Answer: (a) Show that the pressure exerted by a fluid P

Name five elements and five compounds that exist as gases at room temperature.

List the physical characteristics of gases

Define pressure and give the common units for pressure

When you are in a plane flying at high altitudes, your ears often experience pain. This discomfort can be temporarily relieved by yawning or swallowing some water. Explain.

Why is mercury a more suitable substance to use in a barometer than water?

Explain why the height of mercury in a barometer is independent of the cross-sectional area of the tube. Would the barometer still work if the tubing were tilted at an angle, say 15 (see Figure 5.3)?

Explain how a unit of length (mmHg) can be used as a unit for pressure.

Describe what would happen to the column of mercury in the following manometers when the stopcock is opened. (a) (b) Vacuum

What is the difference between a gas and a vapor? At 25C, which of the following substances in the gas phase should be properly called a gas and which should be called a vapor: molecular nitrogen (N2), mercury?

If the maximum distance that water may be brought up a well by a suction pump is 34 ft (10.3 m), how is it possible to obtain water and oil from hundreds of feet below the surface of Earth?

Why is it that if the barometer reading falls in one part of the world, it must rise somewhere else?

Why do astronauts have to wear protective suits when they are on the surface of the moon?

Convert 562 mmHg to atm.

The atmospheric pressure at the summit of Mt. McKinley is 606 mmHg on a certain day. What is the pressure in atm and in kPa?

State the following gas laws in words and also in the form of an equation: Boyles law, Charles law, Avogadros law. In each case, indicate the conditions under which the law is applicable, and give the units for each quantity in the equation.

A certain amount of gas is contained in a closed mercury manometer as shown here. Assuming no other parameters change, would h increase, decrease, or remain the same if (a) the amount of the gas were increased; (b) the molar mass of the gas were doubled; (c) the temperature of the gas was increased; (d) the atmospheric pressure in the room was increased; (e) the mercury in the tube were replaced with a less dense fluid; (f) some gas was added to the vacuum at the top of the right-side tube; (g) a hole was drilled in the top of the right-side tube? h Vacuum

A gaseous sample of a substance is cooled at constant pressure. Which of the following diagrams best represents the situation if the final temperature is (a) above the boiling point of the substance and (b) below the boiling point but above the freezing point of the substance? (a) (b) (c) (d)

Consider the following gaseous sample in a cylinder fitted with a movable piston. Initially there are n moles of the gas at temperature T, pressure P, and volume V. Choose the cylinder that correctly represents the gas after each of the following changes. (1) The pressure on the piston is tripled at constant n and T. (2) The temperature is doubled at constant n and P. (3) n moles of another gas are added at constant T and P. (4) T is halved and pressure on the piston is reduced to a quarter of its original value. (a) (b) (c)

A gas occupying a volume of 725 mL at a pressure of 0.970 atm is allowed to expand at constant temperature until its pressure reaches 0.541 atm. What is its final volume?

At 46C a sample of ammonia gas exerts a pressure of 5.3 atm. What is the pressure when the volume of the gas is reduced to one-tenth (0.10) of the original value at the same temperature?

The volume of a gas is 5.80 L, measured at 1.00 atm. What is the pressure of the gas in mmHg if the volume is changed to 9.65 L? (The temperature remains constant.)

A sample of air occupies 3.8 L when the pressure is 1.2 atm. (a) What volume does it occupy at 6.6 atm? (b) What pressure is required in order to compress it to 0.075 L? (The temperature is kept constant.)

A 36.4-L volume of methane gas is heated from 25C to 88C at constant pressure. What is the final volume of the gas?

Under constant-pressure conditions a sample of hydrogen gas initially at 88C and 9.6 L is cooled until its final volume is 3.4 L. What is its final temperature?

Ammonia burns in oxygen gas to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure?

Molecular chlorine and molecular fluorine combine to form a gaseous product. Under the same conditions of temperature and pressure it is found that one volume of Cl2 reacts with three volumes of F2 to yield two volumes of the product. What is the formula of the product?

List the characteristics of an ideal gas. Write the ideal gas equation and also state it in words. Give the units for each term in the equation

Use Equation (5.9) to derive all the gas laws.

What are standard temperature and pressure (STP)? What is the significance of STP in relation to the volume of 1 mole of an ideal gas?

Why is the density of a gas much lower than that of a liquid or solid under atmospheric conditions? What units are normally used to express the density of gases?

A sample of nitrogen gas kept in a container of volume 2.3 L and at a temperature of 32C exerts a pressure of 4.7 atm. Calculate the number of moles of gas present.

Given that 6.9 moles of carbon monoxide gas are present in a container of volume 30.4 L, what is the pressure of the gas (in atm) if the temperature is 62C?

What volume will 5.6 moles of sulfur hexafluoride (SF6) gas occupy if the temperature and pressure of the gas are 128C and 9.4 atm?

A certain amount of gas at 25C and at a pressure of 0.800 atm is contained in a glass vessel. Suppose that the vessel can withstand a pressure of 2.00 atm. How high can you raise the temperature of the gas without bursting the vessel?

A gas-filled balloon having a volume of 2.50 L at 1.2 atm and 25C is allowed to rise to the stratosphere (about 30 km above the surface of Earth), where the temperature and pressure are 223C and 3.00 3 1023 atm, respectively. Calculate the final volume of the balloon.

The temperature of 2.5 L of a gas initially at STP is raised to 250C at constant volume. Calculate the final pressure of the gas in atm

The pressure of 6.0 L of an ideal gas in a flexible container is decreased to one-third of its original pressure, and its absolute temperature is decreased by one-half. What is the final volume of the gas?

A gas evolved during the fermentation of glucose (wine making) has a volume of 0.78 L at 20.1C and 1.00 atm. What was the volume of this gas at the fermentation temperature of 36.5C and 1.00 atm pressure?

An ideal gas originally at 0.85 atm and 66C was allowed to expand until its final volume, pressure, and temperature were 94 mL, 0.60 atm, and 45C, respectively. What was its initial volume?

Calculate its volume (in liters) of 88.4 g of CO2 at STP

A gas at 772 mmHg and 35.0C occupies a volume of 6.85 L. Calculate its volume at STP.

Dry ice is solid carbon dioxide. A 0.050-g sample of dry ice is placed in an evacuated 4.6-L vessel at 30C. Calculate the pressure inside the vessel after all the dry ice has been converted to CO2 gas

At STP, 0.280 L of a gas weighs 0.400 g. Calculate the molar mass of the gas.

At 741 torr and 44C, 7.10 g of a gas occupy a volume of 5.40 L. What is the molar mass of the gas?

Ozone molecules in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are 250 K and 1.0 3 1023 atm, respectively. How many ozone molecules are present in 1.0 L of air under these conditions?

Assuming that air contains 78 percent N2, 21 percent O2, and 1 percent Ar, all by volume, how many molecules of each type of gas are present in 1.0 L of air at STP?

A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.0C. (a) Calculate the density of the gas in grams per liter. (b) What is the molar mass of the gas?

Calculate the density of hydrogen bromide (HBr) gas in grams per liter at 733 mmHg and 46C.

A certain anesthetic contains 64.9 percent C, 13.5 percent H, and 21.6 percent O by mass. At 120C and 750 mmHg, 1.00 L of the gaseous compound weighs 2.30 g. What is the molecular formula of the compound?

A compound has the empirical formula SF4. At 20C, 0.100 g of the gaseous compound occupies a volume of 22.1 mL and exerts a pressure of 1.02 atm. What is the molecular formula of the gas?

What pressure will be required for neon at 30C to have the same density as nitrogen at 20C and 1.0 atm?

The density of a mixture of fluorine and chlorine gases is 1.77 g/L at 14C and 0.893 atm. Calculate the mass percent of the gases.

Consider the formation of nitrogen dioxide from nitric oxide and oxygen: 2NO(g) 1 O2(g) 2NO2(g) If 9.0 L of NO are reacted with excess O2 at STP, what is the volume in liters of the NO2 produced?

Methane, the principal component of natural gas, is used for heating and cooking. The combustion process is CH4(g) 1 2O2(g) CO2(g) 1 2H2O(l) If 15.0 moles of CH4 are reacted, what is the volume of CO2 (in liters) produced at 23.0C and 0.985 atm?

When coal is burned, the sulfur present in coal is converted to sulfur dioxide (SO2), which is responsible for the acid rain phenomenon. S(s) 1 O2(g) SO2(g) If 2.54 kg of S are reacted with oxygen, calculate the volume of SO2 gas (in mL) formed at 30.5C and 1.12 atm

In alcohol fermentation, yeast converts glucose to ethanol and carbon dioxide: C6H12O6(s) 2C2H5OH(l) 1 2CO2(g) If 5.97 g of glucose are reacted and 1.44 L of CO2 gas are collected at 293 K and 0.984 atm, what is the percent yield of the reaction?

A compound of P and F was analyzed as follows: Heating 0.2324 g of the compound in a 378-cm3 container turned all of it to gas, which had a pressure of 97.3 mmHg at 77C. Then the gas was mixed with calcium chloride solution, which turned all of the F to 0.2631 g of CaF2. Determine the molecular formula of the compound

A quantity of 0.225 g of a metal M (molar mass 5 27.0 g/mol) liberated 0.303 L of molecular hydrogen (measured at 17C and 741 mmHg) from an excess of hydrochloric acid. Deduce from these data the corresponding equation and write formulas for the oxide and sulfate of M.

What is the mass of the solid NH4Cl formed when 73.0 g of NH3 are mixed with an equal mass of HCl? What is the volume of the gas remaining, measured at 14.0C and 752 mmHg? What gas is it?

Dissolving 3.00 g of an impure sample of calcium carbonate in hydrochloric acid produced 0.656 L of carbon dioxide (measured at 20.0C and 792 mmHg). Calculate the percent by mass of calcium carbonate in the sample. State any assumptions.

Calculate the mass in grams of hydrogen chloride produced when 5.6 L of molecular hydrogen measured at STP react with an excess of molecular chlorine gas

Ethanol (C2H5OH) burns in air: C2H5OH(l) 1 O2(g) CO2(g) 1 H2O(l) Balance the equation and determine the volume of air in liters at 35.0C and 790 mmHg required to burn 227 g of ethanol. Assume that air is 21.0 percent O2 by volume

(a) What volumes (in liters) of ammonia and oxygen must react to form 12.8 L of nitric oxide according to the equation at the same temperature and pressure? 4NH3(g) 1 5O2(g) 4NO(g) 1 6H2O(g) (b) What volumes (in liters) of propane and water vapor must react to form 8.96 L of hydrogen according to the equation at the same temperature and pressure? C3H8(g) 1 3H2O(g) 3CO(g) 1 7H2(g)

A 4.00-g sample of FeS containing nonsulfide impurities reacted with HCl to give 896 mL of H2S at 14C and 782 mmHg. Calculate mass percent purity of the sample.

State Daltons law of partial pressures and explain what mole fraction is. Does mole fraction have units?

A sample of air contains only nitrogen and oxygen gases whose partial pressures are 0.80 atm and 0.20 atm, respectively. Calculate the total pressure and the mole fractions of the gases.

A mixture of gases contains 0.31 mol CH4, 0.25 mol C2H6, and 0.29 mol C3H8. The total pressure is 1.50 atm. Calculate the partial pressures of the gases

A 2.5-L flask at 15C contains a mixture of N2, He, and Ne at partial pressures of 0.32 atm for N2, 0.15 atm for He, and 0.42 atm for Ne. (a) Calculate the total pressure of the mixture. (b) Calculate the volume in liters at STP occupied by He and Ne if the N2 is removed selectively

Dry air near sea level has the following composition by volume: N2, 78.08 percent; O2, 20.94 percent; Ar, 0.93 percent; CO2, 0.05 percent. The atmospheric pressure is 1.00 atm. Calculate (a) the partial pressure of each gas in atm and (b) the concentration of each gas in moles per liter at 0C. (Hint: Because volume is proportional to the number of moles present, mole fractions of gases can be expressed as ratios of volumes at the same temperature and pressure.)

A mixture of helium and neon gases is collected over water at 28.0C and 745 mmHg. If the partial pressure of helium is 368 mmHg, what is the partial pressure of neon? (Vapor pressure of water at 28C 5 28.3 mmHg.)

A piece of sodium metal reacts completely with water as follows: 2Na(s) 1 2H2O(l) 2NaOH(aq) 1 H2(g) The hydrogen gas generated is collected over water at 25.0C. The volume of the gas is 246 mL measured at 1.00 atm. Calculate the number of grams of sodium used in the reaction. (Vapor pressure of water at 25C 5 0.0313 atm.)

A sample of zinc metal reacts completely with an excess of hydrochloric acid: Zn(s) 1 2HCl(aq) ZnCl2(aq) 1 H2(g) The hydrogen gas produced is collected over water at 25.0C using an arrangement similar to that shown in Figure 5.15. The volume of the gas is 7.80 L, and the pressure is 0.980 atm. Calculate the amount of zinc metal in grams consumed in the reaction. (Vapor pressure of water at 25C 5 23.8 mmHg.)

Helium is mixed with oxygen gas for deep-sea divers. Calculate the percent by volume of oxygen gas in the mixture if the diver has to submerge to a depth where the total pressure is 4.2 atm. The partial pressure of oxygen is maintained at 0.20 atm at this depth.

A sample of ammonia (NH3) gas is completely decomposed to nitrogen and hydrogen gases over heated iron wool. If the total pressure is 866 mmHg, calculate the partial pressures of N2 and H2.

Consider the three gas containers shown here. All of them have the same volume and are at the same temperature. (a) Which container has the smallest mole fraction of gas A (blue sphere)? (b) Which container has the highest partial pressure of gas B (green sphere)? (i) (ii) (iii)

The volume of the box on the right is twice that of the box on the left. The boxes contain helium atoms (red) and hydrogen molecules (green) at the same temperature. (a) Which box has a higher total pressure? (b) Which box has a lower partial pressure of helium?

What are the basic assumptions of the kinetic molecular theory of gases? How does the kinetic molecular theory explain Boyles law, Charles law, Avogadros law, and Daltons law of partial pressures?

What does the Maxwell speed distribution curve tell us? Does Maxwells theory work for a sample of 200 molecules? Explain

Which of the following statements is correct? (a) Heat is produced by the collision of gas molecules against one another. (b) When a gas is heated, the molecules collide with one another more often.

What is the difference between gas diffusion and effusion? State Grahams law and define the terms in Equation (5.17).

Compare the root-mean-square speeds of O2 and UF6 at 65C.

The temperature in the stratosphere is 223C. Calculate the root-mean-square speeds of N2, O2, and O3 molecules in this region.

The average distance traveled by a molecule between successive collisions is called mean free path. For a given amount of a gas, how does the mean free path of a gas depend on (a) density, (b) temperature at constant volume, (c) pressure at constant temperature, (d) volume at constant temperature, and (e) size of the atoms?

At a certain temperature the speeds of six gaseous molecules in a container are 2.0 m/s, 2.2 m/s, 2.6 m/s, 2.7 m/s, 3.3 m/s, and 3.5 m/s. Calculate the rootmean-square speed and the average speed of the molecules. These two average values are close to each other, but the root-mean-square value is always the larger of the two. Why?

Based on your knowledge of the kinetic theory of gases, derive Grahams law [Equation (5.17)].

The 235U isotope undergoes fission when bombarded with neutrons. However, its natural abundance is only 0.72 percent. To separate it from the more abundant 238U isotope, uranium is first converted to UF6, which is easily vaporized above room temperature. The mixture of the 235UF6 and 238UF6 gases is then subjected to many stages of effusion. Calculate the separation factor, that is, the enrichment of 235U relative to 238U after one stage of effusion.

A gas evolved from the fermentation of glucose is found to effuse through a porous barrier in 15.0 min. Under the same conditions of temperature and pressure, it takes an equal volume of N2 12.0 min to effuse through the same barrier. Calculate the molar mass of the gas and suggest what the gas might be.

Nickel forms a gaseous compound of the formula Ni(CO)x. What is the value of x given the fact that under the same conditions of temperature and pressure, methane (CH4) effuses 3.3 times faster than the compound?

Cite two pieces of evidence to show that gases do not behave ideally under all conditions.

Under what set of conditions would a gas be expected to behave most ideally? (a) High temperature and low pressure, (b) high temperature and high pressure, (c) low temperature and high pressure, (d) low temperature and low pressure.

Shown here are plots of PVyRT against P for one mole of a nonideal gas at two different temperatures. Which curve is at the higher temperature? P PV RT 1.0

(a) A real gas is introduced into a flask of volume V. Is the corrected volume of the gas greater or less than V? (b) Ammonia has a larger a value than neon does (see Table 5.4). What can you conclude about the relative strength of the attractive forces between molecules of ammonia and between atoms of neon?

Using the data shown in Table 5.4, calculate the pressure exerted by 2.50 moles of CO2 confined in a volume of 5.00 L at 450 K. Compare the pressure with that predicted by the ideal gas equation.

At 27C, 10.0 moles of a gas in a 1.50-L container exert a pressure of 130 atm. Is this an ideal gas?

Discuss the following phenomena in terms of the gas laws: (a) the pressure increase in an automobile tire on a hot day, (b) the popping of a paper bag, (c) the expansion of a weather balloon as it rises in the air, (d) the loud noise heard when a lightbulb shatters

Under the same conditions of temperature and pressure, which of the following gases would behave most ideally: Ne, N2, or CH4? Explain

Nitroglycerin, an explosive compound, decomposes according to the equation 4C3H5(NO3)3(s) 12CO2(g) 1 10H2O(g) 1 6N2(g) 1 O2(g) Calculate the total volume of gases when collected at 1.2 atm and 25C from 2.6 3 102 g of nitroglycerin. What are the partial pressures of the gases under these conditions?

The empirical formula of a compound is CH. At 200C, 0.145 g of this compound occupies 97.2 mL at a pressure of 0.74 atm. What is the molecular formula of the compound?

When ammonium nitrite (NH4NO2) is heated, it decomposes to give nitrogen gas. This property is used to inflate some tennis balls. (a) Write a balanced equation for the reaction. (b) Calculate the quantity (in grams) of NH4NO2 needed to inflate a tennis ball to a volume of 86.2 mL at 1.20 atm and 22C.

The percent by mass of bicarbonate (HCO3 2) in a certain Alka-Seltzer product is 32.5 percent. Calculate the volume of CO2 generated (in mL) at 37C and 1.00 atm when a person ingests a 3.29-g tablet. (Hint: The reaction is between HCO3 2 and HCl acid in the stomach.)

The boiling point of liquid nitrogen is 2196C. On the basis of this information alone, do you think nitrogen is an ideal gas?

In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at 43C: Ni(s) 1 4CO(g) Ni(CO)4(g) This reaction separates nickel from other solid impurities. (a) Starting with 86.4 g of Ni, calculate the pressure of Ni(CO)4 in a container of volume 4.00 L. (Assume the above reaction goes to completion.) (b) At temperatures above 43C, the pressure of the gas is observed to increase much more rapidly than predicted by the ideal gas equation. Explain.

The partial pressure of carbon dioxide varies with seasons. Would you expect the partial pressure in the Northern Hemisphere to be higher in the summer or winter? Explain

A healthy adult exhales about 5.0 3 102 mL of a gaseous mixture with each breath. Calculate the number of molecules present in this volume at 37C and 1.1 atm. List the major components of this gaseous mixture.

Sodium bicarbonate (NaHCO3) is called baking soda because when heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, doughnuts, and bread. (a) Calculate the volume (in liters) of CO2 produced by heating 5.0 g of NaHCO3 at 180C and 1.3 atm. (b) Ammonium bicarbonate (NH4HCO3) has also been used for the same purpose. Suggest one advantage and one disadvantage of using NH4HCO3 instead of NaHCO3 for baking

A barometer having a cross-sectional area of 1.00 cm2 at sea level measures a pressure of 76.0 cm of mercury. The pressure exerted by this column of mercury is equal to the pressure exerted by all the air on 1 cm2 of Earths surface. Given that the density of mercury is 13.6 g/mL and the average radius of Earth is 6371 km, calculate the total mass of Earths atmosphere in kilograms. (Hint: The surface area of a sphere is 4r 2 where r is the radius of the sphere.)

Some commercial drain cleaners contain a mixture of sodium hydroxide and aluminum powder. When the mixture is poured down a clogged drain, the following reaction occurs: 2NaOH(aq) 1 2Al(s) 1 6H2O(l) 2NaAl(OH)4(aq) 1 3H2(g) The heat generated in this reaction helps melt away obstructions such as grease, and the hydrogen gas released stirs up the solids clogging the drain. Calculate the volume of H2 formed at 23C and 1.00 atm if 3.12 g of Al are treated with an excess of NaOH.

The volume of a sample of pure HCl gas was 189 mL at 25C and 108 mmHg. It was completely dissolved in about 60 mL of water and titrated with an NaOH solution; 15.7 mL of the NaOH solution were required to neutralize the HCl. Calculate the molarity of the NaOH solution

Propane (C3H8) burns in oxygen to produce carbon dioxide gas and water vapor. (a) Write a balanced equation for this reaction. (b) Calculate the number of liters of carbon dioxide measured at STP that could be produced from 7.45 g of propane.

Consider the following apparatus. Calculate the partial pressures of helium and neon after the stopcock is open. The temperature remains constant at 16C. He Ne 1.2 L 0.63 atm 3.4 L 2.8 atm

Nitric oxide (NO) reacts with molecular oxygen as follows: 2NO(g) 1 O2(g) 2NO2(g) Initially NO and O2 are separated as shown here. When the valve is opened, the reaction quickly goes to completion. Determine what gases remain at the end and calculate their partial pressures. Assume that the temperature remains constant at 25C. 4.00 L at 0.500 atm 2.00 L at 1.00 atm NO O2

Consider the apparatus shown here. When a small amount of water is introduced into the flask by squeezing the bulb of the medicine dropper, water is squirted upward out of the long glass tubing. Explain this observation. (Hint: Hydrogen chloride gas is soluble in water.) H2O H2O Rubber bulb HCl gas

Describe how you would measure, by either chemical or physical means, the partial pressures of a mixture of gases of the following composition: (a) CO2 and H2, (b) He and N2.

A certain hydrate has the formula MgSO4 ? xH2O. A quantity of 54.2 g of the compound is heated in an oven to drive off the water. If the steam generated exerts a pressure of 24.8 atm in a 2.00-L container at 120C, calculate x

A mixture of Na2CO3 and MgCO3 of mass 7.63 g is reacted with an excess of hydrochloric acid. The CO2 gas generated occupies a volume of 1.67 L at 1.24 atm and 26C. From these data, calculate the percent composition by mass of Na2CO3 in the mixture

The following apparatus can be used to measure atomic and molecular speed. Suppose that a beam of metal atoms is directed at a rotating cylinder in a vacuum. A small opening in the cylinder allows the atoms to strike a target area. Because the cylinder is rotating, atoms traveling at different speeds will strike the target at different positions. In time, a layer of the metal will deposit on the target area, and the variation in its thickness is found to correspond to Maxwells speed distribution. In one experiment it is found that at 850C some bismuth (Bi) atoms struck the target at a point 2.80 cm from the spot directly opposite the slit. The diameter of the cylinder is 15.0 cm and it is rotating at 130 revolutions per second. (a) Calculate the speed (m/s) at which the target is moving. (Hint: The circumference of a circle is given by 2r, where r is the radius.) (b) Calculate the time (in seconds) it takes for the target to travel 2.80 cm. (c) Determine the speed of the Bi atoms. Compare your result in (c) with the urms of Bi at 850C. Comment on the difference. Rotating cylinder Target Slit Bi atoms

If 10.00 g of water are introduced into an evacuated flask of volume 2.500 L at 65C, calculate the mass of water vaporized. (Hint: Assume that the volume of the remaining liquid water is negligible; the vapor pressure of water at 65C is 187.5 mmHg.)

Commercially, compressed oxygen is sold in metal cylinders. If a 120-L cylinder is filled with oxygen to a pressure of 132 atm at 22C, what is the mass (in grams) of O2 present? How many liters of O2 gas at 1.00 atm and 22C could the cylinder produce? (Assume ideal behavior.)

The shells of hard-boiled eggs sometimes crack due to the rapid thermal expansion of the shells at high temperatures. Suggest another reason why the shells may crack.

Ethylene gas (C2H4) is emitted by fruits and is known to be responsible for their ripening. Based on this information, explain why a bunch of bananas ripens faster in a closed paper bag than in a bowl.

About 8.0 3 106 tons of urea [(NH2)2CO] are used annually as a fertilizer. The urea is prepared at 200C and under high-pressure conditions from carbon dioxide and ammonia (the products are urea and steam). Calculate the volume of ammonia (in liters) measured at 150 atm needed to prepare 1.0 ton of urea.

Some ballpoint pens have a small hole in the main body of the pen. What is the purpose of this hole?

The gas laws are vitally important to scuba divers. The pressure exerted by 33 ft of seawater is equivalent to 1 atm pressure. (a) A diver ascends quickly to the surface of the water from a depth of 36 ft without exhaling gas from his lungs. By what factor will the volume of his lungs increase by the time he reaches the surface? Assume that the temperature is constant. (b) The partial pressure of oxygen in air is about 0.20 atm. (Air is 20 percent oxygen by volume.) In deep-sea diving, the composition of air the diver breathes must be changed to maintain this partial pressure. What must the oxygen content (in percent by volume) be when the total pressure exerted on the diver is 4.0 atm? (At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gases.) (Hint: See the Chemistry in Action essay on p. 200.)

Nitrous oxide (N2O) can be obtained by the thermal decomposition of ammonium nitrate (NH4NO3). (a) Write a balanced equation for the reaction. (b) In a certain experiment, a student obtains 0.340 L of the gas at 718 mmHg and 24C. If the gas weighs 0.580 g, calculate the value of the gas constant

Two vessels are labeled A and B. Vessel A contains NH3 gas at 70C, and vessel B contains Ne gas at the same temperature. If the average kinetic energy of NH3 is 7.1 3 10221 J/molecule, calculate the meansquare speed of Ne atoms in m2 /s2 .

Which of the following molecules has the largest a value: CH4, F2, C6H6, Ne?

The following procedure is a simple though somewhat crude way to measure the molar mass of a gas. A liquid of mass 0.0184 g is introduced into a syringe like the one shown here by injection through the rubber tip using a hypodermic needle. The syringe is then transferred to a temperature bath heated to 45C, and the liquid vaporizes. The final volume of the vapor (measured by the outward movement of the plunger) is 5.58 mL and the atmospheric pressure is 760 mmHg. Given that the compounds empirical formula is CH2, determine the molar mass of the compound. 5 4 3 2 1 Rubber tip

In 1995 a man suffocated as he walked by an abandoned mine in England. At that moment there was a sharp drop in atmospheric pressure due to a change in the weather. Suggest what might have caused the mans death.

Acidic oxides such as carbon dioxide react with basic oxides like calcium oxide (CaO) and barium oxide (BaO) to form salts (metal carbonates). (a) Write equations representing these two reactions. (b) A student placed a mixture of BaO and CaO of combined mass 4.88 g in a 1.46-L flask containing carbon dioxide gas at 35C and 746 mmHg. After the reactions were complete, she found that the CO2 pressure had dropped to 252 mmHg. Calculate the percent composition by mass of the mixture. Assume volumes of the solids are negligible.

Identify the Maxwell speed distribution curves shown here with the following gases: Br2, CH4, N2, SO3. 0 500 Number of molecules Molecular speed (m/s) 1000 1500

The running engine of an automobile produces carbon monoxide (CO), a toxic gas, at the rate of about 188 g CO per hour. A car is left idling in a poorly ventilated garage that is 6.0 m long, 4.0 m wide, and 2.2 m high at 20C. (a) Calculate the rate of CO production in moles per minute. (b) How long would it take to build up a lethal concentration of CO of 1000 ppmv (parts per million by volume)?

Interstellar space contains mostly hydrogen atoms at a concentration of about 1 atom/cm3 . (a) Calculate the pressure of the H atoms. (b) Calculate the volume (in liters) that contains 1.0 g of H atoms. The temperature is 3 K.

Atop Mt. Everest, the atmospheric pressure is 210 mmHg and the air density is 0.426 kg/m3 . (a) Calculate the air temperature, given that the molar mass of air is 29.0 g/mol. (b) Assuming no change in air composition, calculate the percent decrease in oxygen gas from sea level to the top of Mt. Everest.

Relative humidity is defined as the ratio (expressed as a percentage) of the partial pressure of water vapor in the air to the equilibrium vapor pressure (see Table 5.3) at a given temperature. On a certain summer day in North Carolina the partial pressure of water vapor in the air is 3.9 3 103 Pa at 30C. Calculate the relative humidity.

Under the same conditions of temperature and pressure, why does one liter of moist air weigh less than one liter of dry air? In weather forecasts, an oncoming low-pressure front usually means imminent rainfall. Explain

Air entering the lungs ends up in tiny sacs called alveoli. It is from the alveoli that oxygen diffuses into the blood. The average radius of the alveoli is 0.0050 cm and the air inside contains 14 percent oxygen. Assuming that the pressure in the alveoli is 1.0 atm and the temperature is 37C, calculate the number of oxygen molecules in one of the alveoli. (Hint: The volume of a sphere of radius r is 4 3r 3 .)

A student breaks a thermometer and spills most of the mercury (Hg) onto the floor of a laboratory that measures 15.2 m long, 6.6 m wide, and 2.4 m high. (a) Calculate the mass of mercury vapor (in grams) in the room at 20C. The vapor pressure of mercury at 20C is 1.7 3 1026 atm. (b) Does the concentration of mercury vapor exceed the air quality regulation of 0.050 mg Hg/m3 of air? (c) One way to treat small quantities of spilled mercury is to spray sulfur powder over the metal. Suggest a physical and a chemical reason for this action.

Consider two bulbs containing argon (left) and oxygen (right) gases. After the stopcock is opened, the pressure of the combined gases is 1.08 atm. Calculate the volume of the right bulb. The temperature is kept at 20C. Assume ideal behavior. n 5 0.227 mol V 5 3.60 L n 5 0.144 mol V 5 ? Ar O2

Nitrogen dioxide (NO2) cannot be obtained in a pure form in the gas phase because it exists as a mixture of NO2 and N2O4. At 25C and 0.98 atm, the density of this gas mixture is 2.7 g/L. What is the partial pressure of each gas?

The Chemistry in Action essay on p. 208 describes the cooling of rubidium vapor to 5.0 3 1028 K. Calculate the root-mean-square speed and average kinetic energy of a Rb atom at this temperature.

Lithium hydride reacts with water as follows: LiH(s) 1 H2O(l) LiOH(aq) 1 H2(g) During World War II, U.S. pilots carried LiH tablets. In the event of a crash landing at sea, the LiH would react with the seawater and fill their life belts and lifeboats with hydrogen gas. How many grams of LiH are needed to fill a 4.1-L life belt at 0.97 atm and 12C?

The atmosphere on Mars is composed mainly of carbon dioxide. The surface temperature is 220 K and the atmospheric pressure is about 6.0 mmHg. Taking these values as Martian STP, calculate the molar volume in liters of an ideal gas on Mars

Venuss atmosphere is composed of 96.5 percent CO2, 3.5 percent N2, and 0.015 percent SO2 by volume. Its standard atmospheric pressure is 9.0 3 106 Pa. Calculate the partial pressures of the gases in pascals.

A student tries to determine the volume of a bulb like the one shown on p. 191. These are her results: Mass of the bulb filled with dry air at 23C and 744 mmHg 5 91.6843 g; mass of evacuated bulb 5 91.4715 g. Assume the composition of air is 78 percent N2, 21 percent O2, and 1 percent argon. What is the volume (in milliliters) of the bulb? (Hint: First calculate the average molar mass of air, as shown in Problem 3.152.)

Apply your knowledge of the kinetic theory of gases to the following situations. (a) Two flasks of volumes V1 and V2 (V2 . V1) contain the same number of helium atoms at the same temperature. (i) Compare the root-mean-square (rms) speeds and average kinetic energies of the helium (He) atoms in the flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (b) Equal numbers of He atoms are placed in two flasks of the same volume at temperatures T1 and T2 (T2 . T1). (i) Compare the rms speeds of the atoms in the two flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (c) Equal numbers of He and neon (Ne) atoms are placed in two flasks of the same volume, and the temperature of both gases is 74C. Comment on the validity of the following statements: (i) The rms speed of He is equal to that of Ne. (ii) The average kinetic energies of the two gases are equal. (iii) The rms speed of each He atom is 1.47 3 103 m/s.

It has been said that every breath we take, on average, contains molecules that were once exhaled by Wolfgang Amadeus Mozart (17561791). The following calculations demonstrate the validity of this statement. (a) Calculate the total number of molecules in the atmosphere. (Hint: Use the result in Problem 5.106 and 29.0 g/mol as the molar mass of air.) (b) Assuming the volume of every breath (inhale or exhale) is 500 mL, calculate the number of molecules exhaled in each breath at 37C, which is the body temperature. (c) If Mozarts life span was exactly 35 years, what is the number of molecules he exhaled in that period? (Given that an average person breathes 12 times per minute.) (d) Calculate the fraction of molecules in the atmosphere that was exhaled by Mozart. How many of Mozarts molecules do we breathe in with every inhalation of air? Round off your answer to one significant figure. (e) List three important assumptions in these calculations

At what temperature will He atoms have the same urms value as N2 molecules at 25C?

Estimate the distance (in nanometers) between molecules of water vapor at 100C and 1.0 atm. Assume ideal behavior. Repeat the calculation for liquid water at 100C, given that the density of water is 0.96 g/cm3 at that temperature. Comment on your results. (Assume water molecule to be a sphere with a diameter of 0.3 nm.) (Hint: First calculate the number density of water molecules. Next, convert the number density to linear density, that is, number of molecules in one direction.)

Which of the noble gases would not behave ideally under any circumstance? Why?

A relation known as the barometric formula is useful for estimating the change in atmospheric pressure with altitude. The formula is given by P 5 P0e2gmhyRT , where P and P0 are the pressures at height h and sea level, respectively, g is the acceleration due to gravity (9.8 m/s2 ), m is the average molar mass of air (29.0 g/mol), and R is the gas constant. Calculate the atmospheric pressure in atm at a height of 5.0 km, assuming the temperature is constant at 5C and P0 5 1.0 atm

A 5.72-g sample of graphite was heated with 68.4 g of O2 in a 8.00-L flask. The reaction that took place was C(graphite) 1 O2(g) CO2(g) After the reaction was complete, the temperature in the flask was 182C. What was the total pressure inside the flask?

An equimolar mixture of \(H_2\) and \(D_2\) effuses through an orifice (small hole) at a certain temperature. Calculate the composition (in mole fractions) of the gases that pass through the orifice. The molar mass of \(D_2\) is 2.014 g/mol.

A mixture of calcium carbonate (CaCO3) and magnesium carbonate (MgCO3) of mass 6.26 g reacts completely with hydrochloric acid (HCl) to generate 1.73 L of CO2 at 48C and 1.12 atm. Calculate the mass percentages of CaCO3 and MgCO3 in the mixture

A 6.11-g sample of a Cu-Zn alloy reacts with HCl acid to produce hydrogen gas. If the hydrogen gas has a volume of 1.26 L at 22C and 728 mmHg, what is the percent of Zn in the alloy? (Hint: Cu does not react with HCl.)

A stockroom supervisor measured the contents of a partially filled 25.0-gallon acetone drum on a day when the temperature was 18.0C and atmospheric pressure was 750 mmHg, and found that 15.4 gallons of the solvent remained. After tightly sealing the drum, an assistant dropped the drum while carrying it upstairs to the organic laboratory. The drum was dented and its internal volume was decreased to 20.4 gallons. What is the total pressure inside the drum after the accident? The vapor pressure of acetone at 18.0C is 400 mmHg. (Hint: At the time the drum was sealed, the pressure inside the drum, which is equal to the sum of the pressures of air and acetone, was equal to the atmospheric pressure.)

In 2.00 min, 29.7 mL of He effuse through a small hole. Under the same conditions of pressure and temperature, 10.0 mL of a mixture of CO and CO2 effuse through the hole in the same amount of time. Calculate the percent composition by volume of the mixture.

Referring to Figure 5.22, explain the following: (a) Why do the curves dip below the horizontal line labeled ideal gas at low pressures and then why do they arise above the horizontal line at high pressures? (b) Why do the curves all converge to 1 at very low pressures? (c) Each curve intercepts the horizontal line labeled ideal gas. Does it mean that at that point the gas behaves ideally?

A mixture of methane (CH4) and ethane (C2H6) is stored in a container at 294 mmHg. The gases are burned in air to form CO2 and H2O. If the pressure of CO2 is 356 mmHg measured at the same temperature and volume as the original mixture, calculate the mole fractions of the gases

Use the kinetic theory of gases to explain why hot air rises.

One way to gain a physical understanding of b in the van der Waals equation is to calculate the excluded volume. Assume that the distance of closest approach between two similar atoms is the sum of their radii (2r). (a) Calculate the volume around each atom into which the center of another atom cannot penetrate. (b) From your result in (a), calculate the excluded volume for 1 mole of the atoms, which is the constant b. How does this volume compare with the sum of the volumes of 1 mole of the atoms?

Use the van der Waals constants in Table 5.4 to estimate the radius of argon in picometers. (Hint: See Problem 5.160.)

Identify the gas whose root-mean-square speed is 2.82 times that of hydrogen iodide (HI) at the same temperature

A 5.00-mole sample of NH3 gas is kept in a 1.92-L container at 300 K. If the van der Waals equation is assumed to give the correct answer for the pressure of the gas, calculate the percent error made in using the ideal gas equation to calculate the pressure.

The root-mean-square speed of a certain gaseous oxide is 493 m/s at 20C. What is the molecular formula of the compound?

Referring to Figure 5.17, we see that the maximum of each speed distribution plot is called the most probable speed (ump) because it is the speed possessed by the largest number of molecules. It is given by ump 5 12RTym. (a) Compare ump with urms for nitrogen at 25C. (b) The following diagram shows the Maxwell speed distribution curves for an ideal gas at two different temperatures T1 and T2. Calculate the value of T2. 0 T1 5 300 K T2 5 ? Number of molecules Molecular speed (m/s) 500 1000 1500 2000

A gaseous reaction takes place at constant volume and constant pressure in a cylinder shown here. Which of the following equations best describes the reaction? The initial temperature (T1) is twice that of the final temperature (T2). (a) A 1 B C (b) AB C 1 D (c) A 1 B C 1 D (d) A 1 B 2C 1 D T1 T2

A gaseous hydrocarbon (containing C and H atoms) in a container of volume 20.2 L at 350 K and 6.63 atm reacts with an excess of oxygen to form 205.1 g of CO2 and 168.0 g of H2O. What is the molecular formula of the hydrocarbon?

Three flasks containing gases A (red) and B (green) are shown here. (i) If the pressure in (a) is 4.0 atm, what are the pressures in (b) and (c)? (ii) Calculate the total pressure and partial pressure of each gas after the valves are opened. The volumes of (a) and (c) are 4.0 L each and that of (b) is 2.0 L. The temperature is the same throughout. (a) (b) (c)

(a) Show that the pressure exerted by a fluid P (in pascals) is given by P 5 hdg, where h is the column of the fluid in meters, d is the density in kg/m3 , and g is the acceleration due to gravity (9.81 m/s2 ). (Hint: See Appendix 2.) (b) The volume of an air bubble that starts at the bottom of a lake at 5.24C increases by a factor of 6 as it rises to the surface of water where the temperature is 18.73C and the air pressure is 0.973 atm. The density of the lake water is 1.02 g/cm3 . Use the equation in (a) to determine the depth of the lake in meters.

A student first measured the total pressure of a mixture of gases methane (CH4), ethane (C2H6), and propane (C3H8) at a certain temperature, which turned out to be 4.50 atm. She then recorded the mass spectra of the gases shown here. Calculate the partial pressure of the gases. 0 0 Intensity of peaks (arbitrary units) Molecular mass (amu) 10 20 30 40 50 1 2 3 4 5

In 2012, Felix Baumgartner jumped from a balloon roughly 24 mi above Earth, breaking the record for the highest skydive. He reached speeds of more than 700 miles per hour and became the first skydiver to exceed the speed of sound during free fall. The helium-filled plastic balloon used tocarry Baumgartner to the edge of space was designed to expand to 8.5 3 108L in order to accommodate the low pressures at the altituderequired to break the record. (a) Calculate the mass of helium in the balloon from the conditions at the time of the jump (8.5 3 108 L, 267.8C,0.027 mmHg). (b) Determine the volume of the helium in the balloon just before it was released,assuming a pressure of 1.0 atm and a tempera tureof 23C.

Which of the following has a greater mass: a sample of air of volume V at a certain temperature T and pressure P or a sample of air plus water vapor having the same volume and at the same temperature and pressure?

A flask with a volume of 14.5 L contains 1.25 moles of helium gas. Estimate the average distance between He atoms in nanometers.

Hyperbaric oxygen therapy (HBOT) is very effective in treating burns, crush injuries that impede blood flow, and tissue-damaging infections, as well as carbon monoxide poisoning. However, it has generated some controversy in its application to other maladies (for example, autism, multiple sclerosis). A typical oxygen hyperbaric chamber is shown here. HBOT can be administered using pressure up to six atmospheres, but lower pressures are more common. (a) If this chamber was pressurized to 3.0 atm with pure oxygen, how many moles of O2 would be contained in an empty chamber? (b) Given that a full tank of oxygen contains about 2500 moles of the gas, how many times could the chamber be filled with a single tank of oxygen?

(a) Fluorescent lightbulbs contain a small amount of mercury, giving a mercury vapor pressure of around 1 3 1025 atm. When excited electrically, the Hg atoms emit UV light, which excites the phosphor coating of the inner tube, which then emits visible (white) light. Estimate the mass of Hg vapor present in the type of long, thin fluorescent tubes used in offices. (b) Ordinary tungsten incandescent lightbulbs used in households are filled with argon gas at about 0.5 atm to retard the sublimation of the tungsten filament. Estimate the number of moles of Ar in a typical lightbulb

(a) Estimate the volume of air at 1.0 atm and 22C needed to fill a bicycle tire to a pressure of 5.0 atm at the same temperature. (Note that the 5.0 atm is the gauge pressure, which is the difference between the pressure in the tire and atmospheric pressure.) (b) The tire is pumped by filling the cylinder of a hand pump with air at 1.0 atm and then, by compressing the gas in the cylinder, adding all the air in the pump to the air in the tire. If the volume of the pump is 33 percent of the tires volume, what is the gauge pressure in the tire after three full strokes of the pump?

On October 15, 2009, a homemade helium balloon was released, and for a while authorities were led to believe that a 6-year-old boy had been carried away in the balloon. (The incident was later revealed to be a hoax.) The balloon traveled more than 50 mi and reached a height of 7000 ft. The shape and span of the balloon are shown in the figure. How much weight could this balloon lift? (A helium balloon can lift a mass equal to the difference in the mass of air and the mass of helium that would be contained in the balloon.) Could it actually lift a 6-year-old boy? 20 ft