Chapter 5 Study Guide
Standard Temperature And Pressure
STP: 0*C (273.15 K) and 1 atm (760 torr)
By what factor would a scuba diver's lungs expand if she ascended rapidly to the surface from a depth of 125 ft without inhaling or exhaling? If an expansion factor greater than 1.5 causes lung rupture, how far could she safely ascend from 125 ft without breathing? Assume constant temperature. (d of seawater = 1.04 g/mL; d of Hg = 13.5 g/mL)
The lungs would expand by a factor of 4.86. The diver can safely ascend 52.5 ft to a depth of 73 ft.
Atmosphere
The mixture of gases that extends from a planet's surface and eventually merges with outer space. The gaseous region of Earth's crust.
Kinetic-Molecular Theory
The model that explains macroscopic gas behavior in terms of particles in random motion whose volumes and interactions are negligible.
Diffusion
The movement of one fluid through another.
Partial Pressure
The portion of the total pressure contributed by a gas in a mixture of gases.
Effusion
The process by which a gas escapes from its container through a tiny hole into an evacuated space.
Standard Temperature And Pressure (STP)
The reference conditions for a gas: 0*C (273.15 K) and 1 atm (760 torr).
RMS (Root-Mean-Square) Speed (URMS)
The speed of a molecule having the average kinetic energy. Very close to the most probable speed.
Standard Molar Volume
The volume of 1 mol of an ideal gas at standard temperature and pressure: 22.4141 L.
How does a sample of gas differ in its behavior from a sample of liquid in each of the following situations? The sample is heated in an expandable container, but no change of state occurs.
The volume of the container holding the gas sample increases when heated, but the volume of the container holding the liquid sample remains essentially constant when heated.
How does a sample of gas differ in its behavior from a sample of liquid in each of the following situations? The sample is transferred from one container to a larger one.
The volume of the liquid remains constant, but the volume of the gas increases to the volume of the larger container.
How does a sample of gas differ in its behavior from a sample of liquid in each of the following situations? The sample is placed in a cylinder with a piston, and an external force is applied.
The volume of the liquid remains essentially constant, but the volume of the gas is reduced.
Three 5-L flasks, fixed with pressure gauges and small valves, each contain 4 g of gas at 273 K. Flask A contains H2, flask B contains He, and flask C contains CH4. Rank the flask contents in terms of total kinetic energy of the particles.
Total EA > Total EB > Total EC.
Boyle's Law
V is proportional to (1)/(P) or PV = constant [T and n fixed]
Charles's Law
V is proportional to T or (V)/(T) = constant [P and n fixed]
Avogadro's Law
V is proportional to n or (V)/(n) = constant [P and T fixed]
What is the effect of the following on the volume of 1 mol of an ideal gas? Temperature decreases from 800 K to 400 K (at constant P).
Volume decreases by a factor of 2.
What is the effect of the following on the volume of 1 mol of an ideal gas? Pressure increases from 2 atm to 6 atm (at constant T).
Volume decreases by a factor of 3.
What is the effect of the following on the volume of 1 mol of an ideal gas? The pressure is tripled (at constant 7).
Volume decreases to one-third of the original volume.
What is the effect of the following on the volume of 1 mol of an ideal gas? Temperature increases from 250*C to 500*C (at constant P).
Volume increases by a factor of 1.48.
What is the effect of the following on the volume of 1 mol of an ideal gas? The absolute temperature is increased by a factor of 3.0 (at constant P).
Volume increases by a factor of 3.0.
What is the effect of the following on the volume of 1 mol of an ideal gas? Three more moles of the gas is added (at constant P and T).
Volume increases by a factor of 4.
For each of the following, which shows the greater deviation from ideal behavior at the same set of conditions? Explain. Water vapor or methane.
Water vapor.
For each of the following, which shows the greater deviation from ideal behavior at the same set of conditions? Explain. Water vapor or neon.
Water vapor.
For each of the following, which shows the greater deviation from ideal behavior at the same set of conditions? Explain. Argon or xenon.
Xenon.
A gas-filled weather balloon with a volume of 65.0 L is released at sea-level conditions of 745 torr and 25*C. The balloon can expand to a maximum volume of 835 L. When the balloon rises to an altitude at which the temperature is -5*C and the pressure is 0.066 atm, will it have expanded to its maximum volume?
Yes.
Three 5-L flasks, fixed with pressure gauges and small valves, each contain 4 g of gas at 273 K. Flask A contains H2, flask B contains He, and flask C contains CH4. Rank the flask contents in terms of density.
dA = dB = dC.
Rearranging The Ideal Gas Law To Find Molar Mass
n = (m)/(M) = (PV)/(RT) so M = (mRT)/(PV)
RMS Speed As A Function Of Molar Mass And Temperature
urms = sqr rt of (3RT)/(M)
Van Der Waals Equation To Find The Pressure Or Volume Of A Gas Under Extreme Conditions
(P + (n^2a)/(V^2)) (V - nb) = nRT
Graham's Law Of Effusion
(RateA)/(RateB) = (sqr rt of MB)/(sqr rt of MA) = sqr rt of (MB)/(MA)
A sample of sulfur hexafluoride gas occupies 9.10 L at 198*C. Assuming that the pressure remains constant, what temperature (in *C) is needed to reduce the volume to 2.50 L?
-144*C.
At 1450. mmHg and 286 K, a skin diver exhales a 208-mL bubble of air that is 77% N2, 17% O2, and 6.0% CO2 by volume. How many moles of N2 are in the bubble?
0.013 mol N2.
Aluminum reacts with excess hydrochloric acid to form aqueous aluminum chloride and 35.8 mL of hydrogen gas over water at 27*C and 751 mmHg. How many grams of aluminum react?
0.0249 g Al.
Popcorn pops because the horny endosperm, a tough, elastic material, resists gas pressure within the heated kernel until the pressure reaches explosive force. A 0.25-mL kernel has a water content of 1.6% by mass, and the water vapor reaches 170*C and 9.0 atm before the kernel ruptures. Assume that water vapor can occupy 75% of the kernel's volume. What is the mass (in g) of the kernel?
0.052 g.
A sample of chlorine gas is confined in a 5.0-L container at 328 torr and 37*C. How many moles of gas are in the sample?
0.085 mol Cl2
Xenon hexafluoride was one of the first noble gas compounds synthesized. The solid reacts rapidly with the silicon dixoxide in glass or quartz containers to form liquid XeOF4 and gaseous silicon tetrafluoride. What is the pressure in a 1.00-L container at 25*C after 2.00 g of xenon hexafluoride reacts? (Assume that silicon tetrafluoride is the only gas present and that it occupies the entire volume).
0.0997 atm.
An environmental chemist sampling industrial exhaust gases from a coal-burning plant collects a CO2-SO2-H2O mixture in a 21-L steel tank until the pressure reaches 850. torr at 45*C. How many moles of gas are collected?
0.90 mol.
Popcorn pops because the horny endosperm, a tough, elastic material, resists gas pressure within the heated kernel until the pressure reaches explosive force. A 0.25-mL kernel has a water content of 1.6% by mass, and the water vapor reaches 170*C and 9.0 atm before the kernel ruptures. Assume that water vapor can occupy 75% of the kernel's volume. How many milliliters would this amount of water vapor occupy at 25*C and 1.00 atm?
1.1 mL.
You have 357 mL of chlorine trifluoride gas at 699 mmHg and 45*C. What is the mass (in g) of the sample?
1.16 g ClF3.
Convert the following: 992 torr to bar
1.32 bar.
After 0.600 L of Ar at 1.20 atm and 227*C is mixed with 0.200 L of O2 at 501 torr and 127*C in a 400-mL flask at 27*C, what is the pressure in the flask?
1.33 atm.
In preparation for a combustion demonstration, a professor fills a balloon with equal molar amounts of H2 and O2, but the demonstration has to be postponed until the next day. During the night, both gases leak through pores in the balloon. If 35% of the H2 leaks, what is the O2/H2 ratio in the balloon the next day?
1.4.
An atmospheric chemist studying the pollutant SO2 places a mixture of SO2 and O2 in a 2.00-L container at 800. K and 1.90 atm. When the reaction occurs, gaseous SO3 forms, and the pressure falls to 1.65 atm. How many moles of SO3 form?
1.52 x 10^-2 mol SO3.
How many moles of gaseous arsine (AsH3) occupy 0.0400 L at STP?
1.78 x 10^-3 mol AsH3.
A weather balloon is filled with helium to a volume of 1.61 L at 734 torr. What is the volume of the balloon after it has been released and its pressure has dropped to 0.844 atm? Assume that the temperature remains constant.
1.84 L.
Canadian chemists have developed a modern variation of the 1899 Mond process for preparing extremely pure metallic nickel. A sample of impure nickel reacts with carbon monoxide at 50*C to form gaseous nickel carbonyl, Ni(CO)4. How many grams of nickel can be converted to the carbonyl with 3.55 m^3 of CO at 100.7 kPa?
1.95 x 10^3 g Ni.
Convert the following: 804 mmHg to kPa
107 kPa.
What is the ratio of effusion rates for the lightest gas, H2, and the heaviest known gas, UF6?
13.21
At a given pressure and temperature, it takes 4.85 min for a 1.5-L sample of He to effuse through a membrane. How long does it take for 1.5 L of F2 to effuse under the same conditions?
14.9 min.
A large portion of metabolic energy arises from the biological combustion of glucose: C6H12O6 (s) + 6O2 (g) -> 6CO2 (g) + 6H2O (g) If this reaction is carried out in an expandable container at 37*C and 780 torr, what volume of CO2 is produced from 20.0 g of glucose and excess O2?
16.5 L CO2.
A mixture of CO2 and Kr weighs 35.0 g and exerts a pressure of 0.708 atm in its container. Since Kr is expensive, you wish to recover it from the mixture. After the CO2 is completely removed by absorption with NaOH (s), the pressure in the container is 0.250 atm. How many grams of CO2 were originally present? How many grams of Kr can you recover?
17.2 g CO2. 17.8 g Kr.
Chlorine is produced from sodium chloride by the electrochemical chlor-alkali process. During the process, the chlorine is collected in a container that is isolated from the other products to prevent unwanted (and explosive) reactions. If a 15.50-L container holds 0.5950 kg of Cl2 gas at 225*C, calculate: PVDW (use R = 0.08206 (atm x L)/(mol x K))
20.9 atm.
Chlorine is produced from sodium chloride by the electrochemical chlor-alkali process. During the process, the chlorine is collected in a container that is isolated from the other products to prevent unwanted (and explosive) reactions. If a 15.50-L container holds 0.5950 kg of Cl2 gas at 225*C, calculate: PIGL
22.1 atm.
A gas cylinder is filled with argon at a pressure of 177 atm and 25*C. What is the gas pressure when the temperature of the cylinder and its contents are heated to 195*C by exposure to fire?
278 atm.
"Strike anywhere" matches contain the compound tetraphosphorus trisulfide, which burns to form tetraphosphorus decoxide and sulfur dioxide gas. How many milliliters of sulfur dioxide, measured at 725 torr and 32*C, can be produced from burning 0.800 g of tetraphosphorus trisulfide?
286 mL SO2.
What is the density of gaseous arsine?
3.48 g/L.
Canadian chemists have developed a modern variation of the 1899 Mond process for preparing extremely pure metallic nickel. A sample of impure nickel reacts with carbon monoxide at 50*C to form gaseous nickel carbonyl, Ni(CO)4. The carbonyl is then decomposed at 21 atm and 155*C to pure (>99.95%) nickel. How many grams of nickel are obtained per cubic meter of the carbonyl?
3.5 x 10^4 g Ni.
Convert the following: 365 kPa to atm
3.60 atm.
From the relative rates of effusion of 235 UF6 and 238 UF6, find the number of steps needed to produce a sample of the enriched fuel used in many nuclear reactors, which is 3.0 mole % 235 U. The natural abundance of 235 U is 0.72%.
332 steps.
A sample of Freon-12 (CF2Cl2) occupies 25.5 L at 298 K and 153.3 kPa. Find its volume at STP.
35.3 L.
Nitrogen dioxide is used industrially to produce nitric acid, but it contributes to acid rain and photochemical smog. What volume (in L) of nitrogen dioxide is formed at 735 torr and 28.2*C by reacting 4.95cm^3 of copper (d = 8.95 g/cm^3) with 230.0 mL of nitric acid (d = 1.42 g/cm^3, 68.0% HNO3 by mass)? Cu (s) + 4HNO3 (aq) -> Cu(NO3)2 (aq) + 2NO2 (g) + 2H2O (l)
35.7 L NO2.
How many grams of phosphorus react with 35.5 L of O2 at STP to form tetraphosphorus decoxide? P4 (s) + 5O2 (g) -> P4O10 (s)
39.2 g P4
What is the density of Xe gas at STP?
5.86 g/L.
Calculate the molar mass of a gas at 388 torr and 45*C if 206 ng occupies 0.206 uL.
51.1 g/mol.
Convert the following: 0.745 atm to mmHg
566 mmHg.
Dilute aqueous hydrogen peroxide is used as a bleaching agent and for disinfecting surfaces and small cuts. Its concentration is sometimes given as a certain number of "volumes hydrogen peroxide," which refers to the number of volumes of O2 gas, measured at STP, that a given volume of hydrogen peroxide solution will release when it decomposes to O2 and liquid H2O. How many grams of hydrogen peroxide are in 0.100 L of "20 volumes hydrogen peroxide" solution?
6.07 g H2O2.
A barometer tube is 1.00 x 10^2 cm long and has a cross-sectional area of 1.20 cm^2. The height of the mercury column is 74.0 cm, and the temperature is 24*C. A small amount of N2 is introduced into the evacuated space above the mercury, which causes the mercury level to drop to a height of 64.0 cm. How many grams of N2 were introduced?
6.53 x 10^-3 g N2.
An environmental chemist sampling industrial exhaust gases from a coal-burning plant collects a CO2-SO2-H2O mixture in a 21-L steel tank until the pressure reaches 850. torr at 45*C. If the SO2 concentration in the mixture is 7.95 x 10^3 parts per million by volume (ppmv), what is its partial pressure? [Hint: ppmv = (volume of component/volume of mixture) x 10^6.]
6.76 torr.
Hemoglobin is the protein that transports O2 through the blood from the lungs to the rest of the body. To do so, each molecule of hemoglobin combines with four molecules of O2. If 1.00 g of hemoglobin combines with 1.53 mL of O2 at 37*C and 743 torr, what is the molar mass of hemoglobin?
6.81 x 10^4 g/mol.
A balloon filled with 1.92 g of helium has a volume of 12.5 L. What is the balloon's volume after 0.850 g of helium has leaked out through a small hole (assume constant pressure and temperature)?
6.95 L.
Canadian chemists have developed a modern variation of the 1899 Mond process for preparing extremely pure metallic nickel. A sample of impure nickel reacts with carbon monoxide at 50*C to form gaseous nickel carbonyl, Ni(CO)4. The released carbon monoxide is cooled and collected for reuse by passing it through water at 35*C. If the barometric pressure is 769 torr, what volume (in m^3) of CO is formed per cubic meter of carbonyl?
63 m^3 CO.
A gaseous organic compound containing only carbon, hydrogen, and nitrogen is burned in oxygen gas, and the volume of each reactant and product is measured under the same conditions of temperature and pressure. Reaction of four volumes of the compound produces 4 volumes of CO2, 2 volumes of N2, and 10 volumes of water vapor. How many volumes of O2 were required?
9 volumes of O2.
On a cool, rainy day, the barometric pressure is 730 mmHg. Calculate the barometric pressure in centimeters of water (cmH2O). (d of Hg = 13.5 g/mL; d of H2O = 1.00 g/mL)
990 cmH2O
Mole Fraction (X)
A concentration term expressed as the ratio of number of moles of solute to the total number of moles (solute plus solvent).
Barometer
A device used to measure atmospheric pressure. Most commonly, a tube open at one end, which is filled with mercury and inverted into a dish of mercury.
Manometer
A device used to measure the pressure of a gas in a laboratory experiment.
Graham's Law Of Effusion
A gas law stating that the rate of effusion of a gas is inversely proportional to the square root of its density (or molar mass): rate is proportional to (1)/(sqr. root of M)
Dalton's Law Of Partial Pressures
A gas law stating that, in a mixture of unreacting gases, the total pressure is the sum of the partial pressures of the individual gases: Ptotal = P1 + P2 + P3 + ...
Ideal Gas
A hypothetical gas that exhibits linear relationships among volume, pressure, temperature, and amount (mol) at all conditions. Approximated by simple gases at ordinary conditions.
Universal Gas Constant (R)
A proportionality constant that relates the energy, amount of substance, and temperature of a system. R = 0.0820578 (atm x L)/(mol x K) = 8.31447 (J)/(mol x K)
Millimeter Of Mercury (mmHg)
A unit of pressure based on the difference in the heights of mercury in a barometer or manometer. Renamed the torr in honor of Torricelli.
Torr
A unit of pressure identical to 1 mmHg.
Aluminum chloride is easily vaporized above 180*C. The gas escapes through a pinhole 0.122 times as fast as helium at the same conditions of temperature and pressure in the same apparatus. What is the molecular formula of aluminum chloride gas?
Al2Cl6.
Van Der Waals Equation
An equation that accounts for the behavior of real gases.
Ideal Gas Law/Ideal Gas Equation
An equation that expresses the relationships among volume, pressure, temperature, and amount (mol) of an ideal gas: PV = nRT.
Does N2 behave more ideally at 1 atm or at 500 atm? Explain.
At 1 atm. At lower pressures, the gas molecules are farther apart and intermolecular forces are less important.
How does the kinetic-molecular theory explain why 1 mol of krypton and 1 mol of helium have the same volume at STP?
At STP, the volume occupied by a mole of any gas is the same. At the same temperature, all gases have the same average kinetic energy, resulting in the same pressure.
Boyle's law relates gas volume to pressure, and Avogadro's law relates gas volume to amount (mol). State a relationship between gas pressure and amount (mol).
At constant temperature and volume, the pressure of a gas is directly proportional to number of moles of the gas.
To collect a beaker of H2 gas by displacing the air already in the beaker, would you hold the beaker upright or inverted? Why? How would you hold the beaker to collect CO2?
Beaker is inverted to collect H2 and upright for CO2. The molar mass of CO2 is greater than the molar mass of air, which, in turn, has a greater molar mass than H2.
Three 5-L flasks, fixed with pressure gauges and small valves, each contain 4 g of gas at 273 K. Flask A contains H2, flask B contains He, and flask C contains CH4. Rank the flask contents in terms of collision frequency.
Collision frequency in A > collision frequency in B > collision frequency in C.
Three 5-L flasks, fixed with pressure gauges and small valves, each contain 4 g of gas at 273 K. Flask A contains H2, flask B contains He, and flask C contains CH4. Rank the flask contents in terms of average kinetic energy of the particles.
EA = EB = EC.
Van Der Waals Constants
Experimentally determined positive numbers used in the van der Waals equation to account for the interparticle attractions and particle volume of real gases.
For each of the following, which shows the greater deviation from ideal behavior at the same set of conditions? Explain. Mercury vapor or radon.
Mercury vapor.
The lunar surface reaches 370 K at midday. The atmosphere consists of neon, argon, and helium at a total pressure of only 2 x 10^-14 atm. Calculate the rms speed of each component in the lunar atmosphere. [Use R = 8.314 J/(mol x K) and express M in kg/mol].
Ne, 676 m/s. Ar, 481 m/s. He, 1.52 x 10^3 m/s.
Do interparticle attractions cause negative or positive deviations from the PV/RT ratio of an ideal gas? Use Table 5.3 to rank Kr, CO2, and N2 in order of increasing magnitude of these deviations.
Negative deviations. N2 < Kr < CO2.
Amontons's Law
P is proportional to T or (P)/(T) = constant [V and n fixed]
Relating Partial Pressure To Mole Fraction
PA = XA x Ptotal
Three 5-L flasks, fixed with pressure gauges and small valves, each contain 4 g of gas at 273 K. Flask A contains H2, flask B contains He, and flask C contains CH4. Rank the flask contents in terms of pressure.
PA > PB > PC.
A large portion of metabolic energy arises from the biological combustion of glucose: C6H12O6 (s) + 6O2 (g) -> 6CO2 (g) + 6H2O (g) If the reaction is carried out at the same conditions with the stoichiometric amount of O2, what is the partial pressure of each gas when the reaction is 50% complete (10.0 g of glucose remains)?
PH2O = 48.8 torr. PO2 = PCO2 = 3.7 x 10^2 torr.
Rearranging The Ideal Gas Law To Find Gas Density
PV = (m)/(M)RT so (m)/(V) = d = (P x M)/(RT)
Ideal Gas Law
PV = nRT and (P1V1)/(n1T1) = (P2V2)/(n2T2)
When gaseous F2 and solid I2 are heated to high temperatures, the I2 sublimes and gaseous iodine heptafluoride forms. If 350. torr of F2 and 2.50 g of solid I2 are put into a 2.50-L container at 250. K and the container is heated to 550 K, what is the final pressure (in torr)? What is the partial pressure of I2 gas?
Ptotal = 245 torr. PI2 = 25.2 torr
Dalton's Law Of Partial Pressures
Ptotal = P1 + P2 + P3 + ...
The Value Of R
R = (PV)/(nT) = (1 atm x 22.4141 L)/(1 mol x 273.15 K) = 0.082058 (atm x L)/(mol x K) = 0.0821 (atm x L)/(mol x K) [3 sf]
Three 5-L flasks, fixed with pressure gauges and small valves, each contain 4 g of gas at 273 K. Flask A contains H2, flask B contains He, and flask C contains CH4. Rank the flask contents in terms of diffusion rate after the valve is opened.
RateA > RateB > Rate C.
White phosphorus melts and then vaporizes at high temperatures. The gas effuses at a rate that is 0.404 times that of neon in the same apparatus under the same conditions. How many atoms are in a molecule of gaseous white phosphorus?
4 atoms per molecule.
At 1450. mmHg and 286 K, a skin diver exhales a 208-mL bubble of air that is 77% N2, 17% O2, and 6.0% CO2 by volume. What would the volume (in mL) of the bubble be if it were exhaled at the surface at 1 atm and 298 K?
4 x 10^2 mL.
How many grams of phosphine (PH3) can form when 37.5 g of phosphorus and 83.0 L of hydrogen gas react at STP? P4 (s) + H2 (g) -> PH3 (g) [unbalanced]
41.2 g PH3
A sample of a liquid hydrocarbon known to consist of molecules with five carbon atoms is vaporized in a 0.204-L flask by immersion in a water bath at 101*C. The barometric pressure is 767 torr, and the remaining gas weighs 0.482 g. What is the molecular formula of the hydrocarbon?
C5H12.
A gaseous organic compound containing only carbon, hydrogen, and nitrogen is burned in oxygen gas, and the volume of each reactant and product is measured under the same conditions of temperature and pressure. Reaction of four volumes of the compound produces 4 volumes of CO2, 2 volumes of N2, and 10 volumes of water vapor. What is the empirical formula of the compound?
CH5N.
The Volume Of 1 Mol Of An Ideal Gas At STP
Standard molar volume = 22.4141 L or 22.4 L [to 3 sf]
Pascal (Pa)
The SI unit of pressure. 1 Pa = 1 (N)/(m^2).
Standard Atmosphere (ATM)
The average atmospheric pressure measured at sea level and 0*C, defined as 1.01325 x 10^5 Pa.
Mean Free Path
The average distance a particle travels between collisions at a given temperature and pressure.
Collision Frequency
The average number of collisions per second that a particle undergoes.
Pressure (P)
The force exerted per unit of surface area.
Charles's Law
The gas law stating that, at constant pressure, the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature: V is proportional to T.
Boyle's Law
The gas law stating that, at constant temperature and amount of gas, the volume occupied by a gas is inversely proportional to the applied (external) pressure: V is proportional to (1)/(P)
Avogadro's Law
The gas law stating that, at fixed temperature and pressure, equal volumes of any ideal gas contain equal numbers of particles, and, therefore, the volume of a gas is directly proportional to its amount (mol). V is proportional to n.