zchapter5 gases chem

8/11/2019 ZChapter5 Gases chem

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CHAPTER 5 - GASES

Properties of Gases

Gas has no fixed shape or volume;

It contains particles (atoms or molecules) separated by distances very much larger than

the particle size;

Gases are compressible and expandable due to plenty of empty spaces betweenmolecules;

Inter-particles attractions in gases are negligible;

Particles are constantly moving and colliding especially with container walls;

ollisions of particles with surfaces result in pressure!

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5.1 PRESSURE

Pressure is defined as force per unit area; Pressure =Area

Force; (P # $%&)

Force = mass xacceleration!

If mass in 'g and acceleration in m%s

force # 'g!m%s

# *ewton (*)

Pressure #2

meter

Newton # *%m # Pa (Pascal +I unit for pressure)

Atmospheric Pressure or Barometric Pressure,

he atmosphere contains a mixture of gases mainly * and .! Gas moleculesconstantly colliding with the /arth0s surface and results in the atmospheric pressure!

&tmospheric pressure is measured with a barometer hence called barometric pressure! hefirst mercury barometer was invented in 1234 by an Italian scientist /vangelista orricelli

(1256 - 1237)! he first barometer was made of a meter-long glass tubing closed at one end! orricelli

filled the tubing with mercury and then inverted it into a bowl of mercury reservoir! 8efound that the mercury column in the tubing only dropped to a level of about 45 inches

above the mercury reservoir! 8e explained that the mercury column is supported by theair pressure that exerts on the surface of mercury in the bowl thus preventing the

column from completely falling into the bowl! orricelli mainly used his barometer todetermine the relationships between changes in the air pressure with the weather!

Pressure may be expressed in terms of the height of a li9uid column! Pressure exerted by a

li9uid column is directly proportional to the gravitional constant g the density of li9uid d, and

the height of the column h.

Pressure = g.d.h

+incegand dare constant for a given li9uid pressure is proportional only to the height of thatli9uid column! :ased on the mercury barometer pressure is expressed in terms of the height ofmercury column supported by that pressure! &t sea level the atmospheric pressure supports amercury column of 725 mm tall! hus 1 atm = 760.0 mmHg= 760.0 torr!

(In honor of orrichelli 1 torris defined to be e9uivalent to 1 mm8g!)

.ther pressure units are 1 atm = 14.70 psi and 1 atm = 101 325 Pa(1 Pa # 1 *%m)!

Pascal (Pa) is the +I unit for pressure!

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/xercise-1

1! & car tire is inflated to a pressure of 4!5 psi! onvert this pressure unit to atm torr and'ilopascal ('Pa)! (&nswer !53 atm; 1

2


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#harless !a"&t constant pressure the olume o$ a !as sample is "irectly proportio#al to its

temperature i# %eli#!

, T or , = cT; (where cis a numerical constant and is in Belvin!)

$or a given 9uantity of gas at constant pressure if the temperature (in Belvin) changes from 1to then the volume will change from @1to @ such that

2

2

T

V =

1

1

T

V; then @# @1(%1) and # 1(@%@1)

(8ow would the plot of @ versus loo' li'e,)

If the temperature increases but the volume remains unchange then the gas pressure willincrease! he pressure-temperature relationship at constant volume can be summarized by the

expression

1

1

T

P=

2

2

T

P; and P# P1(%1) ; and # 1(P%P1);

/xercise-4

1! If a 43


4/15

/xercise-3

1! ?hat is the volume of 5!264 mol of nitrogen gas at +P, (&nswer 1

! 8ow many moles of helium gas would occupy a volume of 2!6 x 154A at +P,

(&nswer 4!5 x 15moles)

4! &n amount of ozone gas occupies a volume of !53 A at 1 atm and < o! If all of this gas

is converted to oxygen what would be the volume of the oxygen gas under the sametemperature and pressure, he reaction is .4(g) 4 .(g)

(&nswer 4!52 A)""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

*.+ 'he ,deal Gas !a"

ombining :oyleEs harlesEs and &vogadroEs Aaws we obtain the following expression

V

P

Tn; or V =

P

T)R(n; (where Ris a universal gas constant!)

his leads to the ideal gas e9uation PV = nRT

+ince 1!555 mol of ideal gases has a volume of !313 A at +P R# ./0 ".atmmol..

If P is expressed in torr R = 0.20 ".torrmol.

$or a fixed amount of gas :oyle0s and harles0s laws may be combined to yield the followingrelationships between volume pressure and temperature

, 3Tp4; @ # (a constant)(%P)

?hich yields the expression 1

11

T

VP

# 2

22

T

VP

;

Fe-arranging the above expression we obtain other e9uations such as

V2= V1.(1

1

T

P).(

2

2

P

T); P2= P1.(

1

1

T

V).(

2

2

V

T); T2= T1.(

11

22

VP

VP)

/xercise-


5/15

A. etermination of 6olar 6ass7

$or an ideal gas P@ # nF; P@ # (g%)(F);

where g is mass in grams and # molar mass of gas)

which yields P # (g%@)(F)

+ince density "# g%@ P # dF and 6 = dRT%P;

%. Gas ensit&( d=RT

P

1! Gas densities vary greatly with temperature and pressure; it decreases as temperature risesand increases as pressure increases!

! Gas density is directly proportional to its molar mass!

(/xplain how does a hot-air balloon wor'!)

/xercise-21! & !76-g sample of a gas occupies a volume of 3!3 A at 4!2 o and 7


6/15

*a*4(s) *a(s) H 4 *(g)

8ow many grams of *a*4must decompose to produce mm8g of pressure, (&nswer 15 g of *a*4)

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5.5 alton9s "a# of Partial Pressure

Partial Pressure Pi is the pressure that a gas in a mixture would exert if it were to be

present alone in the same container! In a mixture containing non-reacting gases & and : if thepartial pressure of gas & is P& and that of : is P: the total gas pressure is

Ptotal # P&H P:;

If P (n&)(F%@) and P:# (n:)(F%@)

hen Ptotal # P&H P:# (n&H n:)(F%@) # ntotal(F%@)

altonEs Aaw states that Jthe total pressure o$ a miture o$ !ases is e&ual to the sum o$ the

partial pressures o$ i#"ii"ual !ases i# the mitureJ!

Ptotal # Pi# P1H PH P4H!!!

(where P1 P P4 etc! are partial pressures of individual gases in the mixture)

?hen a gas is collected over water the gas contains water vapor which also exerts pressurecalled the water vapor pressure Pw! he total pressure of the collected gas is the +K of the

gas pressure and the water vapor pressure! If the atmospheric (or barometric) pressure andthe vapor pressure of water at a particular temperature are 'nown the pressure of dry gas can

be calculated as follows

P# Pbar # PgasH Pw; Pgas# Pbar> Pw;

/xercise-61! &

8e by mass! ?hat is the total gas pressure inside the container at < o,(&nswer total gas pressure # 14!3 atm)

! &

partial pressure of each gas in the container and the total pressure of the mixture,

(&nswer P.# !1 atm; P*# !6 atm; Ptotal# 3!= atm)

4! & piece of zinc metal is reacted with excess hydrochloric acid 8l(a9) and the hydrogen

gas produced is collected over water at 3!3 o! (a) ?rite a balanced e9uation for thereaction! (b) If the total pressure of the gas mixture (8 and water vapor) is 7


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Ideal gas laws are derived from empirical data and observations of gas behavior! hese

laws are summaries of physical characteristics of gases at relatively low pressures!

he inetic Molecular 'heory(B) of gases consists of a set of postulates which try toexplain this behavior of gases! he theory is summarized as follows

1. +ases co#tai# particles 'molecules or atoms( that are poi#t masses their total molecular

olume is #e!li!ible compare" with the olume occupie" by the !as.

2. olecules are i# co#sta#t ra#"om motio#s;molecular collisio#s are completely elastic

3. *#termolecular $orces are #e!li!ible particles #either attract #or repel each other.

4. he aera!e 6i#etic e#er!y o$ a !as sample is "irectly "epe#"e#t o#ly o# the temperature

i# %eli#!

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Usin+ t!e 6T of +ases to e:plain +as la#s7

Pressure-olume /elationship&t constant temperature gas molecules travel with a constant average speed! Feducing

the volume results in shorter distances traveled by molecules which leads to a higherfre9uency of molecular collisions! his leads to a higher gas pressure as stated by :oyle0s law!

Pressure and 'emperature

Faising the temperature causes an increase in the average molecular speed! his causesthe fre9uency of molecular collision to increase and leads to a higher gas pressure! Gay-Aussac

law states that gas pressure will increase proportionally with temperature at constant volume!

olume and 'emperatureo maintain a constant pressure when the temperature increrases the volume of the gas

must increase so that the fre9uency of collisions is reduced! harles0s law states that gasvolume will increase proportionally as the temperature is increased at constant pressure!

ect o ,ncreasing the 2um3er o Molecules on Gas olume

?hen more molecules are added to the same volume at constant temperature the

number of molecular collisions will increase which leads to an increase in pressure! If thepressure were to be constant the volume must increase in accordance with &vogadro0s law!

'emperature and /oot-Mean-&4uare &peed

he rootmea#s&uare spee"of gas molecules at a given temperature is given by thefollowing expression

urms= (2RT6)

where F # 6!413 M%mol!B # 6!413 'g!m%(s!mol!B)! herefore the molar mass must be given

in 'g%mol! (M # 'g!m

%s

)! $or example the root-mean-s9uare speeds for 8and .at 5o

are

urmsfor 8 # (4 x 6!413 'g!m!s- !mol-1 !B-1 x 74 B)# 1!63 x 154m%s(!512 x 15-4'g!mol-1)

urmsfor . # (4 x 6!413 'g!m!s- !mol-1 !B-1 x 74 B)# 321 m%s(4!55 x 15-4'g!mol-1)

he urmsof 8elium gas at 162=) a +cottish chemist found that the rate o$ e$$usio# o$ a

!as is i#ersely proportio#al to the s&uare root o$ its molar mass!

Fate of effusion 1""

he relative rates of effusion of two gases at the same temperature and pressure are e9ual tothe inverse ratio of the s9uare root of their molar mass! :ased on the 'inetic molecular theory

rate o$ e$$usio# is "irectly proportio#al to the rootmea#s&uare spee" urms of the gas

molecules! he relative rates of two gases can be expressed as follows

$gaso%e%%&siono%Rate

Agaso%e%%&siono%Rate #

$gaso%

Agaso%

rms

rms

u

u#

)(3RT'

)(3RT'

$

A #

A

$

$or a given period the relative number of moles of gas & and : effused is

e%%&sed$gaso%o

e%%&sedAgaso%o #

A

B

M

M

+ince effusion time is the inverse of rate if tais the effusion time for an amount of gas & and tbis the effusion time for the same amount of gas : then

$gaso%ime%%&sion t

Agaso%ime%%&sion t #

B

A

t

t #

B

A

M

M

he relative rate of diffusion of two gases may be expressed in terms of the relative distance

traveled by these gases for a given period of time such that

$moec&e*+tra,eeddistance

Amoec&e*+tra,eeddistance #

A

B

M

M

/xercise-=1! ?hat is the average 'inetic energy and urmsof *molecules at +P, he molar mass of *

is !6 x 15-'g%mol! (F # 6!413 M%mol!B; M # 'g!m!s-) (&nswer urms# 3=4 m%s)

! &t a certain temperature and pressure 2! mg of *gas effuses through an opening in =5!

seconds! 8ow much of 8gas would effuse through the same opening in =5! seconds

under the same condition, (&nswer 1!7 mg of 8)

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9/15

4! alculate the relative distance traveled by (i) *84and 8l gases; (ii) *84and 8+ gases

under the same temperature and pressure!(&nswer *84travels 32!3C farther than 8l; *84travels 31!


10/15

1! Kse (a) the ideal gas e9uation and (b) the van der ?aals e9uation to calculate the

pressure exerted by the following gases when the volume and temperature are

(i) 1!55 mol of l(g)(a # 2!3= A!atm!mol-; b # 5!5


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/mbedded within the lower heterosphere is the ionosphere containing species such as

.H *.H .H *

H and free electrons! Ionospheric chemistry involves numerous light-inducedbond brea'ing (photo"issociatio#) and light-induced electron removal (photoio#iatio#)

processes! $or example the formation of oxygen atoms occurs by the following steps

* *H H e- (photo-ionization)

*HH e- * H *

* H . *. H .

* H *. * H .

. . H . Ooverall photo-dissociation of .

>?one in T!e Stratosp!ere

ost of the high-energy solar radiation is absorbed by the thermosphere! 8owever asmall amount reaches the stratosphere causing photo-dissociation which brea's .to . atoms!

he energetic . atoms collide with other .molecules to form ozone (.4)

.(g)

.(g); (photo-dissociation) .(g)H .(g)H *(g) .4(g)H *

Q

8ere *serves as an energy sin' to absorb excess energy produced by the exothermic reactionof .4 formation! +tratospheric temperature increases with altitude due to this exothermic

reaction!he ozone layer in the stratosphere is vital to live on /arth because it absorbs a great

portion of solar ultraviolet (K@) radiation which causes its decomposition

.4(g) H K@ .(g) H .(g)

K@ radiation is extremely harmful because it can cause bond dissociations and thus interruptnormal biological processes! ?ithout the stratospheric ozone much more of this radiation would

reach the /arth surface resulting in increased mutation and cancer incidence!

5epletion o 'he 8one !ayerKnder normal conditions the stratospheric ozone concentration varies seasonally but

remains fairly constant annually through the complex series of atmospheric reactions! woreactions that maintain a balance in ozone concentration are the following

.(g) H .(g) .4(g) Oformation

.4(g) H .(g) .(g) Obrea'down

8owever based on the ground-brea'ing research by Paul rutzen ario M! olina and $!+herwood Fowland for which they received the *obel Prize in 1==


12/15

hlorine atomic is very reactive which readily attac's ozone molecules and brea'ing it down to

oxygen gas .4(g) H l(g) .(g) H l.(g)

l.(g) H .(g) .(g) H l(g)

RRRRRRRRRRRRRRRRRRRR*et reaction .4(g) H .(g) .(g)

RRRRRRRRRRRRRRRRRRRRRRRRRRR

herefore chlorine atoms produced by the photodissociation of $s acts as a homogeneouscatalyst in the brea'down reaction of the ozone gas!

Eart!'s Primiti*e Atmosp!ere

+cientists agree that the primitive /arth0s atmosphere did not contain oxygen gas! heorigin-of>life models propose that about 1 billion years after the earliest organism appeared

blue-green algae evolved! hese on-celled organisms used solar energy to produce glucose by

photosynthesis

2.(g) H 28.(l)H h 281.2(a9)H 2.(g)

&s a result of this reaction the .content of the atmosphere increased and .decreased! he

increase in .allowed more oxidation reactions to occur which changed the geological andbiological ma'eup of the early /arth! Iron(II) minerals changed to iron(III) minerals sulfites

changed to sulfates and eventually organisms evolved that could oxidize other organisms toobtained energy! It has been estimated that the level of .may have increased to the current

level of about 5C approximately 1!< billion years ago!

Atmospheric Pollutantshe chemistry of the troposphere is strongly influenced by human activities! Aarge amount

of gases and particulates are released into the troposphere by our highly industrial civilization!+evere air pollution occurs especially around many large and industrial cities! he two maNor

sources of air pollution are transportation and processing plants that use petroleum and coal asfuel sources! he combustion of petroleum in vehicles produces . . *. and *. along

with unburned molecules from petroleum! ?hen this mixture is trapped close to the ground in

stagnant air reactions occur producing chemicals that are potentially irritating and harmful!

he complex chemistry of air pollution seems to center around the nitrogen oxides (*. x)!&t the internal combustion engines of cars and truc's where temperatures are high *and .(from air) react to form *. that is released into the air with other exhaust gases! *. is then

immediately oxidized to *. which absorbs K@-radiation and brea's up into *. molecules andoxygen atoms (.)

*(g) H .(g) *.(g)

*.(g)H .(g) *.(g)

*.(g)H K@ *.(g)H .(g)

.xygen atoms may combine with .to form ozone

.(g) H .(g) .4(g)

.zone is a very strong oxidizing reagent which attac's other pollutants as well as materials

causing the latter to be degraded at a faster rate! .zone on the /arth0s surface also undergoesphoto-dissociation producing energetically excited .molecules (.

Q) and oxygen atom (.Q)!

he latter readily react with water molecule to form hydroxyl radicals (.8) which is strongoxidizing agent!

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13/15

.Q H 8. .8

.8 radical can oxidize *.to form nitric acid .8 H *. 8*.4!

he free radical .8 can also react with unburned hydrocarbons in the polluted air to produce

other chemical that are irritating and harmful to the respiratory system! he end product of thiscomplex processes is often referred to as p!otoc!emical smo+ so called because light is

re9uired to initiate some of the reactions! O*ote that while ozone layer is desirable in thestratosphere to bloc' most of the uv-radiation from the sun it is highly harmful on the /arth0s

surface because of its strong oxidizing property!

he other maNor source of pollution results from burning coal power plants! uch of thecoal found in the idwest contains significant amount of sulfur which when burned produces

sulfur dioxide

+(in coal) H .(g) +.(g)

Feaction of +.with oxygen in the air produces +.4 which readily dissolves in rainwater toform sulfuric acid

+.(g) H .(g)

+.4(g)

+.4(g) H 8.(l) 8+.3(a9)

+ulfuric acid is highly corrosive to both living things and building materials; its present in acid

rain has resulted in damaging effects on the environments! In many parts of the northeasternKnited +tates and southeastern anada acid rain has caused some freshwater la'es to become

too acidic to support a9uatic life!

he use of high-sulfur coal by power plants further aggravates the pollution problems! &nindustrial method to reduce the amount of +. released into the atmosphere is by using a

system called a scrubberbefore it is emitted into the power plant stac'! & common method ofscrubbing is to blow powdered limestone (a.4) into the combustion chamber where it is

decomposed to lime and carbon dioxide

a.4(s) a.(s) H .(g)

he lime then combines with +.to form calcium sulfite

a.(s) H +.(g) a+.4(s)

o remove the calcium sulfite and any remaining unreacted +.gas an a9ueous suspension oflime is inNected into the exhaust gases to produce slurry of a+.4!

Knfortunately there are many problems associated with scrubbing! he systems are

complicated expensive and consume a great deal of energy! he large 9uantities of calciumsulfite produced in the process present a disposal problem! ?ith a typical scrubber

approximately 1 ton of a+.4per year is produced per person served by the power plant! +inceno use has been found for this compound it is buried in a landfill! hus air pollution by sulfur

dioxide will continue to be a maNor problem one that is expensive in terms of damage to theenvironment and human health as well as in monetary terms!

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Appen)i:

'emperature and /oot-Mean-&4uare &peed

he goals of B of gas are to provide plausible explanations of the molecular behaviorof gases that are related to pressure and temperature of the gas! he 'inetic energy of a

molecule of mass mand traveling at speed uxinx-direction is ex# Smux!

+imilarly the 'inetic energy of an identical molecule traveling in the y- and z-direction is

ey# Smuy and ez# Smuz respectively!

he average 'inetic energy of a molecule traveling in any direction is e k#1%4(

4%mu)

hen the average 'inetic energy of a mole of gas particles is

,k# 8&(Smu) # Su where 8&is the &vogadro0s number!

+ince molar mass # 8&m, ,k# Su

$orce is the change in momentum per unit time! ?hen a molecule traveling with speed ucollides with the wall head-on and bounces in the opposite direction with the same speed the

change in its momentum # muper collision.

If the molecule is in a cubic box of length 9 the distance traveled by molecule between collision

is 9 and the time ta'en between collision is t# 9'u! onse9uently

$orce # mu # mu = mu!t 9'u 9

If this force were concentrated on one face of the wall of area 9 the pressure exerted on that

face of the wall is $orce # mu%9area 9

If the same force is applied on all the six faces of the cubic box the average pressure exerted

on each wall is P # mu%9 # mu

29 4@

In a mole of gas the average pressure exerted by the &vogadro0s number of molecules in @

volume is

P #3V

)( 2A muN #3V

)(22

21

A muN #V

))(( 221

32 Mu

:ut for one mole of gas the pressure P =V

RT =

V

))((2

21

32 u

= (2)k

his implies that the average molar 'inetic energy of gas is k=16u

#(2)RT!

hat is the average molecular 'inetic energy of a gas is dependent only on the temperature (inBelvin) but is independent of the 9uantity or the molar mass of the gas!

+ince molar mass is # 8&m then *&(1%mu) # 1%u # 4%F

+ince 1%u # 4%F u# 4F% and urms= (u) = (2RT6)

where F # 6!413 M%mol!B # 6!413 'g!m%(s!mol!B) and urmsis called the rootmea#s&uare

spee"!

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&t constant temperature the root-mean-s9uare speed urms is i#ersely proportio#al to thes&uare root o$ the molecular mass! &t constant temperature the ratio of the rootmea#s&uare

spee"of two gases with molar masses &and :is given as

(urmsof gas &) # (4F%&) # (:%&)

(urmsof gas :) (4F%:)

$or example under the same temperature the urmsof 8is about 3 times that of .

(urmsof 8) # (olar mass of .) # (4!5 g%mol) # 3(urmsof .) (olar mass of 8) (!5 g%mol)

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A))itional E:ercises1! &n aerosol-spray can contains a gas at 1!6 atm when the temperature is !5 o! ?hat

is the pressure inside the can when it is placed in a boiling water at 155! o! (&ssume gas

temperature e9uals that of boiling water) (&nswer !45 atm)

! ?hat volume of * measured at 74< torr and 35o

is produced when

7! If the density of acetone vapor is !5= g%A at 1!55 atm and 2

zchapter5 gases chem

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