density, ρ, and maximum allowable stress σ of the material in addition to the pressu... | 3930 | 0.21 | 524.0 | 3.0 | -131.1 | D |
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. | After the removal of the partition, the n_i = nx_i moles of component i may explore the combined volume V\,, which causes an entropy increase equal to nx_i R \ln(V/V_i) = - nR x_i \ln x_i for each component gas. However, the residual entropy is often quite negligible and can be accounted for when it occurs using statis... | +4.1 | 9.73 | 0.0 | 7.136 | -1.46 | C |
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-tr... | Note the trend of the CClF2-X series in the table below. ==Ozone depleting potential of common compounds== Compound R No. ODP Trichlorofluoromethane (CCl3F) R-11 1.00 1,1,1,2-Tetrafluoroethane (CF3-CH2F) R-134a 0.000015 Chlorodifluoromethane (CClF2-H) R-22 0.05 Chlorotrifluoromethane (CClF2-F) R-13 1.00 Dichlorodifluor... | 0.23 | -2.99 | 10.7598 | 1.1 | 0.2115 | B |
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 $80^{\circ} \mathrm{C}$. | Latest generation gas turbine engines have achieved an efficiency of 46% in simple cycle and 61% when used in combined cycle. ==External combustion engines== ===Steam engine=== ::See also: Steam engine#Efficiency ::See also: Timeline of steam power ====Piston engine==== Steam engines and turbines operate on the Rankine... | 0.9731 | 22 | 0.38 | 35.64 | 6.6 | C |
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 standar... | Argon was first isolated from air in 1894 by Lord Rayleigh and Sir William Ramsay at University College London by removing oxygen, carbon dioxide, water, and nitrogen from a sample of clean air. After the two men identified argon, Ramsay investigated other atmospheric gases. Until 1957, the symbol for argon was "A", bu... | 5.1 | 200 | 0.011 | 8 | 4.5 | C |
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 expan... | If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. A carbon dioxide generator or CO2 generator is a machine used to enhance carbon dioxide levels in order to promote plant growth in g... | 4.16 | -20 | 0.264 | -2.5 | 15.425 | B |
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... | The temperature change produced during a Joule–Thomson expansion is quantified by the Joule–Thomson coefficient, \mu_{\mathrm{JT}}. This equation can be used to obtain Joule–Thomson coefficients from the more easily measured isothermal Joule–Thomson coefficient. The temperature of this point, the Joule–Thomson inversio... | 0.444444444444444 | 0.9992093669 | 3.2 | -1.32 | 0.71 | E |
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... | == Vapor pressure == P/(Pa) 1 10 100 200 1 k 2 k 5 k 10 k 20 k 50 k 100 k 101325 reference 1 H hydrogen use (T/K) 15 20 CRC.a (T/°C) -258.6 -252.8 KAL (T/K) 10 (s) 11.4 (s) 12.2 (s) 13.4 (s) 14.5 16.0 18.2 20.3 2 He helium use (T/K) 3 4 CRC.b (T/°C) -270.6 -268.9 KAL (T/K) 1.3 1.66 1.85 2.17 2.48 2.87 3.54 4.22 3 Li li... | 0.00131 | 5840 | 12.0 | 29.36 | 0.03 | A |
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 \mat... | Solving for the standard of enthalpy of formation, :\Delta_\text{f} H^\ominus (\text{CH}_4) = [ \Delta_\text{f} H^\ominus (\text{CO}_2) + 2 \Delta_\text{f} H^\ominus (\text{H}_2 \text{O})] - \Delta_\text{comb} H^\ominus (\text{CH}_4). ==Critical point== ref Tc(K) Tc(°C) Pc(MPa) Pc(other) Vc(cm3/mol) ρc(g/cm3) 1 H hydro... | 0.33333333 | 7200 | 116.0 | 1068 | 4 | C |
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, o... | So if the tire was filled at 80 °F to 32 psi (or 47 psi absolute when we add atmospheric pressure), the change would be 4.7 psi for this 30 Celsius degree change, or 0.16 psi per Celsius degree or 0.1 psi per Fahrenheit degree or 1 psi for every 10 Fahrenheit degrees. Hence, for a tire filled to 32 psi, the approximati... | 30 | 4.49 | 0.00131 | 2 | 0.5768 | A |
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. | The Van der Waals equation includes intermolecular interaction by adding to the observed pressure P in the equation of state a term of the form a /V_m^2, where a is a constant whose value depends on the gas. The Van der Waals equation may be solved for VG and VL as functions of the temperature and the vapor pressure pV... | -11.2 | 1410 | 1.4 | 35.2 | 4.5 | D |
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. | Values from other sources may differ significantly (see text) The van der Waals radius, r, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It may be calculated for atoms if the Van der Waals radius is known, and for molecules if its atoms radii and th... | 2 | 210 | 22.0 | 0.8561 | 0.139 | E |
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 \m... | Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT:... | 524 | +65.49 | 0.33333333 | 635.7 | +4.1 | E |
1.7(a) 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 $25^{\circ} \mathrm{C}$. Ca... | Note that data could have been collected with three different amounts of the same gas, which would have rendered this experiment easy to do in the eighteenth century. ==History== == See also == * Thermodynamic instruments * Boyle's law * Combined gas law * Gay-Lussac's law * Avogadro's law * Ideal gas law ==References=... | -6.42 | 0.66666666666 | 15.0 | 8.3147 | 1260 | D |
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{... | Therefore, a table of values for \frac{C_{p_k}}{T} is required to find the total molar entropy. However the standard enthalpy of combustion is readily measurable using bomb calorimetry. The standard molar entropy at pressure = P^0 is usually given the symbol , and has units of joules per mole per kelvin (J⋅mol−1⋅K−1). ... | -50 | 0.3085 | 537.0 | 200 | 258.14 | A |
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 expan... | In the second case, the gas will both heat and expand, causing the piston to do mechanical work on the atmosphere. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399... | −1.642876 | 0.042 | 16.0 | -59.24 | -20 | E |
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 sid... | The open end of the manometer is then connected to a pressure measuring device. Therefore, the pressure difference between the applied pressure Pa and the reference pressure P0 in a U-tube manometer can be found by solving . The pressure at the bottom of the barometer, Point B, is equal to the atmospheric pressure. It ... | 32 | 0.9984 | 102.0 | -100 | 4.8 | C |
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 \mat... | Regardless, if each reactant and product can be prepared in its respective standard state, then the contribution of each species is equal to its molar enthalpy of formation multiplied by its stoichiometric coefficient in the reaction, and the enthalpy of reaction at constant (standard) pressure P^{\ominus} and constant... | +17.7 | 3.38 | 0.2553 | 0.11 | 1.95 | A |
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 $60^{\circ} \mathrm{C}$. | Latest generation gas turbine engines have achieved an efficiency of 46% in simple cycle and 61% when used in combined cycle. ==External combustion engines== ===Steam engine=== ::See also: Steam engine#Efficiency ::See also: Timeline of steam power ====Piston engine==== Steam engines and turbines operate on the Rankine... | 52 | 5.51 | 4500.0 | 129 | 0.11 | E |
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 w... | Observe further that the pressure p goes to infinity when the container is completely filled with particles so that there is no void space left for the particles to move; this occurs when V = nb. ===Gas mixture=== If a mixture of n gases is being considered, and each gas has its own a (attraction between molecules) and... | -11.875 | 140 | 131.0 | 655 | 13.45 | B |
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 $\l... | Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? J/(mol·K) Std enthalpy change of vaporizationΔvapH ~~o~~ ? kJ/mol Std entropy change of vaporizationΔvapS ~~o~~ ? \\!| cdf =| mean =\mu + \frac{\delta \beta K_{\lambda+1}(\delta \gamma)}{\gamma K_\lambda(\delta\gamma)}| media... | 5.1 | 240 | '-8.0' | 2.25 | 0.9731 | B |
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 unt... | In the second case, additional work is done as the volume changes, so the amount of heat required to raise the gas temperature (the specific heat capacity) is higher for this constant-pressure case. == Ideal- gas relations == For an ideal gas, the molar heat capacity is at most a function of temperature, since the inte... | 16 | 3.07 | 7200.0 | 15.1 | -88 | E |
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}... | The barometric formula is a formula used to model how the pressure (or density) of the air changes with altitude. == Pressure equations == thumb|300px|Pressure as a function of the height above the sea level There are two equations for computing pressure as a function of height. Subscript b Height Above Sea Level (h) M... | 0.01961 | 0.00017 | 0.2553 | 362880 | 0.6296296296 | B |
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 $T_{\mathrm{c}}=647.4 \mathrm{~K}, p_{\mathrm{c}}=218.3 \mathrm{~atm}, a=5.464 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}$, $b=0.03049 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, a... | The Antoine equation \log_{10}P = A - \frac{B}{C + T} is in degrees Celsius (°C) and the vapour pressure is in mmHg. The (unattributed) constants are given as {| class="wikitable" , °C , °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374 ===Accuracy of different formulations=== Here is a comparison of the ... | -1.32 | -9.54 | '-13.598' | 4.49 | 0.1353 | E |
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 expan... | If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. For light-duty CNG cars to become a viable short-term climate strategy, methane leakage would need to be kept below 1.6% of total na... | 0 | 1000 | 0.18 | -1.5 | 1855 | A |
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 \m... | Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT:... | 0 | 650000 | 4.68 | 0.925 | -0.38 | A |
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 a... | For a gas obeying the van der Waals equation, the explicit formula for the fugacity coefficient is RT \ln \varphi = \frac{RTb}{V_\mathrm{m}-b} - \frac{2a}{V_\mathrm{m}} - RT \ln \left ( 1 - \frac{a(V_\mathrm{m}-b)}{RTV_\mathrm{m}^2}\right ) This formula is difficult to use, since the pressure depends on the molar volum... | 6.6 | 0.03 | 0.9974 | -4564.7 | 2.3613 | C |
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 $298 \mathrm{~K}$. | For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H... | 54.7 | 91.7 | '-233.0' | 817.90 | 0 | D |
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 $\l... | Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? Pa Std enthalpy change of fusionΔfusH ~~o~~ ? kJ/mol Std entropy change of fusionΔfusS ~~o~~ ? ==Critical point== ref Tc(K) Tc(°C) Pc(MPa) Pc(other) Vc(cm3/mol) ρc(g/cm3) 1 H hydrogen use 32.97 −240.18 1.293 CRC.a 32.97 −240.... | +37 | 0.9522 | 3.2 | 228 | 22.2036033112 | D |
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 expan... | In the second case, the gas will both heat and expand, causing the piston to do mechanical work on the atmosphere. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399... | 30 | +0.60 | 0.2553 | 0.14 | 0.1792 | B |
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 $T_{\mathrm{c}}=647.4 \mathrm{~K}, p_{\mathrm{c}}=218.3 \mathrm{~atm}, a=5.464 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}$, $b=0.03049 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, a... | Observe further that the pressure p goes to infinity when the container is completely filled with particles so that there is no void space left for the particles to move; this occurs when V = nb. ===Gas mixture=== If a mixture of n gases is being considered, and each gas has its own a (attraction between molecules) and... | -167 | 0.7158 | 0.18 | 9.8 | 0.123 | B |
Express the van der Waals parameters $a=0.751 \mathrm{~atm} \mathrm{dm}^6 \mathrm{~mol}^{-2}$ in SI base units. | * Analytical calculation of Van der Waals surfaces and volumes. Petitjean, On the Analytical Calculation of Van der Waals Surfaces and Volumes: Some Numerical Aspects, Journal of Computational Chemistry, Volume 15, Number 5, 1994, pp. 507–523. == External links == * VSAs for various molecules by Anton Antonov, The Wolf... | 0.0761 | 0.3359 | 2.3 | 0.0625 | 9.30 | A |
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 $100 \mathrm{~atm}$. | Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. Moran and Shapiro, Fundamentals of Engineering Thermodynamics, Wiley, 4th Ed, 2000 In case of air, using the perfect gas... | 0.1591549431 | +10 | 1.33 | 35.64 | 0.0024 | B |
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 $T_{\mathrm{c}}=647.4 \mathrm{~K}, p_{\mathrm{c}}=218.3 \mathrm{~atm}, a=5.464 \mathrm{dm}^6 \mathrm{~atm} \mathrm{~mol}^{-2}$, $b=0.03049 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, a... | The Antoine equation \log_{10}P = A - \frac{B}{C + T} is in degrees Celsius (°C) and the vapour pressure is in mmHg. The (unattributed) constants are given as {| class="wikitable" , °C , °C 8.07131 1730.63 233.426 1 99 8.14019 1810.94 244.485 100 374 ===Accuracy of different formulations=== Here is a comparison of the ... | +93.4 | 2.3 | 1.0 | 0.6957 | 311875200 | D |
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 $3000 \mathrm{~atm}$. | Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. This means that the molar Gibbs energy of real nitrogen at a pressure of 100 atm is equal to the molar Gibbs energy of n... | 5 | 0.68 | 152.67 | -167 | 12 | E |
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 t... | Rounding up 1.98°C to 2°C, this approximation simplifies to become :\begin{align} \text{DA} & \approx \text{PA} + 118.8 ~ \frac{\text{ft}}{^\circ \text{C}} \left[ T_\text{OA} + \frac{\text{PA}}{500 ~ \text{ft}} {^\circ \text{C}} - 15 ~ {^\circ \text{C}} \right] \\\\[3pt] & = 1.2376 \, \text{PA} + 118.8 ~ \frac{\text{ft... | -100 | -273 | 4.946 | -7.5 | +65.49 | B |
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 compressi... | The complete Van der Waals equation is therefore: :\left(P+a\frac1{V_m^2}\right)(V_m-b)=R T For n moles of gas, it can also be written as: :\left(P+a \frac{n^2}{V^2}\right)(V-n b)=n R T When the molar volume Vm is large, b becomes negligible in comparison with Vm, a/Vm2 becomes negligible with respect to P, and the Van... | 0.0761 | 7.136 | 4.0 | 2 | 0.66 | E |
Calculate the pressure exerted by $1.0 \mathrm{~mol} \mathrm{Xe}$ when it is confined to $1.0 \mathrm{dm}^3$ at $25^{\circ} \mathrm{C}$. | The CGS unit of pressure is the barye (Ba), equal to 1 dyn·cm−2, or 0.1 Pa. Pressure is sometimes expressed in grams-force or kilograms-force per square centimetre (g/cm2 or kg/cm2) and the like without properly identifying the force units. :P=\frac {2 \sigma_\theta s} {D}thumb|252x252px|Cylinder, where :P : internal p... | 21 | 4152 | '-20.0' | 24 | -0.347 | A |
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. | The total molar entropy is the sum of many small changes in molar entropy, where each small change can be considered a reversible process. ==Chemistry== The standard molar entropy of a gas at STP includes contributions from: * The heat capacity of one mole of the solid from 0K to the melting point (including heat absor... | 0.25 | 0 | '9.2e-06' | 0.2307692308 | 2 | B |
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... | Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1... | 2.3613 | 0 | 65.49 | 14 | 0.086 | B |
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. | The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture (Dalton's Law). The partial pressures obey Dalton's law: P_i = y_i P, where is the total pressure and is the mole fraction of the component (so the partial pressures add up to the total pressure). It is equal to t... | 7.00 | 3.38 | 0.4 | 0.6296296296 | +5.41 | B |
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 $p_{\mathrm{ex}}=0$. | However, the residual entropy is often quite negligible and can be accounted for when it occurs using statistical mechanics. ==Thermodynamics== If a mole of a solid substance is a perfectly ordered solid at 0K, then if the solid is warmed by its surroundings to 298.15K without melting, its absolute molar entropy would ... | 0 | -6.9 | 3.07 | 34 | +2.9 | E |
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 $298 \mathrm{~K}$. | The standard molar entropy at pressure = P^0 is usually given the symbol , and has units of joules per mole per kelvin (J⋅mol−1⋅K−1). Then the molar mass of air is computed by M0 = R/Rair = . ==U.S. Standard Atmosphere== The U.S. Standard Atmosphere, 1976 (USSA1976) defines the gas constant R∗ as: Part 1, p. 3, (Linked... | 4.56 | 0.24995 | '-3.8' | +11 | 0.7854 | D |
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. | The partial pressures obey Dalton's law: P_i = y_i P, where is the total pressure and is the mole fraction of the component (so the partial pressures add up to the total pressure). The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture (Dalton's Law). The partial pres... | 10.7598 | 5654.86677646 | 1.43 | 3.42 | 2 | D |
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... | The δ34S (pronounced delta 34 S) value is a standardized method for reporting measurements of the ratio of two stable isotopes of sulfur, 34S:32S, in a sample against the equivalent ratio in a known reference standard. With VCDT as the reference standard, natural δ34S value variations have been recorded between -72‰ an... | 1.154700538 | 4.3 | '-22.1' | 169 | 2.567 | C |
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 \m... | Values can also be determined through finite-difference approximation. == Adiabatic process == This ratio gives the important relation for an isentropic (quasistatic, reversible, adiabatic process) process of a simple compressible calorically-perfect ideal gas: : PV^\gamma is constant Using the ideal gas law, PV = nRT:... | +5.41 | 0.68 | 0.59 | 3.8 | 58.2 | A |
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. | For a fixed number of moles of gas n, a thermally perfect gas * is in thermodynamic equilibrium * is not chemically reacting * has internal energy U, enthalpy H, and constant volume / constant pressure heat capacities C_V, C_P that are solely functions of temperature and not of pressure P or volume V, i.e., U = U(T), H... | 1.2 | 0.042 | 152.67 | 9.90 | 0.9984 | B |
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 $... | In this case the work is given by (where is the pressure at the surface, is the increase of the volume of the system). When a system, for example, moles of a gas of volume at pressure and temperature , is created or brought to its present state from absolute zero, energy must be supplied equal to its internal energy pl... | -11.2 | -100 | 6.2 | 3.54 | +93.4 | B |
Use the van der Waals parameters for chlorine to calculate approximate values of the Boyle temperature of chlorine. | J/(mol K) Enthalpy of combustion –473.2 kJ/mol ΔcH ~~o~~ Heat capacity, cp 114.25 J/(mol K) Gas properties Std enthalpy change of formation, ΔfH ~~o~~ gas –103.18 kJ/mol Standard molar entropy, S ~~o~~ gas 295.6 J/(mol K) at 25 °C Heat capacity, cp 65.33 J/(mol K) at 25 °C van der Waals' constantsLange's Handbook of Ch... | 1410 | 3.8 | 313.0 | 7.82 | 144 | A |
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 expan... | Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1... | -0.347 | 257 | 3.42 | 0.925 | 4096 | A |
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 $298 \mathrm{~K}$. | Coefficients from this source: :* ===KAL=== National Physical Laboratory, Kaye and Laby Tables of Physical and Chemical Constants; Section 3.4.4, D. Ambrose, Vapour pressures from 0.2 to 101.325 kPa. The standard Gibbs free energy of formation (Gf°) of a compound is the change of Gibbs free energy that accompanies the ... | 817.90 | 4.979 | '-191.2' | +107 | 27 | D |
Could $131 \mathrm{g}$ of xenon gas in a vessel of volume $1.0 \mathrm{dm}^3$ exert a pressure of $20 \mathrm{atm}$ at $25^{\circ} \mathrm{C}$ if it behaved as a perfect gas? If not, what pressure would it exert? | If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. After repeating the experiment several times and using different amounts of mercury he found that under controlled conditions, the p... | 0.4207 | 48.6 | 24.0 | 5.1 | 5.0 | C |
Could $131 \mathrm{g}$ of xenon gas in a vessel of volume $1.0 \mathrm{dm}^3$ exert a pressure of $20 \mathrm{atm}$ at $25^{\circ} \mathrm{C}$ if it behaved as a perfect gas? If not, what pressure would it exert? | If the internal pressure exceeds the mechanical limitations of the cylinder and there are no means to safely vent the pressurized gas to the atmosphere, the vessel will fail mechanically. After repeating the experiment several times and using different amounts of mercury he found that under controlled conditions, the p... | 4.85 | 24 | 4.56 | 226 | 4.738 | B |
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}... | The other two values (pressure P and density ρ) are computed by simultaneously solving the equations resulting from: * the vertical pressure gradient resulting from hydrostatic balance, which relates the rate of change of pressure with geopotential altitude: :: \frac{dP}{dh} = - \rho g , and * the ideal gas law in mola... | 344 | 0 | 399.0 | 0.72 | 0.66666666666 | D |
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 $100.00^{\circ} \mathrm{C}$? | By the 1940s, the triple point of water had been experimentally measured to be about 0.6% of standard atmospheric pressure and very close to 0.01 °C per the historical definition of Celsius then in use. The 13th CGPM also held in Resolution 4 that "The kelvin, unit of thermodynamic temperature, is equal to the fraction... | 1410 | 1.2 | 9.14 | 420 | 1.4 | C |
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 i... | The above value of 1.4 is highly consistent with the measured adiabatic indices for dry air within a temperature range of 0–200 °C, exhibiting a deviation of only 0.2% (see tabulation above). This will depend on the latent heat release as: T_e \approx T + \frac{L_v}{c_{pd}} r where: * L_v : latent heat of evaporation (... | 537 | 7 | 4.09 | 0.241 | 2.24 | C |
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? | Historically, the Kelvin scale was developed from the Celsius scale, such that 273.15 K was 0 °C (the approximate melting point of ice) and a change of one kelvin was exactly equal to a change of one degree Celsius. The numerical value of an absolute temperature, , on the 1848 scale is related to the absolute temperatu... | -1270 | 0.0245 | 41.4 | 0.375 | 1.81 | B |
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... | Then the molar heat capacity (at constant volume) would be :cV,m = fR where R is the ideal gas constant. This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume.Lange's Handbook of Chemistry, 10th ed. p. 1524 All methods for ... | -20 | +11 | 17.7 | 22 | 269 | D |
Express the van der Waals parameters $b=0.0226 \mathrm{dm}^3 \mathrm{~mol}^{-1}$ in SI base units. | * Analytical calculation of Van der Waals surfaces and volumes. Petitjean, On the Analytical Calculation of Van der Waals Surfaces and Volumes: Some Numerical Aspects, Journal of Computational Chemistry, Volume 15, Number 5, 1994, pp. 507–523. == External links == * VSAs for various molecules by Anton Antonov, The Wolf... | −2 | 5 | 0.41887902047 | 0.000226 | 0.5 | D |
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. | * Volume reduction of the air in an open bell due to increasing hydrostatic pressure as the bell is lowered is compensated. The bell is lowered into the water and to the working depth at a rate recommended by the decompression schedule, and which allows the divers to equalize comfortably. The bell is lowered through th... | 92 | 35.91 | 0.05882352941 | 0.5 | 8.87 | D |
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. | The Gibbs energy of any system is and an infinitesimal change in G, at constant temperature and pressure, yields :dG=dU+pdV-TdS. The Gibbs free energy is expressed as : G(p,T) = U + pV - TS = H - TS where p is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy... | 1000 | +107 | 0.70710678 | -36.5 | +116.0 | D |
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-ex... | The Sugden Award is an annual award for contributions to combustion research. Part V - Evaluation of Models for the chemical source term" Combustion and Flame, 127 2023 (2001). * 2000. This gives the same result as the Weir formula at RQ = 1 (burning only carbohydrates), and almost the same value at RQ = 0.7 (burning o... | -100 | 0.0029 | 4.0 | -21 | 0.000216 | D |
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 $25^{\circ} \mathrm{C}$. Wha... | Total atmospheric mass is 5.1480×1018 kg (1.135×1019 lb), about 2.5% less than would be inferred from the average sea level pressure and Earth's area of 51007.2 megahectares, this portion being displaced by Earth's mountainous terrain. Hp is 8.4km, but for different gasses (measuring their partial pressure), it is agai... | 0.0029 | 14 | 1.16 | 1.2 | 2 | A |
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 ... | Copper has a thermal conductivity of 231 Btu/(hr-ft-F). However, the thermal conductivity of stainless steel is 1/30th times than that of copper. Copper heat exchangers for improving indoor ait quality: Cooling season at Ft. Jackson. Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 ... | 11000 | 0.59 | 169.0 | +93.4 | +3.03 | D |
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 $2.35 \mathrm{~kJ}$... | Heat capacity ratio for various gases Gas Temp. [°C] H2 −181 1.597 −76 1.453 20 1.410 100 1.404 400 1.387 1000 1.358 2000 1.318 He 20 1.660 Ar −180 1.760 20 1.670 O2 −181 1.450 −76 1.415 20 1.400 100 1.399 200 1.397 400 1.394 N2 −181 1.470 Cl2 20 1.340 Ne 19 1.640 Xe 19 1.660 Kr 19 1.680 Hg 360 1.670 H2O 20 1.330 100 1... | 1.92 | -57.2 | 2.35 | 30 | 1.2 | C |
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. | For example, the standard enthalpy of combustion of ethane gas refers to the reaction C2H6 (g) + (7/2) O2 (g) → 2 CO2 (g) + 3 H2O (l). However the standard enthalpy of combustion is readily measurable using bomb calorimetry. * Standard enthalpy of combustion is the enthalpy change when one mole of an organic compound r... | 0.63 | -4564.7 | '-2.0' | 7.58 | -50 | B |
A scientist proposed the following equation of state:
$$
p=\frac{R T}{V_{\mathrm{m}}}-\frac{B}{V_{\mathrm{m}}^2}+\frac{C}{V_{\mathrm{m}}^3}
$$
Show that the equation leads to critical behaviour. Find the critical constants of the gas in terms of $B$ and $C$ and an expression for the critical compression factor. | When the equation expressed in reduced form, an identical equation is obtained for all gases: : P_\text{r} = \frac{3 T_\text{r}}{V_\text{r} - b'} - \frac{1}{b' \sqrt{T_\text{r}} V_\text{r} \left(V_\text{r}+b'\right)} where b' is: : b' = 2^{1/3}-1 \approx 0.25992 In addition, the compressibility factor at the critical p... | 0.333333 | 4.86 | '-114.4' | 0.5 | +0.60 | A |
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 enthalp... | The standard enthalpy of formation is then determined using Hess's law. Solving for the standard of enthalpy of formation, :\Delta_\text{f} H^\ominus (\text{CH}_4) = [ \Delta_\text{f} H^\ominus (\text{CO}_2) + 2 \Delta_\text{f} H^\ominus (\text{H}_2 \text{O})] - \Delta_\text{comb} H^\ominus (\text{CH}_4). For tabulatio... | 4 | 0.0024 | 0.0 | -383 | 7.00 | D |
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 don... | Such work done by compression is thermodynamic work as here defined. When work, for example pressure–volume work, is done on its surroundings by a closed system that cannot pass heat in or out because it is confined by an adiabatic wall, the work is said to be adiabatic for the system as well as for the surroundings. C... | 21 | -32 | 0.36 | 3.2 | -194 | E |
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. | Other definitions which roughly produce the same numbers have been devised, such as: : \text{1 MET}\ = 1 \, \frac{\text{kcal}}{\text{kg}\times\text{h}}\ = 4.184 \, \frac{\text{kJ}}{\text{kg}\times\text{h}} = 1.162 \, \frac{\text{W}}{\text{kg}} where * kcal = kilocalorie * kg = kilogram * h = hour * kJ = kilojoule * W =... | 2.0 | 2600 | 0.082 | 12 | +87.8 | B |
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? | * ISO 11439: Compressed natural gas (CNG) cylinders. Further the volume of the gas is (4πr3)/3. Pressure vessels for gas storage may also be classified by volume. * IS 2825–1969 (RE1977)_code_unfired_Pressure_vessels. * EN 286 (Parts 1 to 4): European standard for simple pressure vessels (air tanks), harmonized with Co... | 22 | 0.0182 | 1.25 | 3.07 | 260 | A |
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? | :V \propto T\, or :\frac{V}{T}=k V is the volume, T is the thermodynamic temperature, k is the constant for the system. k is not a fixed constant across all systems and therefore needs to be found experimentally for a given system through testing with known temperature values. ==Pressure Thermometer and Absolute Zero==... | 48 | 16 | 2.0 | 0.0182 | 0.0245 | E |
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 $\left(g=1.60 \mathrm{~m} \mathrm{~s}^{-2}\right)$. | The acceleration due to gravity on the surface of the Moon is approximately 1.625 m/s2, about 16.6% that on Earth's surface or 0.166 . The mass of the Moon is M = 7.3458 × 1022 kg and the mean density is 3346 kg/m3. Work in compressed air, compressed air work or hyperbaric work is occupational activity in an enclosed a... | 1.22 | 0.245 | 420.0 | 4 | 0.264 | C |
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 ... | The high heat values are conventionally measured with a bomb calorimeter. The temperature may depend on pressure, because at lower pressure there will be more dissociation of the combustion products, implying a lower adiabatic temperature. ≈6332 Aluminium Oxygen 3732 6750 Lithium Oxygen 2438 4420 Phosphorus (white) Oxy... | 1.6 | 205 | 46.7 | 5.9 | 0.38 | B |
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... | The solubility turned out to be very low: from 0.02 to 0.10 %. thumb|Carbon dioxide pressure-temperature phase diagram == Uses == thumb|219x219px|Fire extinguisher Uses of liquid carbon dioxide include the preservation of food, in fire extinguishers, and in commercial food processes. Liquid carbon dioxide is a type of ... | 0.22222222 | 1.1 | 4.86 | 22 | 49 | D |
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... | Then the molar heat capacity (at constant volume) would be :cV,m = fR where R is the ideal gas constant. This difference is particularly notable in gases where values under constant pressure are typically 30% to 66.7% greater than those at constant volume.Lange's Handbook of Chemistry, 10th ed. p. 1524 All methods for ... | 7.42 | 0.0526315789 | 30.0 | +3.60 | 4 | C |
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. | Taken at the same temperature and pressure, the difference between the molar Gibbs free energies of a real gas and the corresponding ideal gas is equal to . The contribution of nonideality to the molar Gibbs energy of a real gas is equal to . For a gas obeying the van der Waals equation, the explicit formula for the fu... | 7.136 | 0.000216 | 0.0 | 3.8 | -0.55 | E |
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) $\mathrm{H}_2(\mathrm{g})+\mathrm{Cl}_2(\mathrm{g}) \rightarrow 2 \mathrm{HCl}(\mathrm{g})$, $\De... | ==Critical point== ref Tc(K) Tc(°C) Pc(MPa) Pc(other) Vc(cm3/mol) ρc(g/cm3) 1 H hydrogen use 32.97 −240.18 1.293 CRC.a 32.97 −240.18 1.293 65 KAL 33.2 1.297 65.0 SMI −239.9 13.2 kgf/cm² 0.0310 1 H hydrogen (equilibrium) LNG −240.17 1.294 12.77 atm 65.4 0.0308 1 H hydrogen (normal) LNG −239.91 1.297 12.8 atm 65.0 0.0310... | 91.17 | 0.7854 | 2.19 | -0.28 | -111.92 | E |
Radiation from an X-ray source consists of two components of wavelengths $154.433 \mathrm{pm}$ and $154.051 \mathrm{pm}$. Calculate the difference in glancing angles $(2 \theta)$ of the diffraction lines arising from the two components in a diffraction pattern from planes of separation $77.8 \mathrm{pm}$. | In the figure below, the line representing a ray makes an angle θ with the normal (dotted line). right|thumb|Grazing incidence diffraction geometry. * The diffraction angles are invariant under scaling; that is, they depend only on the ratio of the wavelength to the size of the diffracting object. * The diffraction ang... | +37 | 3.38 | 0.14 | 2.14 | 0.020 | D |
A chemical reaction takes place in a container of cross-sectional area $50 \mathrm{~cm}^2$. As a result of the reaction, a piston is pushed out through $15 \mathrm{~cm}$ against an external pressure of $1.0 \mathrm{~atm}$. Calculate the work done by the system. | The work done is given by the dot product of the two vectors. The work is the product of the distance times the spring force, which is also dependent on distance; hence the result. ===Work by a gas=== The work W done by a body of gas on its surroundings is: W = \int_a^b P \, dV where is pressure, is volume, and and are... | -75 | 30 | 0.042 | 0.000216 | 6.07 | A |
A mixture of water and ethanol is prepared with a mole fraction of water of 0.60 . If a small change in the mixture composition results in an increase in the chemical potential of water by $0.25 \mathrm{~J} \mathrm{~mol}^{-1}$, by how much will the chemical potential of ethanol change? | Specific heat = 2.44 kJ/(kg·K) === Acid-base chemistry === Ethanol is a neutral molecule and the pH of a solution of ethanol in water is nearly 7.00. Ethanol-water mixtures have less volume than the sum of their individual components at the given fractions. It can be calculated from this table that at 25 °C, 45 g of et... | -0.38 | 131 | 1.81 | 2 | 8.7 | A |
The enthalpy of fusion of mercury is $2.292 \mathrm{~kJ} \mathrm{~mol}^{-1}$, and its normal freezing point is $234.3 \mathrm{~K}$ with a change in molar volume of $+0.517 \mathrm{~cm}^3 \mathrm{~mol}^{-1}$ on melting. At what temperature will the bottom of a column of mercury (density $13.6 \mathrm{~g} \mathrm{~cm}^{-... | T_M(d) = T_{MB}(1-\frac{4\sigma\,_{sl}}{H_f\rho\,_sd}) Where: TMB = bulk melting temperature ::σsl = solid–liquid interface energy ::Hf = Bulk heat of fusion ::ρs = density of solid ::d = particle diameter ==Semiconductor/covalent nanoparticles== Equation 2 gives the general relation between the melting point of a meta... | 0 | 1.154700538 | 0.6 | 16.3923 | 234.4 | E |
Suppose a nanostructure is modelled by an electron confined to a rectangular region with sides of lengths $L_1=1.0 \mathrm{~nm}$ and $L_2=2.0 \mathrm{~nm}$ and is subjected to thermal motion with a typical energy equal to $k T$, where $k$ is Boltzmann's constant. How low should the temperature be for the thermal energy... | When L is comparable to or smaller than the mean free path (which is of the order 1 µm for carbon nanostructures ), the continuous energy model used for bulk materials no longer applies and nonlocal and nonequilibrium aspects to heat transfer also need to be considered. These issues can be addressed with phonon enginee... | -8 | 1.5 | 5.5 | 0.7812 | 0.0761 | C |
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 atm to 3000 atm. | The Gibbs energy of any system is and an infinitesimal change in G, at constant temperature and pressure, yields :dG=dU+pdV-TdS. The Gibbs free energy is expressed as : G(p,T) = U + pV - TS = H - TS where p is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy... | 12 | 0.00539 | 6.0 | 14.5115 | -17 | A |
The promotion of an electron from the valence band into the conduction band in pure $\mathrm{TIO}_2$ by light absorption requires a wavelength of less than $350 \mathrm{~nm}$. Calculate the energy gap in electronvolts between the valence and conduction bands. | Within the concept of bands, the energy gap between the valence band and the conduction band is the band gap. For materials with a direct band gap, valence electrons can be directly excited into the conduction band by a photon whose energy is larger than the bandgap. In graphs of the electronic band structure of solids... | 0.139 | 5.4 | 3.54 | -0.0301 | 0.6321205588 | C |
Although the crystallization of large biological molecules may not be as readily accomplished as that of small molecules, their crystal lattices are no different. Tobacco seed globulin forms face-centred cubic crystals with unit cell dimension of $12.3 \mathrm{~nm}$ and a density of $1.287 \mathrm{~g} \mathrm{~cm}^{-3}... | The molecular formula C18H22O6 (molar mass: 334.36 g/mol, exact mass: 334.1416 u) may refer to: * Combretastatin * Combretastatin B-1 The molecular formula C3H9O6P (molar mass: 172.07 g/mol, exact mass: 172.0137 u) may refer to: * Glycerol 1-phosphate * Glycerol 2-phosphate (BGP) * Glycerol 3-phosphate Category:Molecul... | 0.6296296296 | 0.5 | 22.0 | 1.8 | 3.61 | E |
An electron is accelerated in an electron microscope from rest through a potential difference $\Delta \phi=100 \mathrm{kV}$ and acquires an energy of $e \Delta \phi$. What is its final speed? | The kinetic energy Ke of an electron moving with velocity v is: :\displaystyle K_{\mathrm{e}} = (\gamma - 1)m_{\mathrm{e}} c^2, where me is the mass of electron. This wavelength, for example, is equal to 0.0037 nm for electrons accelerated across a 100,000-volt potential. The speed of an electron can approach, but neve... | 1.88 | 8 | 0.28209479 | 1.51 | 0.333333 | A |
The following data show how the standard molar constant-pressure heat capacity of sulfur dioxide varies with temperature. By how much does the standard molar enthalpy of $\mathrm{SO}_2(\mathrm{~g})$ increase when the temperature is raised from $298.15 \mathrm{~K}$ to $1500 \mathrm{~K}$ ? | The molar heat capacity generally increases with the molar mass, often varies with temperature and pressure, and is different for each state of matter. The following is a table of some constant- pressure molar heat capacities cP,m of various diatomic gases at standard temperature (25 °C = 298 K), at 500 °C, and at 5000... | 1.94 | 1.07 | 1.2 | 62.2 | 1.06 | D |
Suppose that the normalized wavefunction for an electron in a carbon nanotube of length $L=10.0 \mathrm{~nm}$ is: $\psi=(2 / L)^{1 / 2} \sin (\pi x / L)$. Calculate the probability that the electron is between $x=4.95 \mathrm{~nm}$ and $5.05 \mathrm{~nm}$. | b) Linear dependence of the electron energy on the wave vector in CNTs; c) Dispersion relation near the Fermi energy for a semiconducting CNT; d) Dispersion relation near the Fermi energy for a metallic CNT Conduction in single-walled carbon nanotubes is quantized due to their one-dimensionality and the number of allow... | 0.08 | 226 | 1.0 | 0.020 | 0.011 | D |
A sample of the sugar D-ribose of mass $0.727 \mathrm{~g}$ was placed in a calorimeter and then ignited in the presence of excess oxygen. The temperature rose by $0.910 \mathrm{~K}$. In a separate experiment in the same calorimeter, the combustion of $0.825 \mathrm{~g}$ of benzoic acid, for which the internal energy of... | However the standard enthalpy of combustion is readily measurable using bomb calorimetry. The standard enthalpy of formation is then determined using Hess's law. That is, the heat of combustion, ΔH°comb, is the heat of reaction of the following process: : (std.) + (c + - ) (g) → c (g) + (l) + (g) Chlorine and sulfur ar... | -0.347 | -1270 | 0.4772 | 1.3 | 7.136 | B |
An electron confined to a metallic nanoparticle is modelled as a particle in a one-dimensional box of length $L$. If the electron is in the state $n=1$, calculate the probability of finding it in the following regions: $0 \leq x \leq \frac{1}{2} L$. | To a first approximation (i.e. assuming that the charges are distributed randomly), the molar configurational electronic entropy is given by: :S \approx n_\text{sites} \left [ x \ln x + (1-x) \ln (1-x) \right ] where is the fraction of sites on which a localized electron/hole could reside (typically a transition metal ... | 6 | 0.829 | '-20.0' | 4500 | 0.5 | E |
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