gases dr. ron rusay spring 2008 © copyright 2008 r.j. rusay

GasesGases

Dr. Ron RusayDr. Ron Rusay

Spring 2008Spring 2008

© Copyright 2008 R.J. Rusay© Copyright 2008 R.J. Rusay

GasesGases

Uniformly fill any container.Uniformly fill any container. Exert pressure on its surroundings. Exert pressure on its surroundings. Mix completely with other gasesMix completely with other gases

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Gases: Gases: Pressure, Mass, Volume, TemperaturePressure, Mass, Volume, Temperature

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PressurePressure

is equal to force/unit areais equal to force/unit area SI units = Newton/meterSI units = Newton/meter22 = 1 Pascal = 1 Pascal

(Pa)(Pa) 1 standard atmosphere = 101,325 Pa1 standard atmosphere = 101,325 Pa 1 standard atmosphere = 1 atm =1 standard atmosphere = 1 atm =

760 mm Hg = 760 torr760 mm Hg = 760 torr

QUESTIONQUESTIONFour bicycle tires are inflated to the following pressures. Which one has the highest pressure? Tire A 3.42 atm; Tire B 48 lbs/sq in; Tire C 305 kPa; Tire D 1520 mmHg. (Recall; 1.00 atm = 760 mmHg = 14.7 lb/sq in = 101.3 kPa)

1. Tire A2. Tire B3. Tire C4. Tire D

ANSWERANSWERChoice 1 Even though it has the smallest number, it represents the highest pressure of the four. When all four are changed to a common label (use conversion factors found on page 181 and dimensional analysis) 3.42 atm is a higher pressure than the others.

Section 5.1: Pressure

Toricellian BarometerToricellian Barometer05_47

h = 760mm Hgfor standardatmosphere Vacuum

Pressure & VolumePressure & VolumeBoyle’s LawBoyle’s Law**

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Boyle’s LawBoyle’s Law**

Pressure Pressure Volume = Constant Volume = Constant (T = constant)(T = constant)

PP11VV11 = P = P22VV22 (T = constant) (T = constant) V V 1/ P (T = constant) 1/ P (T = constant)

((**Holds Holds preciselyprecisely only at very low only at very low pressures.)pressures.)

Changing VolumeChanging Volume

A) 4.0 LA) 4.0 LB) 0.57 LB) 0.57 LC) 5.7 LC) 5.7 LD) 0.4 LD) 0.4 L

Pressure vs. VolumePressure vs. Volume

05_50

0V(in3)20406050100PP2V2V(a)

00 1/P (in Hg)0.010.020.032040slope = k

(b)

Definition: A gas that Definition: A gas that strictly obeys strictly obeys Boyle’s Boyle’s Law is called an Law is called an ideal gasideal gas..

Ideal GasesIdeal GasesReal vs. “Ideal”Real vs. “Ideal”

Temperature & Volume Temperature & Volume

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Temperature & VolumeTemperature & Volume

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Charles’s LawCharles’s Law

The volume of a gas is directly The volume of a gas is directly proportional to temperature, and proportional to temperature, and extrapolates to zero at zero Kelvin.extrapolates to zero at zero Kelvin.

V = V = T (P = constant)T (P = constant)

= a proportionality constant= a proportionality constant

Temperature and VolumeTemperature and Volume (@ constant P)(@ constant P)

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Charles’s LawCharles’s LawVTVTP1122==(constant)

Pressure vs. TemperaturePressure vs. Temperature (@ constant V)(@ constant V)

05_1542Pext Pext

Temperature is increasedChanging VolumeChanging Volume

The Meaning of TemperatureThe Meaning of Temperature

Kelvin temperature is an index of the random Kelvin temperature is an index of the random motions of gas particles (higher T means greater motions of gas particles (higher T means greater motion.)motion.)

(KE)32avg=RT

QUESTIONQUESTIONKinetic molecular theory helps explain the definition of temperature based on molecular motion. Which statement describes an important aspect of this connection?

1. Temperature is inversely related to the kinetic energy of thegas particles.

2. At the same temperature, more massive gas particles will bemoving faster than less massive gas particles.

3. As the temperature of a gas sample increases, the average velocity of the gas particles increases.

4. Kinetic energy is directly related to temperature. This is validfor any units of temperature.

ANSWERANSWERChoice 3 states a correct connection between temperature and velocity. The important relationship is summarized in the following equation: ½ mass velocity2 = 3/2 RT (T must be in K).

Section 5.6: The Kinetic Molecular Theory of Gases

Kinetic Molecular TheoryKinetic Molecular Theory

1.1. Volume of individual particles is Volume of individual particles is zero.zero.

2.2. Collisions of particles with container Collisions of particles with container walls cause pressure exerted by gas.walls cause pressure exerted by gas.

3.3. Particles exert no forces on each Particles exert no forces on each other.other.

4.4. Average kinetic energy Average kinetic energy Kelvin Kelvin temperature of a gas.temperature of a gas.

Molecular Motion / TheoryMolecular Motion / TheoryThe Meaning of TemperatureThe Meaning of Temperature

Temperature (Kelvin) is an index of the random motions of gas particles (higher T means greater motion.)(KE)32avg=RT


Velocity & TemperatureVelocity & Temperature

QUESTIONQUESTIONWhy is it critical that the temperature be held constant when applying Boyle’s law to changing the pressure of a trapped gas?

1. Gas molecules may expand at higher temperatures; this wouldchange the volume.

2. Changing the temperature causes the gas to behave in non-idealfashion.

3. Changing the temperature affects the average particle speed,which could affect the pressure.

4. Allowing the temperature to drop below 0°C would cause thetrapped gas to no longer follow Boyle’s Law.

ANSWERANSWERChoice 3 provides the connection between temperature and pressure that would introduce another variable when studying the pressure-volume relationship. Boyle’s law shows that if the molecules of a trapped gas maintain the same average velocity when their volume is changed, the pressure will be inversely related to the volume change.

Section 5.2: The Gas Laws of Boyle, Charles, and Avogadro

QUESTIONQUESTIONAs the temperature of a gas increases, which statement best correlates to information about molecular velocity?

1. The average molecular velocity will increase, but thedistribution of molecular velocities will stay the same.

2. The average molecular velocity will stay the same, but themolecular velocity distribution will spread.

3. The average molecular velocity will increase, and thedistribution of the molecular velocities will spread.

4. The average molecular velocity will stay the same, and thedistribution of the molecular velocities will stay the same.

ANSWERANSWERChoice 3 accurately reflects the connection between molecular velocity and an increase in temperature. Figure 5.21 on page 206 visually shows the relationship. Kelvin temperature is directly related to molecular velocity - with greater temperature the distribution of available velocities also increases.

Section 5.6: The Kinetic Molecular Theory of Gases

View Gas Molecules AppletView Gas Molecules Applethttp://chemconnections.llnl.govJava/molecules/index.html

View Molecular Vibrations: IRGasTutorhttp://chemistry.beloit.edu/Warming/pages/infrared.html

Changes in Temperature Changes in Temperature ((PV&T)PV&T)05_1543

PextPext

Energy (heat) added

Pressure, Volume & TemperaturePressure, Volume & Temperature

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An empty one gallon can An empty one gallon can is hooked to a vacuum is hooked to a vacuum

pump. pump.

What do you expect to What do you expect to happen? happen?

Explain why the Explain why the can collapsed. can collapsed.

V1

An Ideal gasin a cylinder

V2 = 1/ 2 V1

Something(s) happen(s)

What can be going on?

Provide 3 different sets of conditions Provide 3 different sets of conditions (Pressure and Temperature) which can (Pressure and Temperature) which can

account for the volume of the gas account for the volume of the gas decreasing by 1/2.decreasing by 1/2.

Cases 1-3 in the handout.Cases 1-3 in the handout.

Applying a Gas LawApplying a Gas Law

Avogadro’s LawAvogadro’s Law

For a gas at constant temperature For a gas at constant temperature and pressure, the volume is directly and pressure, the volume is directly proportional to the number of moles of proportional to the number of moles of gas (at low pressures).gas (at low pressures).

VV = = nn

= proportionality constant= proportionality constant V = volume of the gasV = volume of the gas n = number of moles of gasn = number of moles of gas

Volume vs. n (moles of a gas)Volume vs. n (moles of a gas)

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QUESTIONQUESTIONEach of the balloons hold 1.0 L of different gases. All four are at 25°C and each contains the same number of molecules. Of the following which would also have to be the same for each balloon? (obviously not their color)

1. Their density2. Their mass3. Their atomic numbers4. Their pressure

ANSWERANSWERChoice 4 is consistent with Avogadro’s Law. The temperature, pressure, number of moles, and volume are related for a sample of trapped gas. If two samples have three variables out of the four the same, the fourth variable must be the same as well.


Ideal Gas LawIdeal Gas Law

An An equation of state equation of state for a gas.for a gas. ““state” is the condition of the gas at a given state” is the condition of the gas at a given

time.time. PV = nRTPV = nRT

[Consider] If the moles remain constant and [Consider] If the moles remain constant and conditions change then:conditions change then:

PP11VV11/ T/ T11 = P = P22VV22/ T/ T22

QUESTIONQUESTIONIf a person exhaled 125 mL of CO2 gas at 37.0°C and 0.950 atm of pressure, what would this volume be at a colder temperature of 10.0°C and 0.900 atm of pressure?

1. 3.12 mL2. 0.130 L3. 0.120 L4. 22.4 L

ANSWERANSWERChoice 3 correctly accounts for the changing conditions. The combination of Charles and Boyle’s laws provides the mathematical basis for the calculation. After converting the temperature to K units, the equation P1V1/T1 = P2V2/T2 may be used by solving for V2.

Section 5.3: The Ideal Gas Law

Ideal Gas LawIdeal Gas Law

PPVV = n = nRRTT R = proportionality constant R = proportionality constant

= 0.08206 L atm = 0.08206 L atm mol mol

P = pressure in atmP = pressure in atm V = volume in litersV = volume in liters n = molesn = moles T = temperature in KelvinsT = temperature in Kelvins Holds closely at P < 1 atmHolds closely at P < 1 atm

Standard Temperature Standard Temperature and Pressureand Pressure

““STP”STP” For 1 mole of a gas at STP:For 1 mole of a gas at STP: P = P = 1 atmosphere1 atmosphere T = T = CC The molar volume of an ideal gas The molar volume of an ideal gas

is is 22.4222.42 liters liters at STP at STP

QUESTIONQUESTIONIf a 10.0 L sample of a gas at 25°C suddenly had its volume doubled, without changing its temperature what would happen to its pressure? What could be done to keep the pressure constant without changing the temperature?

1. The pressure would double; nothing else could be done toprevent this.

2. The pressure would double; the moles of gas could be doubled.3. The pressure would decrease by a factor of two; the moles of gas

could be halved.4. The pressure would decrease by a factor of two; the moles could

be doubled.

ANSWERANSWERChoice 4 describes two opposing changes. When the volume increases, the pressure of a trapped gas will decrease (at constant temperature and constant moles of gas). However, if the pressure drops, more collisions could be restored by adding more particles of gas in the same ratio as the pressure decline.


QUESTIONQUESTIONA typical total capacity for human lungs is approximately 5,800 mL.

At a temperature of 37°C (average body temperature) and pressure of 0.98 atm, how many moles of air do we carry inside our lungs when inflated? (R = 0.08206 L atm/ K mol)

1. 1.9 mol2. 0.22 mol3. 230 mol4. 2.20 mol5. 0 mol: Moles can harm a person’s lungs.

ANSWERANSWERChoice 2 is correct. The units for temperature must be in K, pressure in atm, and volume in L. Then using the universal constant 0.08206 L atm/ K mol in the PV = nRT equation moles may be solved.


n O2(g) = PV / RT

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Do you have enough oxygen to climb Mt. Everest?

http://www.chemcollective.org/applets/everest.php

http://www.chemcollective.org/applets/everest.php

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An average pair of human lungs actually contains only about 3.5 L of air after inhalation and about 3.0 L after exhalation. Assuming that air in your lungs is at 37°C and 1.0 atm

a) How many moles of O2 are actually in a typical breath?.b) What is the mass of O2 in a typical breath?.c) How much of the O2 is essential biochemically?

QUESTIONQUESTIONThe primary source of exhaled CO2 is from the combustion of

glucose, C6H12O6 (molar mass = 180. g/mol.). The balanced equation

is shown here:

C6H12O6 (aq) + 6 O2 (g) 6 CO2 (g) + 6 H2O (l)

If you oxidized 5.42 grams of C6H12O6 while tying your boots to

climb Mt. Everest, how many liters of O2 @ STP conditions did you

use?

1. 0.737 L2. 0.672 L3. 4.05 L4. 22.4 L

ANSWERANSWERChoice 3, assuming you were not holding your breath, is correct. The number of moles of glucose must first be determined (5.42/180. = 0.0301 moles), then this is multiplied by 6 to account for the stoichiometric ratio between glucose and oxygen. From this, PV = nRT may be used with the appropriate substitutions.

Section 5.4: Gas Stoichiometry

Dalton’s Law of Dalton’s Law of Partial PressuresPartial Pressures

For a mixture of gases, the total pressure is the For a mixture of gases, the total pressure is the sum of the pressures of each gas in the mixture.sum of the pressures of each gas in the mixture.

PPTotalTotal = P = P11 + P + P22 + P + P33 + . . . + . . .

PPTotalTotal n n TotalTotal

nnTotalTotal = n = n11 + n + n22 + n + n33 + . . . + . . .

QUESTIONQUESTIONIf the mole fraction of O2 in our atmosphere at standard conditions is approximately 0.209, what is the partial pressure of the oxygen in every breath you take?

1. 1.00 atm2. 4.78 atm3. 159 torr4. 3640 mmHg

ANSWERANSWERChoice 3 shows the correct pressure. This calculation is based on the application of Dalton’s law of partial pressures. For one atmosphere of pressure 0.209 is caused by oxygen so 760 .209 = 159 torr.

Section 5.5: Dalton’s Law of Partial Pressures

Dalton’s Law of Dalton’s Law of Partial PressuresPartial Pressures

For a mixture of gases, the partial gas pressurFor a mixture of gases, the partial gas pressure and total pressure equal the mole fraction of e and total pressure equal the mole fraction of each gas in the mixture.each gas in the mixture.

PP11 / / PPTotalTotal = n= n11 / / n nTotalTotal

QUESTIONQUESTIONFreon-12 had been widely used as a refrigerant in air conditioning systems. However, it has been shown to be related to destroying Earth’s important ozone layer. What is the molar mass of Freon-12 if 9.27 grams was collected by water displacement, in a 2.00 liter volume at 30.0°C and 764 mmHg. Water’s vapor pressure at this temperature is approximately 31.8 mmHg.

1. 120. g/mol2. 12.0 g/mol3. 115 g/mol4. 92.7 g/mol

ANSWERANSWERChoice 1 is the molar mass of Freon-12. The pressure must be corrected for the presence of water by subtracting 31.8 mmHg from the total pressure. This should also be converted to atm. The temperature must be converted to K. Then PV = nRT can be used if n is written as g/mm and solved for mm.

Section 5.5: Dalton’s Law of Partial Pressures

Applying the Ideal Gas LawApplying the Ideal Gas Law

PV = PV = n n RTRT n n = g of gas/ = g of gas/ MM MM gasgas [ [MM MM gasgas =g/mol] =g/mol] PV = (g of gas/ PV = (g of gas/ MM MM gasgas )RT )RT MM MM gasgas = g of gas(RT)/PV = g of gas(RT)/PV MM MM gasgas = g of gas/V (RT/P) = g of gas/V (RT/P) MM MM gasgas = density of gas (RT/P) = density of gas (RT/P)


The density of an unknown The density of an unknown atmospheric gas pollutant was atmospheric gas pollutant was experimentally determined to be experimentally determined to be 1.964 g/ L @ 0 1.964 g/ L @ 0 ooC and 760 torr. C and 760 torr.

•What is the molar mass of the What is the molar mass of the gas? gas?

•What might the gas be?What might the gas be?


MM MM gas gas = density of gas (= density of gas (RRT/P)T/P)

MM MM gas gas = 1.964 g/ L x = 1.964 g/ L x 0.08206 L atm 0.08206 L atm mol mol

x 273K/ 760 torr x 760 torr/ 1atmx 273K/ 760 torr x 760 torr/ 1atm

1.964 g/ L @ 0 1.964 g/ L @ 0 ooC and 760 torr. C and 760 torr. R = 0.08206 L atm R = 0.08206 L atm mol molooC C K Ktorr torr atm atm

MM MM gas gas ==MM MM gas gas = 44.0 g/mol= 44.0 g/mol

QUESTIONQUESTIONUnder STP conditions what is the density of O2 gas?

1. Not enough information is given to solve this.2. 1.31 g/L3. 1.43 g/L4. 0.999 g/L

ANSWERANSWERChoice 3 is the correct density for O2 at STP. At STP conditions the volume of one mole of a gas is approximately 22.4 L. One mole of oxygen = 32.0 grams. The density is calculated by dividing mass by volume.

Or

density of gas (g/L) = MM density of gas (g/L) = MM gas gas P/ RTP/ RT

Section 5.4: Gas Stoichiometry

QUESTIONQUESTIONThe aroma of fresh raspberries can be attributed, at least in part, to 3-(para-hydroxyphenyl)-2-butanone. What is the molar mass of this pleasant smelling compound if at 1.00 atmosphere of pressure and 25.0°C, 0.0820 grams has a volume of 12.2 mL?

1. 13.8 g/mol2. 164 g/mol3. 40.9 g/mol4. 224 g/mol

ANSWERANSWERChoice 2 is correct. Using PV = nRT and properly substituting0.0122 L for V, 298 K for T, using 0.08206 for R and solving for n the number of moles represented by 0.0820 grams can be obtained. Then the grams in one mole can be found.


Effusion: describes the passage of gas into an evacuated chamber.

Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

Diffusion and EffusionDiffusion and Effusion

EffusionEffusion05_60

GasVacuum

Pinhole

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Rate of effusion for gas 1Rate of effusion for gas 221=MMDistance traveled by gas 1Distance traveled by gas 221=MMEffusion:Effusion:

Diffusion:Diffusion:

Effusion and DiffusionEffusion and Diffusion

Applying Gas BehaviorApplying Gas BehaviorPreparation of Preparation of 235235UU

235235UOUO3 (s) 3 (s) + + 238238UOUO3 (s) 3 (s) 235235UFUF6 (g) 6 (g) + + 238238UFUF6 (g)6 (g)

235235U is the unstable isotope that is used in U is the unstable isotope that is used in nuclear fission. Which isoptope is the most nuclear fission. Which isoptope is the most abundant? abundant?

Design a method to separate the isomers.Design a method to separate the isomers. Be very carefulBe very careful

Applying Gas BehaviorApplying Gas BehaviorCentrification of Centrification of 235235U/ U/ 238238UU

235235UFUF6 (g) 6 (g) + + 238238UFUF6 (g)6 (g)

U-238, moves toward the outside of the cylinder and U-235, collects closer to the center. The stream that is slightly enriched in U-235 is withdrawn and fed into the next higher stage, while the slightly depleted stream is recycled back into the next lower stage.


235235UFUF6 (g) 6 (g) + + 238238UFUF6 (g)6 (g)


235235UFUF6 (g) 6 (g) + + 238238UFUF6 (g)6 (g)

February 25, 2008AP) — Iran said Sunday that it started using new centrifuges that can enrich 235U @ 2x the previous speed. The United Nations nuclear watchdog agency confirmed that Iran was using 10 of the new IR-2 centrifuges

Real GasesReal Gases

Must correct ideal gas behavior when at Must correct ideal gas behavior when at high high pressure pressure (smaller volume) and (smaller volume) and low temperature low temperature (attractive forces become important).(attractive forces become important).

Real GasesReal Gases[]PaVnbnRTobs2(/)+↔−()=nV

corrected pressurecorrected pressure corrected volumecorrected volume

PPidealideal VVidealideal

Real GasesReal GasesVolume vs. Temperature @ constant PVolume vs. Temperature @ constant P

QUESTIONQUESTIONAfter examining the figure, which statement is accurate, and consistent about the real gases shown at constant pressure?

1. At –273°C all gases occupy nearly the same volume; the different slopes are because of differences in molar masses.

2. At zero Celsius the gases have different volumes because the larger the molecule, the larger the volume.

3. Since the pressure is constant, the only difference in volume that could cause the different slopes is in the attractive forces (Van der Waal’s forces).

4. Although it does appear to do so, the volumes do not reach zero but if the graph used K instead of °C the volume would reach zero for all the gases.

ANSWERANSWERChoice 3 is the correct conclusion. If all the gases had the same attractive forces (with constant pressure) the volumes would be proportional to their speeds and inversely proprtional to their molecular weights.

Section Section 5.8: Real Gases

QUESTIONQUESTIONReal gases exhibit their most “ideal” behavior at which relative conditions?

1. Low temperatures and low pressures2. High temperatures and high pressures3. High temperatures and low pressures4. Low temperatures and high pressures

ANSWERANSWERChoice 3 provides the correct choice. At those conditions gas molecules are farthest apart and exert their least influence on each other thereby permitting their behavior to follow mathematical predictions.

Section 5.8: Real Gases

Atmospheric PollutantsAtmospheric Pollutants

Gases & AirbagsGases & AirbagsUse of Chemical Reactions and Physical PropertiesUse of Chemical Reactions and Physical Properties

Workshop: Gases IIWorkshop: Gases II


gases dr. ron rusay spring 2008 © copyright 2008 r.j. rusay

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