Chemical Principles 7th edition Steven S. Zumdahl, Donald J. DeCoste - Solutions

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Rubber has a negative average coefficient of linear expansion. What happens to the size of a piece of rubber as it is warmed?
Explain why a column of mercury in a thermometer first descends slightly and then rises when the thermometer is placed into hot water?
Why should the amalgam used in dental fillings have the same average coefficient of expansion as a tooth? What would occur if they were mismatched?
Markings to indicate length are placed on a steel tape in a room that has a temperature of 22°C. Are measurements made with the tape on a day when the temperature is 27°C too long, too short, or accurate? Defend your answer.
Determine the number of grams in a mole of the following gases: (a) Hydrogen (b) Helium (c) Carbon monoxide.
What does the ideal gas law predict about the volume of a sample of gas at absolute zero? Why is this prediction incorrect?
An inflated rubber balloon filled with air is immersed in a flask of liquid nitrogen that is at 77 K. Describe what happens to the balloon, assuming that it remains flexible while being cooled.
Two identical cylinders at the same temperature each contain the same kind of gas and the same number of moles of gas. If the volume of cylinder A is three times greater than the volume of cylinder B, what can you say about the relative pressures in the cylinders?
After food is cooked in a pressure cooker, why is it very important to cool off the container with cold water before attempting to remove the lid?
The shore of the ocean is very rocky at a particular place. The rocks form a cave sloping upward from an underwater opening, as shown in Figure Q19.13a. (a) Inside the cave is falls with the tides, , will the level of water in the cave rise and fall? If so, will it have the same amplitude as
In Colonization: Second Contact (Harry Turtledove, Ballantine Publishing Group, 1999), the Earth has been partially settled by aliens from another planet, whom humans call Lizards. Laboratory study by humans of Lizard science requires “shifting back and forth between the metric system and the one
The pendulum of a certain pendulum clock is made of brass. When the temperature increases, does the period of the clock increase, decrease, or remain the same? Explain.
An automobile radiator is filled to the brim with water while the engine is cool. What happens to the water when the engine is running and the water is heated? What do modern automobiles have in their cooling systems to prevent the loss of coolants?
Metal lids on glass jars can often be loosened by running hot water over them. How is this possible?
When the metal ring and metal sphere in Figure Q19.18 are both at room temperature, the sphere can just be passed through the ring. After the sphere is heated, it cannot be passed through the ring. Explain. What If? What if the ring is heated and the sphere is left at room temperature? Does the
The clean steering wheel system is an important system that all cars should have, specially the cars that are driven by several drivers. The goal of this system is to reduce the number of germs people carry from public places, for example, public restrooms, restaurants, etc. furthermore, this
An explanation of how the CPU simulation works, that is from moment it starts to the moments it ends, a walk through of the source code explaining what the code does. preferably if each section or line is commented to aid understanding. The entire code is well commented but if you still feel
This paper is written by B.B Zhou, X. Qu and R.P Brent working in Computer Sciences laboratory. The title of this journal is Effective scheduling in a Mixed Parallel and Sequential Computing Environment. As this paper consists of 6 pages including all the references but there is nothing written
In this short report it discusses the suitability and lack of incremental, evolutionary and specialized model with regards the requirement phase. Contents: Complete Report Visio Use Cases Word Length: 1122
An incandescent light bulb contains a volume V of argon at pressure Pi. The bulb is switched on and constant power "is transferred to the argon for a time interval "t. (a) Show that the pressure Pf in the bulb at the end of this process is Pf = Pi [1 + (PΔtR) / (PiVCV)]. (b) Find the
A vertical cylinder with a heavy piston contains air at a temperature of 300 K. The initial pressure is 200 kPa, and the initial volume is 0.350 m3. Take the molar mass of air as 28.9 g/mol and assume that CV = 5R/2. (a) Find the specific heat of air at constant volume in units of J/kg °C. (b)
A 1-L Thermos bottle is full of tea at 90°C. You pour out one cup and immediately screw the stopper back on. Make an order-of-magnitude estimate of the change in temperature of the tea remaining in the flask that results from the admission of air at room temperature. State the quantities you take
A 1.00-mol sample of a diatomic ideal gas has pressure P and volume V. When the gas is heated, its pressure triples and its volume doubles. This heating process includes two steps, the first at constant pressure and the second at constant volume. Determine the amount of energy transferred to the
A 1.00-mol sample of an ideal monatomic gas is at an initial temperature of 300 K. The gas undergoes an is volumetric process acquiring 500 J of energy by heat. It then undergoes an isobaric process losing this same amount of energy by heat. Determine (a) The new temperature of the gas and (b)
A vertical cylinder with a movable piston contains 1.00 mol of a diatomic ideal gas. The volume of the gas is Vi, and its temperature is Ti. Then the cylinder is set on a stove and additional weights are piled onto the piston as it moves up, in such a way that the pressure is proportional to the
A container has a mixture of two gases: n1 mol of gas 1 having molar specific heat C1 and n2 mol of gas 2 of molar specific heat C2. (a) Find the molar specific heat of the mixture. (b) What If? What is the molar specific heat if the mixture has m gases in the amounts n1, n2, n3, . . . , nm, with
During the compression stroke of a certain gasoline engine, the pressure increases from 1.00 atm to 20.0 atm. If the process is adiabatic and the fuel–air mixture behaves as a diatomic ideal gas, (a) by what factor does the volume change and (b) by what factor does the temperature change? (c)
A 2.00-mol sample of a diatomic ideal gas expands slowly and adiabatically from a pressure of 5.00 atm and a volume of 12.0 L to a final volume of 30.0 L. (a) What is the final pressure of the gas? (b) What are the initial and final temperatures? (c) Find Q, W, and ΔEint
Air (a diatomic ideal gas) at 27.0°C and atmospheric pressure is drawn into a bicycle pump that has a cylinder with an inner diameter of 2.50 cm and length 50.0 cm. The down stroke adiabatically compresses the air, which reaches a gauge pressure of 800 kPa before entering the tire (Fig. P21.26).
Air in a thundercloud expands as it rises. If its initial temperature is 300 K and no energy is lost by thermal conduction on expansion, what is its temperature when the initial volume has doubled?
The largest bottle ever made by blowing glass has a volume of about 0.720 m3. Imagine that this bottle is filled with air that behaves as an ideal diatomic gas. The bottle is held with its opening at the bottom and rapidly submerged into the ocean. No air escapes or mixes with the water. No energy
A 4.00-L sample of a diatomic ideal gas with specific heat ratio 1.40, confined to a cylinder, is carried through a closed cycle. The gas is initially at 1.00 atm and at 300 K. First, its pressure is tripled under constant volume. Then, it expands adiabatically to its original pressure. Finally,
A diatomic ideal gas (y = 1.40) confined to a cylinder is put through a closed cycle. Initially the gas is at Pi, Vi, and Ti. First, its pressure is tripled under constant volume. It then expands adiabatically to its original pressure and finally is compressed isobarically to its original volume.
How much work is required to compress 5.00 mol of air at 20.0°C and 1.00 atm to one tenth of the original volume? (a) By an isothermal process? (b) By an adiabatic process? (c) What is the final pressure in each of these two cases?
During the power stroke in a four-stroke automobile engine, the piston is forced down as the mixture of combustion products and air undergoes an adiabatic expansion (Fig. P21.32). Assume that (1) the engine is running at 2 500 cycles/min, (2) the gauge pressure right before the expansion is 20.0
Consider 2.00 mol of an ideal diatomic gas. (a) Find the total heat capacity of the gas at constant volume and at constant pressure assuming the molecules rotate but do not vibrate. (b) What If? Repeat, assuming the molecules both rotate and vibrate.
A certain molecule has f degrees of freedom. Show that an ideal gas consisting of such molecules has the following properties: (1) its total internal energy is fnRT / 2; (2) its molar specific heat at constant volume is fR / 2; (3) its molar specific heat at constant pressure is (f + 2) R /2; (4)
In a crude model (Fig. P21.35) of a rotating diatomic molecule of chlorine (Cl2), the two Cl atoms are 2.00 X 10 -10 m apart and rotate about their center of mass with angular speed = 2.00 X 1012 rad/s. What is the rotational kinetic energy of one molecule of Cl2, which has a molar mass of 70.0
One cubic meter of atomic hydrogen at 0°C and atmospheric pressure contains approximately 2.70 X 1025 atoms. The first excited state of the hydrogen atom has an energy of 10.2 eV above the lowest energy level, called the ground state. Use the Boltzmann factor to find the number of atoms in the
Fifteen identical particles have various speeds: one has a speed of 2.00 m/s; two have speeds of 3.00 m/s; three have speeds of 5.00 m/s; four have speeds of 7.00 m/s; three have speeds of 9.00 m/s; and two have speeds of 12.0 m/s. Find (a) The average speed, (b) The rms speed, and (c) The
Two gases in a mixture diffuse through a filter at rates proportional to the gases’ rms speeds. (a) Find the ratio of speeds for the two isotopes of chlorine, 35Cl and 37Cl, as they diffuse through the air. (b) Which isotope moves faster?
From the Maxwell–Boltzmann speed distribution, show that the most probable speed of a gas molecule is given by Equation 21.29. Note that the most probable speed corresponds to the point at which the slope of the speed distribution curve dNv / dv is zero.
Helium gas is in thermal equilibrium with liquid helium at 4.20 K. Even though it is on the point of condensation, model the gas as ideal and determine the most probable speed of a helium atom (mass = 6.64 X 10-27 kg) in it.
At what temperature would the average speed of helium atoms equal? (a) The escape speed from Earth, 1.12 X 104 m/s and (b) The escape speed from the Moon, 2.37 X 103 m/s? (See Chapter 13 for a discussion of escape speed, and note that the mass of a helium atom is 6.64 X 10-27 kg.)
A gas is at 0°C. If we wish to double the rms speed of its molecules, to what temperature must the gas be brought?
Assume that the Earth’s atmosphere has a uniform temperature of 20°C and uniform composition, with an effective molar mass of 28.9 g/mol. (a) Show that the number density of molecules depends on height according to nv(y) = nOe –mgy/kBT Where n0 is the number density at sea level, where y =
If you can’t walk to outer space, can you at least walk halfway? Using the law of atmospheres from Problem 43, we find that the average height of a molecule in the Earth’s atmosphere is given by
In an ultra-high-vacuum system, the pressure is measured to be 1.00 X 10-10 torr (where 1 torr = 133 Pa). Assuming the molecular diameter is 3.00 % 10-10 m, the average molecular speed is 500 m/s, and the temperature is 300 K, find (a) The number of molecules in a volume of 1.00 m3, (b) The mean
In deep space the number density of particles can be one particle per cubic meter. Using the average temperature of 3.00 K and assuming the particle is H2 with a diameter of 0.200 nm, (a) Determine the mean free path of the particle and the average time between collisions. (b) What If? Repeat
Show that the mean free path for the molecules of an ideal gas is
In a tank full of oxygen, how many molecular diameters d (on average) does an oxygen molecule travel (at 1.00 atm and 20.0°C) before colliding with another O2 molecule? (The diameter of the O2 molecule is approximately 3.60 X 10-10 m.)
Argon gas at atmospheric pressure and 20.0°C is confined in a 1.00-m3 vessel. The effective hard-sphere diameter of the argon atom is 3.10 X 10-10 m. (a) Determine the mean free path . (b) Find the pressure when = 1.00 m. (c) Find the pressure when = 3.10 X 10-10 m
The dimensions of a room are 4.20 m X 3.00 m X 2.50 m. (a) Find the number of molecules of air in the room at atmospheric pressure and 20.0°C. (b) Find the mass of this air, assuming that the air consists of diatomic molecules with molar mass 28.9 g/mol. (c) Find the average kinetic energy of
The function Eint = 3.50nRT describes the internal energy of a certain ideal gas. A sample comprising 2.00 mol of the gas always starts at pressure 100 kPa and temperature 300 K. For each one of the following processes, determine the final pressure, volume, and temperature; the change in internal
Twenty particles, each of mass m and confined to a volume V, have various speeds: two have speed v; three have speed 2v; five have speed 3v; four have speed 4v; three have speed 5v; two have speed 6v ; one has speed 7v. Find (a) The average speed, (b) The rms speed, (c) The most probable
A cylinder containing n mol of an ideal gas undergoes an adiabatic process. (a) Starting with the expression W = - fPdV and using the condition PVy = constant, show that the work done on the gas is
As a 1.00-mol sample of a monatomic ideal gas expands adiabatically, the work done on it is - 2 500 J. The initial temperature and pressure of the gas are 500 K and 3.60 atm. Calculate (a) The final temperature and (b) The final pressure. You may use the result of Problem 53
A cylinder is closed at both ends and has insulating walls. It is divided into two compartments by a perfectly insulating partition that is perpendicular to the axis of the cylinder. Each compartment contains 1.00 mol of oxygen, which behaves as an ideal gas with y = 7/5. Initially the two
An air rifle shoots a lead pellet by allowing high-pressure air to expand, propelling the pellet down the rifle barrel. Because this process happens very quickly, no appreciable thermal conduction occurs, and the expansion is essentially adiabatic. Suppose that the rifle starts by admitting to the
Oxygen at pressures much greater than 1 atm is toxic to lung cells. Assume that a deep-sea diver breathes a mixture of oxygen (O2) and helium (He). By weight, what ratio of helium to oxygen must be used if the diver is at an ocean depth of 50.0 m?
A vessel contains 1.00 X 104 oxygen molecules at 500 K. (a) Make an accurate graph of the Maxwell–Boltzmann speed distribution function versus speed with points at speed intervals of 100 m/s. (b) Determine the most probable speed from this graph. (c) Calculate the average and rms speeds for
The compressibility / of a substance is defined as the fractional change in volume of that substance for a given change in pressure:
(a) Show that the speed of sound in an ideal gas is
Model air as a diatomic ideal gas with M # 28.9 g/mol, A cylinder with a piston contains 1.20 kg of air at 25.0°C and 200 kPa. Energy is transferred by heat into the system as it is allowed to expand, with the pressure rising to 400 kPa. Throughout the expansion, the relationship between pressure
Smokin’! A pitcher throws a 0.142-kg baseball at 47.2 m/s (Fig. P21.62). As it travels 19.4 m, the ball slows to a speed of 42.5 m/s because of air resistance. Find the change in temperature of the air through which it passes. To find the greatest possible temperature change, you may make the
For a Maxwellian gas, use a computer or programmable calculator to find the numerical value of the ratio Nv(v)/Nv(vmp) for the following values of v: v = (vmp/50), (vmp/10), (vmp/2), vmp, 2vmp, 10vmp, and 50vmp. Give your results to three significant figures.
Consider the particles in a gas centrifuge, a device used to separate particles of different mass by whirling them in a circular path of radius r at angular speed w. The force acting toward the center of the circular path on a given particle is mw2r. (a) Discuss how a gas centrifuge can be used
Verify Equations 21.27 and 21.28 for the rms and average speed of the molecules of a gas at a temperature T. Note that the average value of vn is
On the PV diagram for an ideal gas, one isothermal curve and one adiabatic curve pass through each point. Prove that the slope of the adiabat is steeper than the slope of the isotherm by the factor y.
A sample of monatomic ideal gas occupies 5.00 L at atmospheric pressure and 300 K (point A in Figure P21.67). It is heated at constant volume to 3.00 atm (point B). Then it is allowed to expand isothermally to 1.00 atm (point C) and at last compressed isobarically to its original state. (a) Find
This problem can help you to think about the size of molecules. In the city of Beijing a restaurant keeps a pot of chicken broth simmering continuously. Every morning it is topped up to contain 10.0 L of water, along with a fresh chicken, vegetables, and spices. The soup is thoroughly stirred. The
(a) If it has enough kinetic energy, a molecule at the surface of the Earth can “escape the Earth’s gravitation,” in the sense that it can continue to move away from the Earth forever, as discussed in Section 13.7. Using the principle of conservation of energy, show that the minimum kinetic
Using multiple laser beams, physicists have been able to cool and trap sodium atoms in a small region. In one experiment the temperature of the atoms was reduced to 0.240 mK. (a) Determine the rms speed of the sodium atoms at this temperature. The atoms can be trapped for about 1.00 s. The trap
Dalton’s law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of the partial pressures of gases making up the mixture. Give a convincing argument for this law based on the kinetic theory of gases.
One container is filled with helium gas and another with argon gas. If both containers are at the same temperature, which molecules have the higher rms speed? Explain.
A gas consists of a mixture of He and N2 molecules. Do the lighter He molecules travel faster than the N2 molecules? Explain.
Although the average speed of gas molecules in thermal equilibrium at some temperature is greater than zero, the average velocity is zero. Explain why this statement must be true.
When alcohol is rubbed on your body, it lowers your skin temperature. Explain this effect.
A liquid partially fills a container. Explain why the temperature of the liquid decreases if the container is then partially evacuated. (Using this technique, it is possible to freeze water at temperatures above 0°C.)
A vessel containing a fixed volume of gas is cooled. Does the mean free path of the molecules increase, decrease, or remain constant in the cooling process? What about the collision frequency?
A gas is compressed at a constant temperature. What happens to the mean free path of the molecules in this process?
If a helium-filled balloon initially at room temperature is placed in a freezer, will its volume increase, decrease, or remain the same?
Which is denser, dry air or air saturated with water vapor? Explain.
What happens to a helium-filled balloon released into the air? Will it expand or contract? Will it stop rising at some height?
Why does a diatomic gas have a greater energy content per mole than a monatomic gas at the same temperature?
An ideal gas is contained in a vessel at 300 K. If the temperature is increased to 900 K, by what factor does each one of the following change? (a) The average kinetic energy of the molecules. (b) The rms molecular speed. (c) The average momentum change of one molecule in a collision with a
A vessel is filled with gas at some equilibrium pressure and temperature. Can all gas molecules in the vessel have the same speed?
In our model of the kinetic theory of gases, molecules were viewed as hard spheres colliding elastically with the walls of the container. Is this model realistic?
In view of the fact that hot air rises, why does it generally become cooler as you climb a mountain? (Note that air has low thermal conductivity.)
Inspecting the magnitudes of CV and CP for the diatomic and polyatomic gases in Table 21.2, we find that the values increase with increasing molecular mass. Give a qualitative explanation of this observation.
A heat engine takes in 360 J of energy from a hot reservoir and performs 25.0 J of work in each cycle. Find (a) The efficiency of the engine and (b) The energy expelled to the cold reservoir in each cycle.
A heat engine performs 200 J of work in each cycle and has an efficiency of 30.0%. For each cycle, how much energy is: (a) Taken in and (b) Expelled by heat?
A particular heat engine has a useful power output of 5.00 kW and an efficiency of 25.0%. The engine expels 8 000 J of exhaust energy in each cycle. Find (a) The energy taken in during each cycle and (b) The time interval for each cycle.
Heat engine X takes in four times more energy by heat from the hot reservoir than heat engine Y. Engine X delivers two times more work, and it rejects seven times more energy by heat to the cold reservoir than heat engine Y. Find the efficiency of (a) Heat engine X and (b) Heat engine Y.
A multicylinder gasoline engine in an airplane, operating at 2 500 rev/min, takes in energy 7.89 X 103 J and exhausts 4.58 X 103 J for each revolution of the crankshaft. (a) How many liters of fuel does it consume in 1.00 h of operation if the heat of combustion is 4.03 X 107 J/L? (b) What is
Suppose a heat engine is connected to two energy reservoirs, one a pool of molten aluminum (660°C) and the other a block of solid mercury ("38.9°C). The engine runs by freezing 1.00 g of aluminum and melting 15.0 g of mercury during each cycle. The heat of fusion of aluminum is 3.97 X 105 J/kg;
A refrigerator has a coefficient of performance equal to 5.00. The refrigerator takes in 120 J of energy from a cold reservoir in each cycle. Find (a) The work required in each cycle and (b) The energy expelled to the hot reservoir.
A refrigerator has a coefficient of performance of 3.00. The ice tray compartment is at -20.0°C, and the room temperature is 22.0°C. The refrigerator can convert 30.0 g of water at 22.0°C to 30.0 g of ice at - 20.0°C each minute. What input power is required? Give your answer in watts
In 1993 the federal government instituted a requirement that all room air conditioners sold in the United States must have an energy efficiency ratio (EER) of 10 or higher. The EER is defined as the ratio of the cooling capacity of the air conditioner, measured in Btu/h, to its electrical power
A Carnot engine has a power output of 150 kW. The engine operates between two reservoirs at 20.0°C and 500°C. (a) How much energy does it take in per hour? (b) How much energy is lost per hour in its exhaust?

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Chemical Principles 7th edition Steven S. Zumdahl, Donald J. DeCoste - Solutions

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