id stringlengths 17 27 | question stringlengths 64 1.23k | answer stringlengths 1 12 |
|---|---|---|
scibench-atkins-p3.17(b) | 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 $298 \mathrm{~K}$.
Respond in this unit: $\mathrm{kJ} \mathrm{mol}^{-1}$ | +107 |
scibench-class-Problem9.60 | A rocket has an initial mass of $7 \times 10^4 \mathrm{~kg}$ and on firing burns its fuel at a rate of 250 $\mathrm{kg} / \mathrm{s}$. The exhaust velocity is $2500 \mathrm{~m} / \mathrm{s}$. If the rocket has a vertical ascent from resting on the earth, how long after the rocket engines fire will the rocket lift off?
Respond in this unit: $\mathrm{~s}$ | 25 |
scibench-class-14.12 | A racer attempting to break the land speed record rockets by two markers spaced $100$ m apart on the ground in a time of $0.4$ $\mu s$ as measured by an observer on the ground. How far apart do the two markers appear to the racer?
Respond in this unit: $m$ | 55.3 |
scibench-thermo-6.4 | The value of $\Delta G_f^{\circ}$ for $\mathrm{Fe}(g)$ is $370.7 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at $298.15 \mathrm{~K}$, and $\Delta H_f^{\circ}$ for $\mathrm{Fe}(g)$ is $416.3 \mathrm{~kJ} \mathrm{~mol}^{-1}$ at the same temperature. Assuming that $\Delta H_f^{\circ}$ is constant in the interval $250-400 \mathrm{~K}$, calculate $\Delta G_f^{\circ}$ for $\mathrm{Fe}(g)$ at 400. K.
Respond in this unit: $\mathrm{~kJ} \mathrm{~mol}^{-1}$ | 355.1 |
scibench-atkins-e1.6(a) | 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 $0.99707 \mathrm{g} \mathrm{cm}^{-3}$.)
Respond in this unit: $\mathrm{kPa}$ | 102 |
scibench-thermo-1.8 | A vessel contains $1.15 \mathrm{~g}$ liq $\mathrm{H}_2 \mathrm{O}$ in equilibrium with water vapor at $30 .{ }^{\circ} \mathrm{C}$. At this temperature, the vapor pressure of $\mathrm{H}_2 \mathrm{O}$ is 31.82 torr. What volume increase is necessary for all the water to evaporate?
Respond in this unit: $\mathrm{~L}$ | 37.9 |
scibench-atkins-e2.24(a) | 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 $\Delta_{\mathrm{r}} H^{\ominus}$.
Respond in this unit: $\mathrm{~kJ} \mathrm{~mol}^{-1}$ | -1368 |
scibench-matter-5.1(a) | 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 $5.05 \mathrm{~nm}$.
Respond in this unit: | 0.020 |
scibench-thermo-2.5 | Count Rumford observed that using cannon boring machinery a single horse could heat $11.6 \mathrm{~kg}$ of ice water $(T=273 \mathrm{~K})$ to $T=355 \mathrm{~K}$ in 2.5 hours. Assuming the same rate of work, how high could a horse raise a $225 \mathrm{~kg}$ weight in 2.5 minutes? Assume the heat capacity of water is $4.18 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~g}^{-1}$.
Respond in this unit: $\mathrm{~m}$ | 30 |
scibench-atkins-e3.7(a)(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 temperature.
Respond in this unit: $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$ | +87.8 |
scibench-atkins-20.1 | What is the mean speed, $\bar{c}$, of $\mathrm{N}_2$ molecules in air at $25^{\circ} \mathrm{C}$ ?
Respond in this unit: $\mathrm{~m} \mathrm{~s}^{-1}$ | 475 |
scibench-class-Problem2.18 | Include air resistance proportional to the square of the ball's speed in the previous problem. Let the drag coefficient be $c_W=0.5$, the softball radius be $5 \mathrm{~cm}$ and the mass be $200 \mathrm{~g}$. Find the initial speed of the softball needed now to clear the fence.
Respond in this unit: $\mathrm{~m} \cdot \mathrm{s}^{-1}$ | 35.2 |
scibench-thermo-5.6 | In this problem, 3.00 mol of liquid mercury is transformed from an initial state characterized by $T_i=300 . \mathrm{K}$ and $P_i=1.00$ bar to a final state characterized by $T_f=600 . \mathrm{K}$ and $P_f=3.00$ bar.
Calculate $\Delta S$ for this process; $\beta=1.81 \times 10^{-4} \mathrm{~K}^{-1}, \rho=13.54 \mathrm{~g} \mathrm{~cm}^{-3}$, and $C_{P, m}$ for $\mathrm{Hg}(l)=27.98 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$.
Respond in this unit: $\mathrm{~J}\mathrm{~K}^{-1}$ | 58.2 |
scibench-matter-35.1(a) | Calculate the molar energy required to reverse the direction of an $\mathrm{H}_2 \mathrm{O}$ molecule located $100 \mathrm{pm}$ from a $\mathrm{Li}^{+}$ ion. Take the magnitude of the dipole moment of water as $1.85 \mathrm{D}$.
Respond in this unit: $10^3 \mathrm{~kJ} \mathrm{~mol}^{-1}$ | 1.07 |
scibench-atkins-p3.35 | 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 $C=1054 \mathrm{~cm}^6 \mathrm{~mol}^{-2}$.
Respond in this unit: $\text{atm}$ | 0.9974 |
scibench-atkins-p2.3(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. 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 $\Delta U$.
Respond in this unit: $\text{kJ}$ | +2.35 |
scibench-class-9.64C. | A new single-stage rocket is developed in the year 2023, having a gas exhaust velocity of $4000$ m/s. The total mass of the rocket is $10^5$ kg, with $90$% of its mass being fuel. The fuel burns quickly in $100$ s at a constant rate. For testing purposes, the rocket is launched vertically at rest from Earth's surface. Neglecting air resistance and assuming that the acceleration of gravity is constant, the launched object can reach 3700 km above the surface of Earth. If the object has a radius of $20$ cm and the air resistance is proportional to the square of the object's speed with $c_w = 0.2$, assuming the density of air is constant, the maximum height reached is 890 km. Now also include the fact that the acceleration of gravity decreases as the object soars above Earth. Find the height reached.
Respond in this unit: km | 950 |
scibench-atkins-e2.18(a) | 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.
Respond in this unit: $\mathrm{kJ} \mathrm{mol}^{-1}$ | -4564.7 |
scibench-atkins-p2.45(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. 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 $C_{p, \mathrm{~m}}=110.0 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$.
Respond in this unit: $\mathrm{K} \mathrm{MPa}^{-1}$ | 29.9 |
scibench-quan-9.9 | Assume that the charge of the proton is distributed uniformly throughout the volume of a sphere of radius $10^{-13} \mathrm{~cm}$. Use perturbation theory to estimate the shift in the ground-state hydrogen-atom energy due to the finite proton size. The potential energy experienced by the electron when it has penetrated the nucleus and is at distance $r$ from the nuclear center is $-e Q / 4 \pi \varepsilon_0 r$, where $Q$ is the amount of proton charge within the sphere of radius $r$. The evaluation of the integral is simplified by noting that the exponential factor in $\psi$ is essentially equal to 1 within the nucleus.
Respond in this unit: $10^{-8} \mathrm{eV}$ | 1.2 |
scibench-thermo-15.2 | For an ensemble consisting of 1.00 moles of particles having two energy levels separated by $h v=1.00 \times 10^{-20} \mathrm{~J}$, at what temperature will the internal energy of this system equal $1.00 \mathrm{~kJ}$ ?
Respond in this unit: $\mathrm{~K}$ | 449 |
scibench-quan-1.31 | Calculate the force on an alpha particle passing a gold atomic nucleus at a distance of $0.00300 Å$.
Respond in this unit: $\mathrm{~N}$ | 0.405 |
scibench-chemmc-5-9 | Example 5-3 shows that a Maclaurin expansion of a Morse potential leads to
$$
V(x)=D \beta^2 x^2+\cdots
$$
Given that $D=7.31 \times 10^{-19} \mathrm{~J} \cdot$ molecule ${ }^{-1}$ and $\beta=1.81 \times 10^{10} \mathrm{~m}^{-1}$ for $\mathrm{HCl}$, calculate the force constant of $\mathrm{HCl}$.
Respond in this unit: $\mathrm{~N} \cdot \mathrm{m}^{-1}$ | 479 |
scibench-thermo-13.27 | A two-level system is characterized by an energy separation of $1.30 \times 10^{-18} \mathrm{~J}$. At what temperature will the population of the ground state be 5 times greater than that of the excited state?
Respond in this unit: $10^4$ | 5.85 |
scibench-atkins-e1.1(a)(a) | 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?
Respond in this unit: $\mathrm{atm}$ | 24 |
scibench-class-9.64A. | A new single-stage rocket is developed in the year 2023, having a gas exhaust velocity of $4000$ m/s. The total mass of the rocket is $10^5$ kg, with $90$% of its mass being fuel. The fuel burns quickly in $100$ s at a constant rate. For testing purposes, the rocket is launched vertically at rest from Earth's surface. Neglect air resistance and assume that the acceleration of gravity is constant. Determine how high the launched object can reach above the surface of Earth.
Respond in this unit: km | 3700 |
scibench-matter-77.1(a) | Calculate the standard potential of the $\mathrm{Ce}^{4+} / \mathrm{Ce}$ couple from the values for the $\mathrm{Ce}^{3+} / \mathrm{Ce}$ and $\mathrm{Ce}^{4+} / \mathrm{Ce}^{3+}$ couples.
Respond in this unit: $\mathrm{V}$ | -1.46 |
scibench-fund-10.11 | There is a disk mounted on a fixed horizontal axle. A block hangs from a massless cord that is wrapped around the rim of the disk. The cord does not slip and there is no friction at the axle. Let the disk start from rest at time $t=0$ and also let the tension in the massless cord be $6.0 \mathrm{~N}$ and the angular acceleration of the disk be $-24 \mathrm{rad} / \mathrm{s}^2$. What is its rotational kinetic energy $K$ at $t=2.5 \mathrm{~s}$ ?
Respond in this unit: J | 90 |
scibench-thermo-9.8 | At 303 . K, the vapor pressure of benzene is 120 . Torr and that of hexane is 189 Torr. Calculate the vapor pressure of a solution for which $x_{\text {benzene }}=0.28$ assuming ideal behavior.
Respond in this unit: $\mathrm{Torr}$ | 170 |
scibench-matter-52.4(a) | The NOF molecule is an asymmetric rotor with rotational constants $3.1752 \mathrm{~cm}^{-1}, 0.3951 \mathrm{~cm}^{-1}$, and $0.3505 \mathrm{~cm}^{-1}$. Calculate the rotational partition function of the molecule at $25^{\circ} \mathrm{C}$.
Respond in this unit: $10^3$ | 7.97 |
scibench-atkins-p1.27(a) | 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.
Respond in this unit: | 0.00017 |
scibench-atkins-2.2 | The change in molar internal energy when $\mathrm{CaCO}_3(\mathrm{~s})$ as calcite converts to another form, aragonite, is $+0.21 \mathrm{~kJ} \mathrm{~mol}^{-1}$. Calculate the difference between the molar enthalpy and internal energy changes when the pressure is 1.0 bar given that the densities of the polymorphs are $2.71 \mathrm{~g} \mathrm{~cm}^{-3}$ and $2.93 \mathrm{~g} \mathrm{~cm}^{-3}$, respectively.
Respond in this unit: $\mathrm{~Pa} \mathrm{~m}^3 \mathrm{~mol}^{-1}$ | -0.28 |
scibench-chemmc-1-49 | The relationship introduced in Problem $1-48$ has been interpreted to mean that a particle of mass $m\left(E=m c^2\right)$ can materialize from nothing provided that it returns to nothing within a time $\Delta t \leq h / m c^2$. Particles that last for time $\Delta t$ or more are called real particles; particles that last less than time $\Delta t$ are called virtual particles. The mass of the charged pion, a subatomic particle, is $2.5 \times 10^{-28} \mathrm{~kg}$. What is the minimum lifetime if the pion is to be considered a real particle?
Respond in this unit: $10^{-23} \mathrm{~s}$ | 2.9 |
scibench-fund-Question21.53 | What would be the magnitude of the electrostatic force between two 1.00 C point charges separated by a distance of $1.00 \mathrm{~m}$ if such point charges existed (they do not) and this configuration could be set up?
Respond in this unit: $10^9 \mathrm{~N}$ | 8.99 |
scibench-atkins-p1.5(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 this temperature?
Respond in this unit: $\mathrm{kPa}$ | 0.0245 |
scibench-fund-Question21.41 | What equal positive charges would have to be placed on Earth and on the Moon to neutralize their gravitational attraction?
Respond in this unit: $10^{13} \mathrm{C}$ | 5.7 |
scibench-class-Problem8.28 | What is the minimum escape velocity of a spacecraft from the moon?
Respond in this unit: $\mathrm{~m} / \mathrm{s}$ | 2380 |
scibench-class-9.66B. | In a typical model rocket (Estes Alpha III) the Estes C6 solid rocket engine provides a total impulse of $8.5$ N-s. Assume the total rocket mass at launch is $54$ g and that it has a rocket engine of mass $20$ g that burns evenly for $1.5$ s. The rocket diameter is $24$ mm. Assume a constant burn rate of the propellent mass ($11$ g), a rocket exhaust speed $800$ m/s, vertical ascent, and drag coefficient $c_w = 0.75$. Take into account the change of rocket mass with time and omit the effect of gravity. The rocket's speed at burn out is 131 m/s. How far has the rocket traveled at that moment?
Respond in this unit: m | 108 |
scibench-atkins-e2.23(a)(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 $\Delta_{\mathrm{r}} U^{\ominus}$ 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) $4 \mathrm{HCl}(\mathrm{g})+\mathrm{O}_2(\mathrm{g}) \rightarrow 2 \mathrm{Cl}_2(\mathrm{g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$
Respond in this unit: $\mathrm{kJ} \mathrm{mol}^{-1}$ | -111.92 |
scibench-matter-40.3 | The flux of visible photons reaching Earth from the North Star is about $4 \times 10^3 \mathrm{~mm}^{-2} \mathrm{~s}^{-1}$. Of these photons, 30 per cent are absorbed or scattered by the atmosphere and 25 per cent of the surviving photons are scattered by the surface of the cornea of the eye. A further 9 per cent are absorbed inside the cornea. The area of the pupil at night is about $40 \mathrm{~mm}^2$ and the response time of the eye is about $0.1 \mathrm{~s}$. Of the photons passing through the pupil, about 43 per cent are absorbed in the ocular medium. How many photons from the North Star are focused onto the retina in $0.1 \mathrm{~s}$ ?
Respond in this unit: $10^3$ | 4.4 |
scibench-quan-5.8 | Let $w$ be the variable defined as the number of heads that show when two coins are tossed simultaneously. Find $\langle w\rangle$.
Respond in this unit: | 1 |
scibench-chemmc-1-8 | The temperature of the fireball in a thermonuclear explosion can reach temperatures of approximately $10^7 \mathrm{~K}$. What value of $\lambda_{\max }$ does this correspond to?
Respond in this unit: $10^{-10} \mathrm{~m}$
| 3 |
scibench-fund-Question21.55 | Of the charge $Q$ on a tiny sphere, a fraction $\alpha$ is to be transferred to a second, nearby sphere. The spheres can be treated as particles. What value of $\alpha$ maximizes the magnitude $F$ of the electrostatic force between the two spheres?
Respond in this unit: | 0.5 |
scibench-chemmc-1-7 | Sirius, one of the hottest known stars, has approximately a blackbody spectrum with $\lambda_{\max }=260 \mathrm{~nm}$. Estimate the surface temperature of Sirius.
Respond in this unit: $\mathrm{~K}$
| 11000 |
scibench-thermo-4.34 | In order to get in shape for mountain climbing, an avid hiker with a mass of $60 . \mathrm{kg}$ ascends the stairs in the world's tallest structure, the $828 \mathrm{~m}$ tall Burj Khalifa in Dubai, United Arab Emirates. Assume that she eats energy bars on the way up and that her body is $25 \%$ efficient in converting the energy content of the bars into the work of climbing. How many energy bars does she have to eat if a single bar produces $1.08 \times 10^3 \mathrm{~kJ}$ of energy upon metabolizing?
Respond in this unit: | 1.8 |
scibench-atkins-e3.7(a)(b) | 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.
Respond in this unit: $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$ | -87.8 |
scibench-quan-16.3 | Frozen-core $\mathrm{SCF} / \mathrm{DZP}$ and CI-SD/DZP calculations on $\mathrm{H}_2 \mathrm{O}$ at its equilibrium geometry gave energies of -76.040542 and -76.243772 hartrees. Application of the Davidson correction brought the energy to -76.254549 hartrees. Find the coefficient of $\Phi_0$ in the normalized CI-SD wave function.
Respond in this unit: | 0.9731 |
scibench-quan-6.29 | What is the value of the angular-momentum quantum number $l$ for a $t$ orbital?
Respond in this unit: | 14 |
scibench-quan-2.13 | When a particle of mass $9.1 \times 10^{-28} \mathrm{~g}$ in a certain one-dimensional box goes from the $n=5$ level to the $n=2$ level, it emits a photon of frequency $6.0 \times 10^{14} \mathrm{~s}^{-1}$. Find the length of the box.
Respond in this unit: $\mathrm{~nm}$ | 1.8 |
scibench-class-7.10 | A particle of mass $m$ starts at rest on top of a smooth fixed hemisphere of radius $a$. Determine the angle at which the particle leaves the hemisphere.
Respond in this unit: $^\circ$ | 48.189685 |
scibench-atkins-20.3 | Suppose the concentration of a solute decays exponentially along the length of a container. Calculate the thermodynamic force on the solute at $25^{\circ} \mathrm{C}$ given that the concentration falls to half its value in $10 \mathrm{~cm}$.
Respond in this unit: $\mathrm{kN} \mathrm{mol}^{-1}$ | 17 |
scibench-fund-Question22.77 | A particle of charge $-q_1$ is at the origin of an $x$ axis. At what location on the axis should a particle of charge $-4 q_1$ be placed so that the net electric field is zero at $x=2.0 \mathrm{~mm}$ on the axis?
Respond in this unit: $\mathrm{~mm}$ | 6.0 |
scibench-matter-50.1 | It is possible to produce very high magnetic fields over small volumes by special techniques. What would be the resonance frequency of an electron spin in an organic radical in a field of $1.0 \mathrm{kT}$ ?
Respond in this unit: $10^{13} \mathrm{~Hz}$ | 2.8 |
scibench-thermo-11.3 | You are given the following reduction reactions and $E^{\circ}$ values:
$$
\begin{array}{ll}
\mathrm{Fe}^{3+}(a q)+\mathrm{e}^{-} \rightarrow \mathrm{Fe}^{2+}(a q) & E^{\circ}=+0.771 \mathrm{~V} \\
\mathrm{Fe}^{2+}(a q)+2 \mathrm{e}^{-} \rightarrow \mathrm{Fe}(s) & E^{\circ}=-0.447 \mathrm{~V}
\end{array}
$$
Calculate $E^{\circ}$ for the half-cell reaction $\mathrm{Fe}^{3+}(a q)+3 \mathrm{e}^{-} \rightarrow \mathrm{Fe}(s)$.
Respond in this unit: $\mathrm{~V}$ | -0.041 |
scibench-fund-Question23.41 | An electron is shot directly
Figure 23-50 Problem 40. toward the center of a large metal plate that has surface charge density $-2.0 \times 10^{-6} \mathrm{C} / \mathrm{m}^2$. If the initial kinetic energy of the electron is $1.60 \times 10^{-17} \mathrm{~J}$ and if the electron is to stop (due to electrostatic repulsion from the plate) just as it reaches the plate, how far from the plate must the launch point be?
Respond in this unit: $\mathrm{~mm}$ | 0.44 |
scibench-chemmc-1-42 | One of the most powerful modern techniques for studying structure is neutron diffraction. This technique involves generating a collimated beam of neutrons at a particular temperature from a high-energy neutron source and is accomplished at several accelerator facilities around the world. If the speed of a neutron is given by $v_{\mathrm{n}}=\left(3 k_{\mathrm{B}} T / m\right)^{1 / 2}$, where $m$ is the mass of a neutron, then what temperature is needed so that the neutrons have a de Broglie wavelength of $50 \mathrm{pm}$ ?
Respond in this unit: $\mathrm{K}$ | 2500 |
scibench-matter-78.10(a) | If $125 \mathrm{~cm}^3$ of hydrogen gas effuses through a small hole in 135 seconds, how long will it take the same volume of oxygen gas to effuse under the same temperature and pressure?
Respond in this unit: $\mathrm{s}$ | 537 |
scibench-matter-14.1 | Determine the energies and degeneracies of the lowest four energy levels of an ${ }^1 \mathrm{H}^{35} \mathrm{Cl}$ molecule freely rotating in three dimensions. What is the frequency of the transition between the lowest two rotational levels? The moment of inertia of an ${ }^1 \mathrm{H}^{35} \mathrm{Cl}$ molecule is $2.6422 \times 10^{-47} \mathrm{~kg} \mathrm{~m}^2$.
Respond in this unit: $\mathrm{GHz}$ | 635.7 |
scibench-matter-51.4(a) | What is the temperature of a two-level system of energy separation equivalent to $400 \mathrm{~cm}^{-1}$ when the population of the upper state is one-third that of the lower state?
Respond in this unit: $ \mathrm{~K}$ | 524 |
scibench-quan-1.13 | A one-particle, one-dimensional system has the state function
$$
\Psi=(\sin a t)\left(2 / \pi c^2\right)^{1 / 4} e^{-x^2 / c^2}+(\cos a t)\left(32 / \pi c^6\right)^{1 / 4} x e^{-x^2 / c^2}
$$
where $a$ is a constant and $c=2.000 Å$. If the particle's position is measured at $t=0$, estimate the probability that the result will lie between $2.000 Å$ and $2.001 Å$.
Respond in this unit: | 0.000216 |
scibench-atkins-e1.14(a)(a) | Express the van der Waals parameters $a=0.751 \mathrm{~atm} \mathrm{dm}^6 \mathrm{~mol}^{-2}$ in SI base units.
Respond in this unit: $\mathrm{kg} \mathrm{~m}^5 \mathrm{~s}^{-2} \mathrm{~mol}^{-2}$ | 0.0761 |
scibench-quan-6.4 | The lowest-frequency pure-rotational absorption line of ${ }^{12} \mathrm{C}^{32} \mathrm{~S}$ occurs at $48991.0 \mathrm{MHz}$. Find the bond distance in ${ }^{12} \mathrm{C}^{32} \mathrm{~S}$.
Respond in this unit: $10^{-10} \mathrm{~m}$ | 1.5377 |
scibench-matter-78.6(a) | At what pressure does the mean free path of argon at $20^{\circ} \mathrm{C}$ become comparable to the diameter of a $100 \mathrm{~cm}^3$ vessel that contains it? Take $\sigma=0.36 \mathrm{~nm}^2$
Respond in this unit: $\mathrm{Pa}$ | 0.195 |
scibench-class-Problem3.2 | A simple harmonic oscillator consists of a 100-g mass attached to a spring whose force constant is $10^4 \mathrm{dyne} / \mathrm{cm}$. The mass is displaced $3 \mathrm{~cm}$ and released from rest. Calculate the natural frequency $\nu_0$.
Respond in this unit: $10^{-2} \mathrm{~s}^{-1}$ | 6.9 |
scibench-thermo-5.5 | In this problem, $2.50 \mathrm{~mol}$ of $\mathrm{CO}_2$ gas is transformed from an initial state characterized by $T_i=450 . \mathrm{K}$ and $P_i=1.35$ bar to a final state characterized by $T_f=800 . \mathrm{K}$ and $P_f=$ 3.45 bar. Using Equation (5.23), calculate $\Delta S$ for this process. Assume ideal gas behavior and use the ideal gas value for $\beta$. For $\mathrm{CO}_2$,
$$
\frac{C_{P, m}}{\mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}}=18.86+7.937 \times 10^{-2} \frac{T}{\mathrm{~K}}-6.7834 \times 10^{-5} \frac{T^2}{\mathrm{~K}^2}+2.4426 \times 10^{-8} \frac{T^3}{\mathrm{~K}^3}
$$
Respond in this unit: $\mathrm{~J} \mathrm{~K}^{-1}$ | 48.6 |
scibench-atkins-e2.1(a)(b) | 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 $\left(g=1.60 \mathrm{~m} \mathrm{~s}^{-2}\right)$.
Respond in this unit: $\mathrm{J}$ | 420 |
scibench-atkins-e1.2(a)(a) | 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.
Respond in this unit: $ \mathrm{bar}$ | 3.42 |
scibench-fund-Question21.61 | Three charged particles form a triangle: particle 1 with charge $Q_1=80.0 \mathrm{nC}$ is at $x y$ coordinates $(0,3.00 \mathrm{~mm})$, particle 2 with charge $Q_2$ is at $(0,-3.00 \mathrm{~mm})$, and particle 3 with charge $q=18.0$ $\mathrm{nC}$ is at $(4.00 \mathrm{~mm}, 0)$. In unit-vector notation, what is the electrostatic force on particle 3 due to the other two particles if $Q_2$ is equal to $80.0 \mathrm{nC}$?
Respond in this unit: $\mathrm{~N} \hat{\mathrm{i}}$ | 0.829 |
scibench-thermo-4.15 | Benzoic acid, $1.35 \mathrm{~g}$, is reacted with oxygen in a constant volume calorimeter to form $\mathrm{H}_2 \mathrm{O}(l)$ and $\mathrm{CO}_2(g)$ at $298 \mathrm{~K}$. The mass of the water in the inner bath is $1.55 \times$ $10^3 \mathrm{~g}$. The temperature of the calorimeter and its contents rises $2.76 \mathrm{~K}$ as a result of this reaction. Calculate the calorimeter constant.
Respond in this unit: $10^3 \mathrm{~J}^{\circ} \mathrm{C}^{-1}$
| 6.64 |
scibench-matter-37.1 | 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 $1.287 \mathrm{~g} \mathrm{~cm}^{-3}$. Determine its molar mass.
Respond in this unit: $10^5 \mathrm{~g} \mathrm{~mol}^{-1}$ | 3.61 |
scibench-atkins-p3.37 | 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, $37^{\circ} \mathrm{C}$.
Respond in this unit: $\mathrm{kJ} \mathrm{mol}^{-1}$ | -21 |
scibench-atkins-12.1 | Calculate the moment of inertia of an $\mathrm{H}_2 \mathrm{O}$ molecule around the axis defined by the bisector of the $\mathrm{HOH}$ angle (3). The $\mathrm{HOH}$ bond angle is $104.5^{\circ}$ and the bond length is $95.7 \mathrm{pm}$.
Respond in this unit: $10^{-47} \mathrm{~kg} \mathrm{~m}^2$ | 1.91 |
scibench-thermo-8.7 | A cell is roughly spherical with a radius of $20.0 \times 10^{-6} \mathrm{~m}$. Calculate the work required to expand the cell surface against the surface tension of the surroundings if the radius increases by a factor of three. Assume the cell is surrounded by pure water and that $T=298.15 \mathrm{~K}$.
Respond in this unit: $10^{-9} \mathrm{~J}$ | 2.89 |
scibench-chemmc-5-10 | $$
\beta=2 \pi c \tilde{\omega}_{\mathrm{obs}}\left(\frac{\mu}{2 D}\right)^{1 / 2}
$$
Given that $\tilde{\omega}_{\mathrm{obs}}=2886 \mathrm{~cm}^{-1}$ and $D=440.2 \mathrm{~kJ} \cdot \mathrm{mol}^{-1}$ for $\mathrm{H}^{35} \mathrm{Cl}$, calculate $\beta$.
Respond in this unit: $10^{10} \mathrm{~m}^{-1}$ | 1.81 |
scibench-matter-70.8(a) | The vapour pressure of benzene is $53.3 \mathrm{kPa}$ at $60.6^{\circ} \mathrm{C}$, but it fell to $51.5 \mathrm{kPa}$ when $19.0 \mathrm{~g}$ of an non-volatile organic compound was dissolved in $500 \mathrm{~g}$ of benzene. Calculate the molar mass of the compound.
Respond in this unit: $\mathrm{~g} \mathrm{~mol}^{-1}$ | 85 |
scibench-class-10.20B. | Calculate the effective gravitational field vector $\textbf{g}$ at Earth's surface at the equator. Take account of the difference in the equatorial (6378 km) and polar (6357 km) radius as well as the centrifugal force.
Respond in this unit: $m/s^2$ | 9.780 |
scibench-matter-4.8(a) | Electron diffraction makes use of electrons with wavelengths comparable to bond lengths. To what speed must an electron be accelerated for it to have a wavelength of $100 \mathrm{pm}$ ?
Respond in this unit: $10^6 \mathrm{~m} \mathrm{~s}^{-1}$ | 7.27 |
scibench-matter-36.1 | Estimate the molar volume of $\mathrm{CO}_2$ at $500 \mathrm{~K}$ and 100 atm by treating it as a van der Waals gas.
Respond in this unit: $\mathrm{dm}^3 \mathrm{~mol}^{-1}$ | 0.366 |
scibench-fund-Question23.37 | A square metal plate of edge length $8.0 \mathrm{~cm}$ and negligible thickness has a total charge of $6.0 \times 10^{-6} \mathrm{C}$. Estimate the magnitude $E$ of the electric field just off the center of the plate (at, say, a distance of $0.50 \mathrm{~mm}$ from the center) by assuming that the charge is spread uniformly over the two faces of the plate.
Respond in this unit: $10^7 \mathrm{~N} / \mathrm{C}$ | 5.4 |
scibench-class-Problem2.4 | A clown is juggling four balls simultaneously. Students use a video tape to determine that it takes the clown $0.9 \mathrm{~s}$ to cycle each ball through his hands (including catching, transferring, and throwing) and to be ready to catch the next ball. What is the minimum vertical speed the clown must throw up each ball?
Respond in this unit: $\mathrm{~m} \cdot \mathrm{s}^{-1}$ | 13.2 |
scibench-quan-6.6.1 | Calculate the ground-state energy of the hydrogen atom using SI units and convert the result to electronvolts.
Respond in this unit: $\mathrm{eV}$ | -13.598 |
scibench-chemmc-1-51 | When an excited nucleus decays, it emits a $\gamma$ ray. The lifetime of an excited state of a nucleus is of the order of $10^{-12} \mathrm{~s}$. What is the uncertainty in the energy of the $\gamma$ ray produced?
Respond in this unit: $10^{-22} \mathrm{~J}$ | 7 |
scibench-atkins-e3.19(a) | Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in chemical potential of a perfect gas when its pressure is increased isothermally from $1.8 \mathrm{~atm}$ to $29.5 \mathrm{~atm}$ at $40^{\circ} \mathrm{C}$.
Respond in this unit: $\mathrm{kJ} \mathrm{mol}^{-1}$ | +7.3 |
scibench-atkins-e3.20(a) | 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.
Respond in this unit: $\mathrm{kJ} \mathrm{mol}^{-1}$ | -0.55 |
scibench-fund-14.01 | A living room has floor dimensions of $3.5 \mathrm{~m}$ and $4.2 \mathrm{~m}$ and a height of $2.4 \mathrm{~m}$.
What does the air in the room weigh when the air pressure is $1.0 \mathrm{~atm}$ ?
Respond in this unit: N | 418 |
scibench-chemmc-1-44 | Two narrow slits separated by $0.10 \mathrm{~mm}$ are illuminated by light of wavelength $600 \mathrm{~nm}$. If a detector is located $2.00 \mathrm{~m}$ beyond the slits, what is the distance between the central maximum and the first maximum?
Respond in this unit: mm | 12 |
scibench-class-Problem2.54 | A potato of mass $0.5 \mathrm{~kg}$ moves under Earth's gravity with an air resistive force of $-k m v$. Find the terminal velocity if the potato is released from rest and $k=$ $0.01 \mathrm{~s}^{-1}$.
Respond in this unit: $\mathrm{~m} / \mathrm{s}$ | 1000 |
scibench-atkins-e3.1(a)(b) | Assume that all gases are perfect and that data refer to 298.15 K unless otherwise stated. Calculate the change in entropy when $25 \mathrm{~kJ}$ of energy is transferred reversibly and isothermally as heat to a large block of iron at $100^{\circ} \mathrm{C}$.
Respond in this unit: $\mathrm{J} \mathrm{K}^{-1}$ | 67 |
scibench-fund-Question22.51 | Assume that a honeybee is a sphere of diameter 1.000 $\mathrm{cm}$ with a charge of $+45.0 \mathrm{pC}$ uniformly spread over its surface. Assume also that a spherical pollen grain of diameter $40.0 \mu \mathrm{m}$ is electrically held on the surface of the bee because the bee's charge induces a charge of $-1.00 \mathrm{pC}$ on the near side of the grain and a charge of $+1.00 \mathrm{pC}$ on the far side. What is the magnitude of the net electrostatic force on the grain due to the bee?
Respond in this unit: $10^{-10} \mathrm{~N}$ | 2.6 |
scibench-fund-Question21.19 | Particle 1 of charge $+q$ and particle 2 of charge $+4.00 q$ are held at separation $L=9.00 \mathrm{~cm}$ on an $x$ axis. If particle 3 of charge $q_3$ is to be located such that the three particles remain in place when released, what must be the $x$ coordinate of particle 3?
Respond in this unit: $\mathrm{~cm}$ | 3.00 |
scibench-thermo-1.3 | Calculate the pressure exerted by Ar for a molar volume of $1.31 \mathrm{~L} \mathrm{~mol}^{-1}$ at $426 \mathrm{~K}$ using the van der Waals equation of state. The van der Waals parameters $a$ and $b$ for Ar are 1.355 bar dm ${ }^6 \mathrm{~mol}^{-2}$ and $0.0320 \mathrm{dm}^3 \mathrm{~mol}^{-1}$, respectively. Is the attractive or repulsive portion of the potential dominant under these conditions?
Respond in this unit: $\mathrm{~bar}$ | 26.9 |
scibench-atkins-e1.5(a) | 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.
Respond in this unit: $\text{m}^3$ | 0.5 |
scibench-fund-Question21.47 | Point charges of $+6.0 \mu \mathrm{C}$ and $-4.0 \mu \mathrm{C}$ are placed on an $x$ axis, at $x=8.0 \mathrm{~m}$ and $x=16 \mathrm{~m}$, respectively. What charge must be placed at $x=24 \mathrm{~m}$ so that any charge placed at the origin would experience no electrostatic force?
Respond in this unit: $\mu \mathrm{C}$ | -45 |
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