One of the assumptions of the kinetic molecular theory is

According to Charless law, the volume of a gas is directly related to its temperature in Kelvin at constant pressure and number of moles. What if the volume of a gas was directly related to its temperature in Celsius at constant pressure and number of moles? What differences would you notice?

What if STP was defined as normal room temperature (22C) and 1 atm? How would this affect the molar volume of an ideal gas? Include an explanation and a number.

You have learned the postulates of the kinetic molecular theory. What if we could not assume the third postulate to be true? How would this affect the measured pressure of a gas?

You have learned that no gases behave perfectly ideally, but under conditions of high temperature and low pressure (high volume) gases behave more ideally. What if all gases always behaved perfectly ideally? How would the world be different?

Consider the following apparatus: a test tube covered with a nonpermeable elastic membrane inside a container that is closed with a cork. A syringe goes through the cork. Syringe Membrane Cork a. As you push down on the syringe, how does the membrane covering the test tube change? b. You stop pushing the syringe but continue to hold it down. In a few seconds, what happens to the membrane?

Figure 5.1 shows a picture of a barometer. Which of the following statements is the best explanation of how this barometer works? a. Air pressure outside the tube causes the mercury to move in the tube until the air pressure inside and outside the tube is equal. b. Air pressure inside the tube causes the mercury to move in the tube until the air pressure inside and outside the tube is equal. c. Air pressure outside the tube counterbalances the weight of the mercury in the tube. d. Capillary action of the mercury causes the mercury to go up the tube. e. The vacuum that is formed at the top of the tube holds up the mercury. Justify your choice. For choices that you did not pick, explain why they are incorrect. Pictures help!

The barometer in the following diagram shows the level of mercury at a given atmospheric pressure. Fill all the other barometers with mercury for that same atmospheric pressure. Explain your answer. Hg(l)

As you increase the temperature of a gas in a sealed, rigid container, what happens to the density of the gas? Would the results be the same if you did the same experiment in a container with a piston at constant pressure? Explain

A diagram in a chemistry book shows a magnified view of a flask of air as follows: What do you suppose is between the dots (the dots represent air molecules)? a. air c. pollutants e. nothing b. dust d. oxygen

If you put a drinking straw in water, place your finger over the opening, and lift the straw out of the water, some water stays in the straw. Explain.

A chemistry student relates the following story: I noticed my tires were a bit low and went to the gas station. As I was filling the tires, I thought about the kinetic molecular theory (KMT), and I realized that I was increasing both the pressure and volume of the tires as I filled the tires with air. Hmmm, I thought, that goes against what I learned in chemistry, where I was told pressure and volume are inversely proportional. What is the fault of the logic of the chemistry student in this situation? Explain why we think pressure and volume to be inversely related (draw pictures and use the KMT).

Chemicals X and Y (both gases) react to form the gas XY, but it takes a bit of time for the reaction to occur. Both X and Y are placed in a container with a piston (free to move), and you note the volume. As the reaction occurs, what happens to the volume of the container? Explain.

Which statement best explains why a hot-air balloon rises when the air in the balloon is heated? a. According to Charless law, the temperature of a gas is directly related to its volume. Thus the volume of the balloon increases, decreasing the density. b. Hot air rises inside the balloon, and this lifts the balloon. c. The temperature of a gas is directly related to its pressure. The pressure therefore increases, and this lifts the balloon. d. Some of the gas escapes from the bottom of the balloon, thus decreasing the mass of gas in the balloon. This decreases the density of the gas in the balloon, and this lifts the balloon. e. Temperature is related to the root mean square velocity of the gas molecules. Thus the molecules are moving faster, hitting the balloon more often, and thus lifting the balloon. Justify your choice. For those you did not choose, explain why they are incorrect.

Draw a highly magnified view of a sealed, rigid container filled with a gas. Then draw what it would look like if you cooled the gas significantly, but kept the temperature above the boiling point of the substance in the container. Also draw what it would look like if you heated the gas significantly. Finally, draw what each situation would look like if you evacuated enough of the gas to decrease the pressure by a factor of 2.

If you release a helium balloon, it soars upward and eventually pops. Explain.

If you have any two gases in different containers that are the same size at the same pressure and same temperature, what is true about the moles of each gas? Why is this true?

Explain the following seeming contradiction: You have two gases, A and B, in two separate containers of equal volume and at equal pressure and temperature. Therefore, you must have the same number of moles of each gas. Because the two temperatures are equal, the average kinetic energies of the two samples are equal. Therefore, since the energy of such a system corresponds to translational motion, the root mean square velocities of the two are equal, and thus the particles in each sample move, on average, with the same relative speed. Since A and B are different gases, each must have a different molar mass. If A has a higher molar mass than B, the particles of A must be hitting the sides of the container with more force. Thus the pressure in the container of gas A must be higher than that in the container with gas B. However, one of our initial assumptions was that the pressures were equal. Explain

Using postulates of the kinetic molecular theory, give a molecular interpretation of Boyles law, Charless law, and Daltons law of partial pressures

Rationalize the following observations. a. Aerosol cans will explode if heated. b. You can drink through a soda straw. c. A thin-walled can will collapse when the air inside is removed by a vacuum pump. d. Manufacturers produce different types of tennis balls for high and low elevations

Show how Boyles law and Charless law are special cases of the ideal gas law.

At the same conditions of pressure and temperature, ammonia gas is less dense than air. Why is this true?

For each of the quantities (af) listed below, explain which of the following properties (mass of the molecule, density of the gas sample, temperature of the gas sample, size of the molecule, and number of moles of gas) must be known to calculate the quantity. a. average kinetic energy b. average number of collisions per second with other gas molecules c. average force of each impact with the wall of the container d. root mean square velocity e. average number of collisions with a given area of the container f. distance between collisions

You have two containers each with 1 mole of xenon gas at 15C. Container A has a volume of 3.0 L, and container B has a volume of 1.0 L. Explain how the following quantities compare between the two containers. a. the average kinetic energy of the Xe atoms b. the force with which the Xe atoms collide with the container walls c. the root mean square velocity of the Xe atoms d. the collision frequency of the Xe atoms (with other atoms) e. the pressure of the Xe sample

You have a balloon covering the mouth of a flask filled with air at 1 atm. You apply heat to the bottom of the flask until the volume of the balloon is equal to that of the flask. a. Which has more air in itthe balloon or the flask? Or do both contain the same amount of air? Explain. b. In which is the pressure greaterthe balloon or the flask? Or is the pressure the same? Explain.

A sealed-tube manometer as shown below can be used to measure pressures below atmospheric pressure. The tube above the mercury is evacuated. When there is a vacuum in the flask, the mercury levels in both arms of the U-tube are equal. If a gaseous sample is introduced into the flask, the mercury levels are different. The difference h is a measure of the pressure of the gas inside the flask. If h is equal to 4.75 cm, calculate the pressure in the flask in torr, pascals, and atmospheres. Gas

A diagram for an open-tube manometer is shown below. Atmosphere If the flask is open to the atmosphere, the mercury levels are equal. For each of the following situations in which a gas is contained in the flask, calculate the pressure in the flask in torr, atmospheres, and pascals. Atmosphere (760. torr) Atmosphere (760. torr) Flask a. b. 118 mm Flask 215 mm c. Calculate the pressures in the flask in parts a and b (in torr) if the atmospheric pressure is 635 torr.

The gravitational force exerted by an object is given by F 5 mg where F is the force in newtons, m is the mass in kilograms, and g is the acceleration due to gravity, 9.81 m/s2. Calculate the force exerted per unit of area by a column of mercury (density 5 13.59 g/cm3) that is 76.0 cm high. How high would a column of water (density 5 1.00 g/cm3) have to be to exert the same force?

a. If the open-tube manometer in Exercise 22 contains a nonvolatile silicone oil (density 5 1.30 g/cm3) instead of mercury (density 5 13.6 g/cm3), what are the pressures in the flask as shown in parts a and b in torr, atmospheres, and pascals? b. What advantage would there be in using a less dense fluid than mercury in a manometer used to measure relatively small differences in pressure?

A gauge on a compressed gas cylinder reads 2200 psi (pounds per square inch; 1 atm 5 14.7 psi). Express this pressure in each of the following units. a. standard atmospheres b. megapascals (MPa) c. torr

Draw a qualitative graph to show how the first property varies with the second in each of the following (assume 1 mole of an ideal gas and T in kelvins). a. PV versus V with constant T b. P versus T with constant V c. T versus V with constant P d. P versus V with constant T e. P versus 1/V with constant T f. PV/T versus P

As weather balloons rise from the earths surface, the pressure of the atmosphere becomes less, tending to cause the volume of the balloons to expand. However, the temperature is much lower in the upper atmosphere than at sea level. Would this temperature effect tend to make such a balloon expand or contract? Weather balloons do, in fact, expand as they rise. What does this tell you?

Consider the flasks in the following diagrams. Volume  2X Volume  X Volume  X Volume  X Assuming the connecting tube has negligible volume, draw what each diagram will look like after the stopcock between the two flasks is opened. Also, solve for the final pressure in each case, in terms of the original pressure. Assume temperature is constant.

Consider the flask diagramed below. What are the final partial pressures of H2 and N2 after the stopcock between the two flasks is opened? (Assume the final volume is 3.00 L.) What is the total pressure (in torr)? 2.00 L H2 475 torr 1.00 L N2 0.200 atm

Consider the flask apparatus in Exercise 29, which contains 2.00 L of H2 at a pressure of 360. torr and 1.00 L of N2 at an unknown pressure. If the total pressure in the flasks is 320. torr after the stopcock is opened, determine the initial pressure of N2 in the 1.00-L flask.

A mixture of 1.00 g H2 and 1.00 g He is placed in a 1.00-L container at 278C. Calculate the partial pressure of each gas and the total pressure.

A 2.50-L container is filled with 175 g argon. a. If the pressure is 10.0 atm, what is the temperature? b. If the temperature is 225 K, what is the pressure?

A compressed-gas cylinder contains 1.00 3 103 g of argon gas. The pressure inside the cylinder is 2050. psi (pounds per square inch) at a temperature of 188C. How much gas remains in the cylinder if the pressure is decreased to 650. psi at a temperature of 268C?

A sealed balloon is filled with 1.00 L of helium at 238C and 1.00 atm. The balloon rises to a point in the atmosphere where the pressure is 220. torr and the temperature is 2318C. What is the change in the volume of the balloon as it ascends from 1.00 atm to a pressure of 220. torr?

A piece of solid carbon dioxide, with a mass of 22.0 g, is placed in an otherwise empty 4.00-L container at 278C. What is the pressure in the container after all the carbon dioxide vaporizes? If 22.0 g of solid carbon dioxide was placed in a similar container already containing air at 740. torr, what would be the partial pressure of carbon dioxide and the total pressure in the container after the carbon dioxide had vaporized?

An ideal gas is in a cylinder with a volume of 5.0 3 102 mL at a temperature of 30.8C and a pressure of 710 torr. The gas is compressed to a volume of 25 mL, and the temperature is raised to 8208C. What is the new pressure?

Suppose two 200.0-L tanks are to be filled separately with the gases helium and hydrogen. What mass of each gas is needed to produce a pressure of 2.70 atm in its respective tank at 248C?

An ideal gas at 78C is in a spherical flexible container having a radius of 1.00 cm. The gas is heated at constant pressure to 888C. Determine the radius of the spherical container after the gas is heated. (Volume of a sphere 5 4y3pr3.)

A flask that can withstand an internal pressure of 2500 torr, but no more, is filled with a gas at 21.08C and 758 torr and heated. At what temperature will it burst?

A gas sample containing 1.50 moles at 258C exerts a pressure of 400. torr. Some gas is added to the same container, and the temperature is increased to 50.8C. If the pressure increases to 800. torr, how many moles of gas were added to the container? Assume a constantvolume container.

Consider the following chemical equation: 2NO2(g) 88n N2O4(g) If 25.0 mL of NO2 gas is completely converted to N2O4 gas under the same conditions, what volume will the N2O4 occupy?

A bicycle tire is filled with air to a pressure of 75 psi at a temperature of 198C. Riding the bike on asphalt on a hot day increases the temperature of the tire to 588C. The volume of the tire increases by 4.0%. What is the new pressure in the bicycle tire?

A hot-air balloon is filled with air to a volume of 4.00 3 103 m3 at 745 torr and 218C. The air in the balloon is then heated to 628C, causing the balloon to expand to a volume of 4.20 3 103 m3. What is the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon? (Hint: Openings in the balloon allow air to flow in and out. Thus the pressure in the balloon is always the same as that of the atmosphere.)

Determine the partial pressure of each gas as shown in the figure below. Note: The relative numbers of each type of gas are depicted in the figure. He 1.00 atm Ne Ar 45. Consider the flasks in the following diagrams. Volume = X Volume = X Ne He a. Which is greater, the initial pressure of helium or initial pressure of neon? How much greater? b. Assuming the connecting tube has negligible volume, draw what each diagram will look like after the stopcock between the two flasks is opened. c. Solve for the final pressure in terms of the original pressures of helium and neon. Assume temperature is constant. d. Solve for the final partial pressures of helium and neon in terms of their original pressures. Assume the temperature is constant.

A sample of nitrogen gas was collected over water at 20.8C and a total pressure of 1.00 atm. A total volume of 2.50 3 102 mL was collected. What mass of nitrogen was collected? (At 20.8C the vapor pressure of water is 17.5 torr.)

Helium is collected over water at 258C and 1.00 atm total pressure. What total volume of gas must be collected to obtain 0.586 g of helium? (At 258C the vapor pressure of water is 23.8 torr.)

A 2.00-L sample of O2(g) was collected over water at a total pressure of 785 torr and 258C. When the O2(g) was dried (water vapor removed), the gas had a volume of 1.94 L at 258C and 785 torr. Calculate the vapor pressure of water at 258C.

In a mixture of the two gases, the partial pressures of CH4(g) and O2(g) are 0.175 atm and 0.250 atm, respectively. a. What is the mole fraction of each gas in the mixture? b. If the mixture occupies a volume of 10.5 L at 658C, calculate the total number of moles of gas in the mixture. c. Calculate the number of grams of each gas in the mixture.

A 1.00-L gas sample at 100.8C and 600. torr contains 50.0% helium and 50.0% xenon by mass. What are the partial pressures of the individual gases?

A tank contains a mixture of 52.5 g oxygen gas and 65.1 g carbon dioxide gas at 27C. The total pressure in the tank is 9.21 atm. Calculate the partial pressures of each gas in the container.

Given that a sample of air is made up of nitrogen, oxygen, and argon in the mole fractions 78% N2, 21% O2, and 1.0% Ar, what is the density of air at standard temperature and pressure?

Consider two different containers, each filled with 2 moles of Ne(g). One of the containers is rigid and has constant volume. The other container is flexible (like a balloon) and is capable of changing its volume to keep the external pressure and internal pressure equal to each other. If you raise the temperature in both containers, what happens to the pressure and density of the gas inside each container? Assume a constant external pressure.

An unknown diatomic gas has a density of 3.164 g/L at STP. What is the identity of the gas?

A compound contains only nitrogen and hydrogen and is 87.4% nitrogen by mass. A gaseous sample of the compound has a density of 0.977 g/L at 710. torr and 100.8C. What is the molecular formula of the compound?

A compound has the empirical formula CHCl. A 256- mL flask, at 373 K and 750. torr, contains 0.800 g of the gaseous compound. Give the molecular formula.

One of the chemical controversies of the nineteenth century concerned the element beryllium (Be). Berzelius originally claimed that beryllium was a trivalent element (forming Be31 ions) and that it formed an oxide with the formula Be2O3. This assumption resulted in a calculated atomic mass of 13.5 for beryllium. In formulating his periodic table, Mendeleev proposed that beryllium was divalent (forming Be21 ions) and that it gave an oxide with the formula BeO. This assumption gives an atomic mass of 9.0. In 1894 A. Combes (Comptes Rendes, 1894, p. 1221) reacted beryllium with the anion C5H7O2 2 and measured the density of the gaseous product. Combess data for two different experiments are as follows: I II Mass 0.2022 g 0.2224 g Volume 22.6 cm3 26.0 cm3 Temperature 138C 178C Pressure 765.2 torr 764.6 torr If beryllium is a divalent metal, the molecular formula of the product will be Be(C5H7O2)2; if it is trivalent, the formula will be Be(C5H7O2)3. Show how Combess data help to confirm that beryllium is a divalent metal.

Discrepancies in the experimental values of the molar mass of nitrogen provided some of the first evidence for the existence of the noble gases. If pure nitrogen is collected from the decomposition of ammonium nitrite, NH4NO2(s) 8888n N2(g) 1 2H2O(g) its measured molar mass is 28.01. If O2, CO2, and H2O are removed from air, the remaining gas has an average molar mass of 28.15. Assuming this discrepancy is solely a result of contamination with argon (atomic mass 5 39.95), calculate the ratio of moles of Ar to moles of N2 in air.

A sample of methane (CH4) gas contains a small amount of helium. Calculate the volume percentage of helium if the density of the sample is 0.70902 g/L at 0.08C and 1.000 atm.

Metallic molybdenum can be produced from the mineral molybdenite (MoS2). The mineral is first oxidized in air to molybdenum trioxide and sulfur dioxide. Molybdenum trioxide is then reduced to metallic molybdenum using hydrogen gas. The balanced equations are MoS2(s) 1 7 2O2(g) 88n MoO3(s) 1 2SO2(g) MoO3(s) 1 3H2(g) 88n Mo(s) 1 3H2O(l) Calculate the volumes of air and hydrogen gas at 178C and 1.00 atm that are necessary to produce 1.00 3 103 kg of pure molybdenum from MoS2. Assume air contains 21% oxygen by volume and assume 100% yield for each reaction.

In 1897 the Swedish explorer Andre tried to reach the North Pole in a balloon. The balloon was filled with hydrogen gas. The hydrogen gas was prepared from iron splints and diluted sulfuric acid. The reaction is Fe(s) 1 H2SO4(aq) 88n FeSO4(aq) 1 H2(g) The volume of the balloon was 4800 m3, and the loss of hydrogen gas during filling was estimated at 20.%. What mass of iron splints and 98% (by mass) H2SO4 were needed to ensure the complete filling of the balloon? Assume a temperature at 08C, a pressure of 1.0 atm during filling, and 100% yield.

Urea (H2NCONH2) is used extensively as a nitrogen source in fertilizers. It is produced commercially from the reaction of ammonia and carbon dioxide: 2NH3(g) 1 CO2(g) 88888n H2NCONH2(s) 1 H2O(g) Ammonia gas at 2238C and 90. atm flows into a reactor at a rate of 500. L/min. Carbon dioxide at 2238C and 45 atm flows into the reactor at a rate of 600. L/min. What mass of urea is produced per minute by this reaction assuming 100% yield?

Methanol (CH3OH) can be produced by the following reaction: CO(g) 1 2H2(g) 88n CH3OH(g) Hydrogen at STP flows into a reactor at a rate of 16.0 L/min. Carbon monoxide at STP flows into the reactor at a rate of 25.0 L/min. If 5.30 g of methanol is produced per minute, what is the percent yield of the reaction?

Consider the reaction between 50.0 mL of liquid methanol (CH3OH; density 5 0.850 g/mL) and 22.8 L of O2 at 278C and a pressure of 2.00 atm. The products of the reaction are CO2(g) and H2O(g). Calculate the number of moles of H2O formed if the reaction goes to completion.

Some very effective rocket fuels are composed of lightweight liquids. The fuel composed of dimethylhydrazine [(CH3)2N2H2] mixed with dinitrogen tetroxide was used to power the lunar lander in its missions to the moon. The two components react according to the following equation: (CH3)2N2H2(l) 1 2N4O4(l) 88n 3N2(g) 1 4H2O(g) 1 2CO2(g) If 150 g of dimethylhydrazine reacts with excess dinitrogen tetroxide and the product gases are collected at 278C in an evacuated 250-L tank, what is the partial pressure of nitrogen gas produced and what is the total pressure in the tank assuming the reaction has 100% yield?

Air bags are activated when a severe impact causes a steel ball to compress a spring and electrically ignite a detonator cap. This action causes sodium azide (NaN3) to decompose explosively according to the following reaction: 2NaN3(s) 88n 2Na(s) 1 3N2(g) What mass of NaN3(s) must be reacted to inflate an air bag to 70.0 L at STP?

Equal moles of sulfur dioxide gas and oxygen gas are mixed in a flexible reaction vessel and then sparked to initiate the formation of gaseous sulfur trioxide. Assuming that the reaction goes to completion, what is the ratio of the final volume of the gas mixture to the initial volume of the gas mixture if both volumes are measured at the same temperature and pressure?

Silane (SiH4) is the silicon analogue of methane (CH4). It is prepared industrially according to the following equations: Si(s) 1 3HCl(g) 88n HSiCl3(l) 1 H2(g) 4HSiCl3(l) 88n SiH4(g) 1 3SiCl4(l) a. If 156 mL of HSiCl3 (d 5 1.34 g/mL) is isolated when 15.0 L of HCl at 10.0 atm and 358C is used, what is the percent yield of HSiCl3? b. When 156 mL of HSiCl3 is heated, what volume of SiH4 at 10.0 atm and 358C will be obtained if the percent yield of the reaction is 93.1%?

At elevated temperatures, sodium chlorate decomposes to produce sodium chloride and oxygen gas. A 0.8765-g sample of impure sodium chlorate was heated until the production of oxygen gas ceased. The oxygen gas collected over water occupied 57.2 mL at a temperature of 228C and a pressure of 734 torr. Calculate the mass percent of NaClO3 in the original sample. (At 228C the vapor pressure of water is 19.8 torr.)

Xenon and fluorine will react to form binary compounds when a mixture of these two gases is heated to 4008C in a nickel reaction vessel. A 100.0-mL nickel container is filled with xenon and fluorine giving partial pressures of 1.24 atm and 10.10 atm, respectively, at a temperature of 258C. The reaction vessel is heated to 4008C to cause a reaction to occur and then cooled to a temperature at which F2 is a gas and the xenon fluoride is a nonvolatile solid. The remaining F2 gas is transferred to another 100.0-mL nickel container where the pressure of F2 at 258C is 7.62 atm. Assuming all of the xenon has reacted, what is the formula of the product?

The nitrogen content of organic compounds can be determined by the Dumas method. The compound in question is first reacted by passage over hot CuO(s): Compound 88888n N2(g) 1 CO2(g) 1 H2O(g) The gaseous products are then passed through a concentrated solution of KOH to remove the CO2. After passage through the KOH solution, the gas contains N2 and is saturated with water vapor. In a given experiment, a 0.253-g sample of a compound produced 31.8 mL of N2 saturated with water vapor at 258C and 726 torr. What is the mass percent of nitrogen in the compound? (The vapor pressure of water at 258C is 23.8 torr.)

An organic compound contains C, H, N, and O. Combustion of 0.1023 g of the compound in excess oxygen yielded 0.2766 g of CO2 and 0.0991 g of H2O. A sample of 0.4831 g of the compound was analyzed for nitrogen by the Dumas method (see Exercise 71). At STP, 27.6 mL of dry N2 was obtained. In a third experiment, the density of the compound as a gas was found to be 4.02 g/L at 1278C and 256 torr. What are the empirical formula and the molecular formula of the compound?

Nitric acid is produced commercially by the Ostwald process. In the first step, ammonia is oxidized to nitric oxide: 4NH3(g) 1 5O2(g) 88n 4NO(g) 1 6H2O(g) Assume this reaction is carried out in the apparatus diagramed below. 2.00 L NH3 0.500 atm 1.00 L O2 1.50 atm The stopcock between the two reaction containers is opened, and the reaction proceeds using proper catalysts. Calculate the partial pressure of NO after the reaction is complete. Assume 100% yield for the reaction, assume the final container volume is 3.00 L, and assume the temperature is constant.

Consider the following balanced equation in which gas X forms gas X2: 2X(g) 88n X2(g) Equal moles of X are placed in two separate containers. One container is rigid, so the volume cannot change; the other container is flexible, so the volume changes to keep the internal pressure equal to the external pressure. The above reaction is run in each container. What happens to the pressure and density of the gas inside each container as reactants are converted to products?

As NH3(g) is decomposed into nitrogen gas and hydrogen gas at constant pressure and temperature, the volume of the product gases collected is twice the volume of NH3 reacted. Explain. As NH3(g) is decomposed into nitrogen gas and hydrogen gas at constant volume and temperature, the total pressure increases by some factor. Why does the increase in pressure occur, and by what factor does the total pressure increase when reactants are completely converted into products? How do the partial pressures of the product gases compare to each other and to the initial pressure of NH3?

Use the postulates of the kinetic molecular theory (KMT) to explain why Boyles law, Charless law, Avogadros law, and Daltons law of partial pressures hold true for ideal gases. Use the KMT to explain the P versus n (at constant V and T) relationship and the P versus T (at constant V and n) relationship.

You have a gas in a container fitted with a piston and you change one of the conditions of the gas such that a change takes place, as shown below: 1.00 atm State two distinct changes you can make to accomplish this, and explain why each would work.

You have a gas in a container fitted with a piston and you change one of the conditions of the gas such that a change takes place, as shown below: Volume  X Volume  2X State three distinct changes you can make to accomplish this, and explain why each would work.

Consider two gases, A and B, each in a 1.0-L container with both gases at the same temperature and pressure. The mass of gas A in the container is 0.34 g, and the mass of gas B in the container is 0.48 g. A 0.34 g B 0.48 g a. Which gas sample has the most molecules present? Explain. b. Which gas sample has the largest average kinetic energy? Explain. c. Which gas sample has the fastest average velocity? Explain. d. How can the pressure in the two containers be equal to each other since the larger gas B molecules collide with the container walls more forcefully?

Consider the following samples of gases at the same temperature. i ii iii iv Ne Ar v vi vii viii Arrange each of these samples in order from lowest to highest:a. pressure b. average kinetic energy c. density d. root mean square velocity Note: Some samples of gases may have equal values for these attributes. Assume the larger containers have a volume twice the volume of the smaller containers and assume the mass of an argon atom is twice the mass of a neon atom

Calculate the average kinetic energies of the CH4 and N2 molecules at 273 K and 546 K.

Calculate the root mean square velocities of CH4 and N2 molecules at 273 K and 546 K.

Do all the molecules in a 1-mole sample of CH4(g) have the same kinetic energy at 273 K? Do all the molecules in a 1-mole sample of N2(g) have the same velocity at 546 K? Explain.

Consider separate 1.0-L gaseous samples of H2, Xe, Cl2, and O2, all at STP. a. Rank the gases in order of increasing average kinetic energy. b. Rank the gases in order of increasing average velocity. c. How can separate 1.0-L samples of O2 and H2 both have the same average velocity?

Consider three identical flasks filled with different gases. Flask A: CO at 760 torr and 08C Flask B: N2 at 250 torr and 08C Flask C: H2 at 100 torr and 08C a. In which flask will the molecules have the greatest average kinetic energy? b. In which flask will the molecules have the greatest root mean square velocity? c. Which flask will have the greatest number of collisions per second with the walls of the container?

Consider a 1.0-L container of neon gas at STP. Will the average kinetic energy, root mean square velocity, frequency of collisions of gas molecules with each other, frequency of collisions of gas molecules with the walls of the container, and energy of impact of gas molecules with the container increase, decrease, or remain the same under each of the following conditions? a. The temperature is increased to 1008C. b. The temperature is decreased to 2508C. c. The volume is decreased to 0.5 L. d. The number of moles of neon is doubled.

Freon-12 is used as a refrigerant in central home air conditioners. The rate of effusion of Freon-12 to Freon-11 (molar mass 5 137.4 g/mol) is 1.07:1. The formula of Freon-12 is one of the following: CF4, CF3Cl, CF2Cl2, CFCl3, or CCl4. Which formula is correct for Freon-12?

One way of separating oxygen isotopes is by gaseous diffusion of carbon monoxide. The gaseous diffusion process behaves like an effusion process. Calculate the relative rates of effusion of 12C16O, 12C17O, and 12C18O. List some advantages and disadvantages of separating oxygen isotopes by gaseous diffusion of carbon dioxide instead of carbon monoxide.

A compound contains only C, H, and N. It is 58.51% C and 7.37% H by mass. Helium effuses through a porous frit 3.20 times as fast as the compound does. Determine the empirical and molecular formulas of this compound.

It took 4.5 minutes for 1.0 L of helium to effuse through a porous barrier. How long will it take for 1.0 L of Cl2 gas to effuse under identical conditions?

Calculate the pressure exerted by 0.5000 mole of N2 in a 1.0000-L container at 25.08C. (See Table 5.3.) a. Use the ideal gas law. b. Use the van der Waals equation. c. Compare the results from parts a and b

Calculate the pressure exerted by 0.5000 mole of N2 in a 10.000-L container at 25.08C. (See Table 5.3.) a. Use the ideal gas law. b. Use the van der Waals equation. c. Compare the results from parts a and b. d. Compare the results with those in Exercise 91.

Why do real gases not always behave ideally? Under what conditions does a real gas behave most ideally? Why?

Why do real gases not always behave ideally? Under what conditions does a real gas behave most ideally? Why?

In the van der Waals equation, why is a term added to the observed pressure and why is a term subtracted from the container volume to correct for nonideal gas behavior?

Without looking at tables of values, which of the following gases would you expect to have the largest value of the van der Waals constant b: H2, N2, CH4, C2H6, or C3H8?

From the values in Table 5.3 for the van der Waals constant a for the gases H2, CO2, N2, and CH4, predict which molecule shows the strongest intermolecular attractions.

The MaxwellBoltzmann distribution function f(u) increases at small values of u and decreases at large values of u. Identify the parts of the function responsible for this behavior.

Calculate the root mean square, the most probable, and the average velocities for N2(g) at 2278C.

Calculate the kinetic energy possessed by 1.00 3 1020 molecules of methane gas (CH4) at T 5 278C, assuming ideal behavior

A flask contains 1 3 mole of H2 and 2 3 mole of He. Compare the force on the wall per impact of H2 relative to that for He

A certain sample of uranium is reacted with fluorine to form a mixture of 235UF6(g) and 238UF6(g). After 100 diffusion steps, the gas contains 1526 235UF6 molecules per 1.000 3 105 total number of molecules in the gas (235UF6 1 238UF6). What is the ratio of 235U to 238U atoms in the original sample of uranium?

Consider separate 1.0-L samples of O2(g) and He(g), both at 258C and the same pressure. Compare the change in momentum per impact and the number of impacts per second in the two samples

Consider separate 1.00-L samples of Ar(g), both containing the same number of moles, one at 278C and the other at 778C. Compare the change in momentum per impact and the number of impacts per second in the two samples.

Calculate the intermolecular collision frequency and the mean free path in a sample of helium gas with a volume of 5.0 L at 278C and 3.0 atm. Assume that the diameter of a helium atom is 50. pm.

Use the data in Table 5.4 to calculate the partial pressure of He in dry air assuming that the total pressure is 1.0 atm. Assuming a temperature of 258C, calculate the number of He atoms per cubic centimeter.

Atmospheric scientists often use mixing ratios to express the concentrations of trace compounds in air. Mixing ratios are often expressed as ppmv (parts per million volume): ppmv of X 5 vol of X at STP total vol of air at STP 3 106 On a certain November day, the concentration of carbon monoxide in the air in downtown Denver, Colorado, reached 3.0 3 102 ppmv. The atmospheric pressure at that time was 628 torr and the temperature was 08C. a. What was the partial pressure of CO? b. What was the concentration of CO in molecules per cubic meter? c. What was the concentration of CO in molecules per cubic centimeter?

Formaldehyde (CH2O) is sometimes released from foamed insulation used in homes. The federal standard for the allowable amount of CH2O in air is 1.0 ppbv (parts per billion volume; similar to ppmv as defined in Exercise 107). How many molecules per cubic centimeter is 1.0 ppbv at STP? If the concentration of formaldehyde in a room is 1.0 ppbv, what total mass of formaldehyde is present at STP if the room measures 18.0 ft 3 24.0 ft 3 8.0 ft?

A 1.0-L sample of air is collected at 258C at sea level (1.00 atm). Estimate the volume this sample of air would have at an altitude of 15 km (see Fig. 5.27). At 15 km, the pressure is about 0.1 atm.

Write reactions to show how nitric and sulfuric acids are produced in the atmosphere. Write reactions to show how the nitric and sulfuric acids in acid rain react with marble and limestone. (Both marble and limestone are primarily calcium carbonate.)

Trace organic compounds in the atmosphere are first concentrated and then measured by gas chromatography. In the concentration step, several liters of air are pumped through a tube containing a porous substance that traps organic compounds. The tube is then connected to a gas chromatograph and heated to release the trapped compounds. The organic compounds are separated in the column and the amounts are measured. In an analysis for benzene and toluene in air, a 3.00-L sample of air at 748 torr and 238C was passed through the trap. The gas chromatography analysis showed that this air sample contained 89.6 ng of benzene (C6H6) and 153 ng of toluene (C7H8). Calculate the mixing ratio (see Exercise 107) and number of molecules per cubic centimeter for both benzene and toluene.

A form of Boyles law is PV 5 k (at constant T and n). Table 5.1 contains actual data from pressurevolume experiments conducted by Robert Boyle. The value of k in most experiments is 14.1 3 102 in Hg in3. Express k in units of atm L. In Example 5.1, k was determined for NH3 at various pressures and volumes. Give some reasons why the k values differ so dramatically between Example 5.1 and Table 5.1.

Consider two separate gas containers at the following conditions: Container A Container B Contents: SO2(g) Contents: unknown gas Pressure 5 PA Pressure 5 PB Moles of gas 5 1.0 mol Moles of gas 5 2.0 mol Volume 5 1.0 L Volume 5 2.0 L Temperature 5 78C Temperature 5 2878C How is the pressure in container B related to the pressure in container A?

Which of the following statements is(are) true? For the false statements, correct them. a. At constant temperature, the lighter the gas molecules, the faster the average velocity of the gas molecules. b. At constant temperature, the heavier the gas molecules, the larger the average kinetic energy of the gas molecules. c. A real gas behaves most ideally when the container volume is relatively large and the gas molecules are moving relatively quickly d. As temperature increases, the effect of interparticle interactions on gas behavior is increased. e. At constant V and T, as gas molecules are added into a container, the number of collisions per unit area increases, resulting in a higher pressure. f. The kinetic molecular theory predicts that pressure is inversely proportional to temperature at constant volume and moles of gas.

A person accidentally swallows a drop of liquid oxygen, O2(l), which has a density of 1.149 g/mL. Assuming the drop has a volume of 0.050 mL, what volume of gas will be produced in the persons stomach at body temperature (378C) and a pressure of 1.0 atm?

Hydrogen azide, HN3, decomposes on heating by the following unbalanced reaction: HN3(g) 88n N2(g) 1 H2(g) If 3.0 atm of pure HN3(g) is decomposed initially, what is the final total pressure in the reaction container? What are the partial pressures of nitrogen and hydrogen gas? Assume the volume and temperature of the reaction container are constant

A 20.0 L stainless steel container at 258C was charged with 2.00 atm of hydrogen gas and 3.00 atm of oxygen gas. A spark ignited the mixture, producing water. What is the pressure in the tank at 258C? If the same experiment were performed, but the temperature was 1258C instead of 258C, what would be the pressure in the tank?

In the Mthode Champenoise, grape juice is fermented in a wine bottle to produce sparkling wine. The reaction is C6H12O6(aq) 88n 2C2H5OH(aq) 1 2CO2(g) Fermentation of 750. mL of grape juice (density 5 1.0 g/cm3) is allowed to take place in a bottle with a total volume of 825 mL until 12% by volume is ethanol (C2H5OH). Assuming that the CO2 is insoluble in H2O (actually a wrong assumption), what would be the pressure of CO2 inside the wine bottle at 258C? (The density of ethanol is 0.79 g/cm3.)

A 2.747-g sample of manganese metal is reacted with excess HCl gas to produce 3.22 L of H2(g) at 373 K and 0.951 atm and a manganese chloride compound (MnClx). What is the formula of the manganese chloride compound produced in the reaction?

The total mass that can be lifted by a balloon is given by the difference between the mass of air displaced by the balloon and the mass of the gas inside the balloon. Consider a hot-air balloon that approximates a sphere 5.00 m in diameter and contains air heated to 658C. The surrounding air temperature is 218C. The pressure in the balloon is equal to the atmospheric pressure, which is 745 torr. a. What total mass can the balloon lift? Assume the average molar mass of air is 29.0 g/mol. (Hint: Heated air is less dense than cool air.) b. If the balloon is filled with enough helium at 218C and 745 torr to achieve the same volume as in part a, what total mass can the balloon lift? c. What mass could the hot-air balloon (from part a) lift if it were on the ground in Denver, Colorado, where a typical atmospheric pressure is 630. torr? d. What mass could the hot-air balloon (from part a) lift if it were a cold day with a temperature of 288C?

At STP, 1.0 L Br2 reacts completely with 3.0 L F2, producing 2.0 L of a product. What is the formula of the product? (All substances are gases.)

Natural gas is a mixture of hydrocarbons, primarily methane (CH4) and ethane (C2H6). A typical mixture might have xmethane 5 0.915 and xethane 5 0.085. What are the partial pressures of the two gases in a 15.00-L container of natural gas at 20.8C and 1.44 atm? Assuming complete combustion of both gases in the natural gas sample, what is the total mass of water formed?

An important process for the production of acrylonitrile (C3H3N) (annual U.S. production is greater than 109 lb) is given by the following equation: 2C3H6(g) 1 2NH3(g) 1 3O2(g) 88n 2C3H3N(g) 1 6H2O(g) A 150.-L reactor is charged to the following partial pressures at 258C: PC3H6 5 0.500 MPa PNH3 5 0.800 MPa PO2 5 1.500 MPa What mass of acrylonitrile can be produced from this mixture (MPa 5 106 Pa)?

The oxides of Group 2A metals (symbolized by M here) react with carbon dioxide according to the following reaction: MO(s) 1 CO2(g) 88n MCO3(s) A 2.85-g sample containing only MgO and CuO is placed in a 3.00-L container. The container is filled with CO2 to a pressure of 740. torr at 20.8C. After the reaction has gone to completion, the pressure inside the flask is 390. torr at 20.8C. What is the mass percent of MgO in the mixture? Assume that only the MgO reacts with CO2.

Small quantities of hydrogen gas can be prepared in the laboratory by the addition of aqueous hydrochloric acid to metallic zinc. Zn(s) 1 2HCl(aq) 88n ZnCl2(aq) 1 H2(g) Typically, the hydrogen gas is bubbled through water for collection and becomes saturated with water vapor. Suppose 240. mL of hydrogen gas is collected at 30.8C and has a total pressure of 1.032 atm by this process. What is the partial pressure of hydrogen gas in the sample? How many grams of zinc must have reacted to produce this quantity of hydrogen? (The vapor pressure of water is 32 torr at 308C.)

Nitrogen gas (N2) reacts with hydrogen gas (H2) to form ammonia gas (NH3). You have nitrogen and hydrogen gases in a 15.0-L container fitted with a movable piston (the piston allows the container volume to change so as to keep the pressure constant inside the container). Initially, the partial pressure of each reactant gas is 1.00 atm. Assume the temperature is constant and the reaction goes to completion. a. Calculate the partial pressure of ammonia in the container after the reaction has reached completion. b. Calculate the volume of the container after the reaction has reached completion.

Consider the three flasks in the diagram below. Assuming the connecting tubes have negligible volume, what is the partial pressure of each gas and the total pressure after all the stopcocks are opened? He 1.00 L 200. torr Ne Ar 1.00 L 0.400 atm 2.00 L 24.0 kPa

We state that the ideal gas law tends to hold best at low pressures and high temperatures. Show how the van der Waals equation simplifies to the ideal gas law under these conditions.

Boyles law can be represented graphically in several ways. Which of the following plots does not correctly represent Boyles law (assuming constant T and n)? Explain. P PV V P 1/P V 1/V

A compound containing only C, H, and N yields the following data. i. Complete combustion of 35.0 mg of the compound produced 33.5 mg of CO2 and 41.1 mg of H2O. ii. A 65.2-mg sample of the compound was analyzed for nitrogen by the Dumas method (see Exercise 71), giving 35.6 mL of dry N2 at 740. torr and 258C. iii. The effusion rate of the compound as a gas was measured and found to be 24.6 mL/min. The effusion rate of argon gas, under identical conditions, is 26.4 mL/min. What is the formula of the compound?

A 15.0-L tank is filled with H2 to a pressure of 2.00 3 102 atm. How many balloons (each 2.00 L) can be inflated to a pressure of 1.00 atm from the tank? Assume that there is no temperature change and that the tank cannot be emptied below 1.00 atm pressure.

Consider the following diagram. B A H2 A porous container (A), filled with air at STP, is contained in a large enclosed container (B), which is flushed with H2(g). What will happen to the pressure inside container A? Explain your answer

A 100.-L flask contains a mixture of methane (CH4) and argon at 258C. The mass of argon present is 228 g and the mole fraction of methane in the mixture is 0.650. Calculate the total kinetic energy of the gaseous mixture.

Represent the following plots. a. PV/n (y axis) versus P (x axis) for a real gas that obeys the equation PV/n 5 a 1 bP b. change in momentum per impact versus mass of an individual gas particle for a series of ideal gases all at the same temperature c. P versus T (8C) for an ideal gas where n and V are constant

A spherical glass container of unknown volume contains helium gas at 258C and 1.960 atm. When a portion of the helium is withdrawn and adjusted to 1.00 atm at 258C, it is found to have a volume of 1.75 cm3. The gas remaining in the first container shows a pressure of 1.710 atm. Calculate the volume of the spherical container

A compound Z is known to have a composition of 34.38% Ni, 28.13% C, and 37.48% O. In an experiment 1.00 L of gaseous Z is mixed with 1.00 L of argon, where each gas is at P 5 2.00 atm and T 5 258C. When this mixture of gases is put in an effusion chamber, the ratio of Z molecules to Ar molecules in the effused mixture is 0.4837. Using these data, calculate the following. a. the empirical formula for Z b. the molar mass for Z c. the molecular formula for Z d. the mole ratio of Z to argon in a sample of gas obtained by five effusion steps (starting with the original mixture)

Hydrogen cyanide gas is commercially prepared by the reaction of methane [CH4(g)], ammonia [NH3(g)], and oxygen [O2(g)] at a high temperature. The other product is gaseous water. a. Write a balanced chemical equation for the reaction. b. Methane and ammonia gases flow into a reactor at a rate of 20.0 L/s. Oxygen gas is introduced at a flow rate of 40.0 L/s. All the reactant gases are at 1.00 atm and 150.8C. What mass of HCN is produced per second by this reaction assuming 100% yield?

A glass vessel contains 28 g of nitrogen gas. Assuming ideal behavior, which of the processes listed below would double the pressure exerted on the walls of the vessel? a. Adding 28 g of oxygen gas b. Raising the temperature of the container from 2738C to 1278C c. Adding enough mercury to fill one-half the container d. Adding 32 g of oxygen gas e. Raising the temperature of the container from 30.8C to 60.8C

A steel cylinder contains 150.0 moles of argon gas at a temperature of 258C and a pressure of 8.93 MPa. After some argon has been used, the pressure is 2.00 MPa at a temperature of 198C. What mass of argon remains in the cylinder?

A certain flexible weather balloon contains helium gas at a volume of 855 L. Initially, the balloon is at sea level where the temperature is 258C and the barometric pressure is 730. torr. The balloon then rises to an altitude of 6000 ft, where the pressure is 605 torr and the temperature is 158C. What is the change in volume of the balloon as it ascends from sea level to 6000 ft?

A large flask with a volume of 936 mL is evacuated and found to have a mass of 134.66 g. It is then filled to a pressure of 0.967 atm at 318C with a gas of unknown molar mass and then reweighed to give a new mass of 135.87 g. What is the molar mass of this gas?

A 20.0-L nickel container was charged with 0.859 atm of xenon gas and 1.37 atm of fluorine gas at 4008C. The xenon and fluorine react to form xenon tetrafluoride. What mass of xenon tetrafluoride can be produced assuming 100% yield?

Consider the unbalanced chemical equation below: CaSiO3 1s2 1 HF1g2 h CaF2 1aq2 1 SiF4 1g2 1 H2O1l2 Suppose a 32.9-g sample of CaSiO3 is reacted with 31.8 L of HF at 27.08C and 1.00 atm. Assuming the reaction goes to completion, calculate the mass of the SiF4 and H2O produced in the reaction.

Consider separate 2.5-L gaseous samples of He, N2, and F2, all at STP and all acting ideally. Rank the gases in order of increasing average kinetic energy and in order of increasing average velocity.

Which of the following statements is(are) true? a. If the number of moles of a gas is doubled, the volume will double, assuming the pressure and temperature of the gas remain constant. b. If the temperature of a gas increases from 258C to 508C, the volume of the gas would double, assuming that the pressure and the number of moles of gas remain constant. c. The device that measures atmospheric pressure is called a barometer. d. If the volume of a gas decreases by one half, then the pressure would double, assuming that the number of moles and the temperature of the gas remain constant.

Consider a childrens cartoon illustrating a child holding the strings of several helium balloons and being lifted into the sky. a. Estimate the minimum number of 10.-L balloons it would take to lift a 50.-lb child. Assume air has an average molar mass of 29 g/mol, and assume the masses of the balloons and strings are negligible. b. Explain why the balloons can lift the child.

A 16.0-g sample of methane (CH4) reacts with 64.0 g of oxygen gas in a container fitted with a piston (at 1.00 atm and 425 K). Methane can react with oxygen to form carbon dioxide and water vapor or carbon monoxide and water vapor. After the combustion reaction is complete, the gas density at the given conditions is observed to be 0.7282 g/L. Calculate the mole fraction of methane that reacts to form carbon monoxide rather than carbon dioxide.

You have two samples of helium gas at the same pressure in separate steel containers of the same volume. You want the number of collisions of helium atoms with the walls of container 1 to be twice the number of collisions of helium atoms with the walls of container 2. Assume ideal behavior. a. How does the temperature in container 1 compare to the temperature in container 2? That is, which temperature is larger and by what factor? Explain your answer and support it mathematically. b. If the number of collisions is different in each container, how can the pressure be the same? Provide a written explanation with mathematical support.

A mixture of chromium and zinc weighing 0.362 g was reacted with an excess of hydrochloric acid. After all the metals in the mixture reacted, 225 mL of dry hydrogen gas was collected at 278C and 750. torr. Determine the mass percent of Zn in the metal sample. [Zinc reacts with hydrochloric acid to produce zinc chloride and hydrogen gas; chromium reacts with hydrochloric acid to produce chromium(III) chloride and hydrogen gas.]

You have a sealed, flexible balloon filled with argon gas. The atmospheric pressure is 1.00 atm and the temperature is 258C. The air has a mole fraction of nitrogen of 0.79, the rest being oxygen. a. Explain why the balloon would float when heated. Make sure to discuss which factors change and which remain constant, and why this matters. Be complete. b. Above what temperature would you heat the balloon so that it would float?

Derive a linear relationship between gas density and temperature, and use it to estimate the value of absolute zero temperature (in 8C to the nearest 0.18C) from an air sample whose density is 1.2930 g/L at 0.08C and 0.9460 g/L at 100.08C. Assume air obeys the ideal gas law and that the pressure is held constant.

A chemist weighed out 5.14 g of a mixture containing unknown amounts of BaO(s) and CaO(s) and placed the sample in a 1.50-L flask containing CO2(g) at 30.08C and 750. torr. After the reaction to form BaCO3(s) and CaCO3(s) was completed, the pressure of CO2(g) remaining was 230. torr. Calculate the mass percents of CaO(s) and BaO(s) in the mixture.

The density of a pure gaseous compound was measured at 0.008C as a function of pressure to give the following results: Density (g/L) Pressure (atm) 0.17893 0.2500 0.35808 0.5000 0.53745 0.7500 0.71707 1.000 Calculate the molar mass of this compound, corrected for any nonideal behavior of the gas. Assume the nonideal gas obeys the equation PV/nRT 5 1 1 bP. (Hint: Derive an equation for P/d and plot P/d versus P.)

Consider separate 1.0-L samples of He(g) and UF6(g), both at 1.00 atm and containing the same number of moles. What ratio of temperatures for the two samples would produce the same collision frequency with the vessel walls?

The most probable velocity ump is the velocity possessed by the greatest number of gas particles. At a certain temperature, the probability that a gas particle has the most probable velocity is equal to one-half the probability that the same gas particle has the most probable velocity at 300. K. Is the temperature higher or lower than 300. K? Calculate the temperature.

Derive Daltons law of partial pressures from the kinetic molecular theory of gases. What assumptions are necessary?

One of the assumptions of the kinetic molecular theory is that the volume of a gas particle is negligible. If this were the case, the ratio of the number of collisions of gas particles with the walls of the container compared to the number of collisions a given gas particle experiences with other gas particles should be quite high. Determine the volume of a cube (in L) filled with helium such that the ratio of the number of collisions of helium atoms with the container walls to the number of intermolecular collisions for a given helium atom is 1 quintillion (1 quintillion 5 1.00 3 1018). The atomic radius of helium is 3.2 3 10211 m.

Consider a sample of a hydrocarbon (a compound consisting of only carbon and hydrogen) at 0.959 atm and 298 K. Upon combusting the entire sample in oxygen, you collect a mixture of gaseous carbon dioxide and water vapor at 1.51 atm and 375 K. This mixture has a density of 1.391 g/L and occupies a volume four times as large as that of the pure hydrocarbon. Determine the molecular formula of the hydrocarbon

A steel cylinder contains 5.00 moles of graphite (pure carbon) and 5.00 moles of O2. The mixture is ignited and all the graphite reacts. Combustion produces a mixture of CO gas and CO2 gas. After the cylinder has cooled to its original temperature, it is found that the pressure of the cylinder has increased by 17.0%. Calculate the mole fractions of CO, CO2, and O2 in the final gaseous mixture

You have an equimolar mixture of the gases SO2 and O2, along with some He, in a container fitted with a piston. The density of this mixture at STP is 1.924 g/L. Assume ideal behavior and constant temperature. a. What is the mole fraction of He in the original mixture? b. The SO2 and O2 react to completion to form SO3. What is the density of the gas mixture after the reaction is complete?

Methane (CH4) gas flows into a combustion chamber at a rate of 200. L/min at 1.50 atm and ambient temperature. Air is added to the chamber at 1.00 atm and the same temperature, and the gases are ignited. a. To ensure complete combustion of CH4 to CO2(g) and H2O(g), three times as much oxygen as is necessary is reacted. Assuming air is 21 mole percent O2 and 79 mole percent N2, calculate the flow rate of air necessary to deliver the required amount of oxygen. b. Under the conditions in part a, combustion of methane was not complete as a mixture of CO2(g) and CO(g) was produced. It was determined that 95.0% of the carbon in the exhaust gas was present in the CO2. The remainder was present as carbon in the CO. Calculate the composition of the exhaust gas in terms of mole fractions of CO, CO2, O2, N2, and H2O. Assume CH4 is completely reacted and N2 is unreacted. c. Assuming a total pressure of the exhaust gas of 1.00 atm, calculate the partial pressures of the gases in part b.

A spherical vessel with a volume of 1.00 L was evacuated and sealed. Twenty-four hours later the pressure of air in the vessel was found to be 1.20 3 1026 atm. During this 24-h period, the vessel had been surrounded by air at 278C and 1.00 atm. Assuming that air is 78 mole percent nitrogen and that the remainder is oxygen, calculate the diameter of the tiny circular hole in the vessel that allowed the air to leak in.

Calculate the number of stages needed to change a mixture of 13CO2 and 12CO2 that is originally 0.10% (by moles) 13CO2 to a mixture that is 0.010% 13CO2 by a gaseous diffusion process. (The mass of 13C is 13.003355 u.)

Two samples of gas are separated in two rectangular 1.00-L chambers by a thin metal wall. One sample is pure helium and the other is pure radon. Both samples are at 27C and show a pressure of 2.00 3 1026 atm. Assuming that the metal wall separating the gases suddenly develops a circular hole of radius 1.00 3 1026 m, calculate the pressure in each chamber after 10.0 h have passed.

You have a helium balloon at 1.00 atm and 258C. You want to make a hot-air balloon with the same volume and same lift as the helium balloon. Assume air is 79.0% nitrogen and 21.0% oxygen by volume. The lift of a balloon is given by the difference between the mass of air displaced by the balloon and the mass of gas inside the balloon. a. Will the temperature in the hot-air balloon have to be higher or lower than 258C? Explain. b. Calculate the temperature of the air required for the hot-air balloon to provide the same lift as the helium balloon at 1.00 atm and 258C. Assume atmospheric conditions are 1.00 atm and 258C.

You are given an unknown gaseous binary compound (that is, a compound consisting of two different elements). When 10.0 g of the compound is burned in excess oxygen, 16.3 g of water is produced. The compound has a density 1.38 times that of oxygen gas at the same conditions of temperature and pressure. Give a possible identity for the unknown compound

Consider an equimolar mixture (equal number of moles) of two diatomic gases (A2 and B2) in a container fitted with a piston. The gases react to form one product (which is also a gas) with the formula AxBy. The density of the sample after the reaction is complete (and the temperature returns to its original state) is 1.50 times greater than the density of the reactant mixture. a. Specify the formula of the product, and explain if more than one answer is possible based on the given data. b. Can you determine the molecular formula of the product with the information given or only the empirical formula?