8th 10th Day Gases

8/9/2019 8th 10th Day Gases

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DEAL GASES

Louie Paolo D. CarpioInstructor 3

Institute of Chemistry, UP Diliman


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OBJECTIVES for today

1. Define gases

2. Define different variables of a gas

3. Define an ideal gas

4. Define and apply gas laws

5. Discuss Kinetic olecular !"eoryof gases


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S I!!S that you "ill need

1. #olving ideal gas e$uations

2. #olving gas laws

3. #toic"io%etry involving gases

4. Kinetic %olecular t"eory proble%s


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#!&!'# () &!!'*


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+,- #! D- /'#0

# /'# would be an ideal %odel to

describe t"e inetic be"avior of%olecules.


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P*(P'*! '# () /'#

# /ases "ave no definite s"ape.# /ases "ave no definite volu%e.

# /ases enclosed in a non rigidcontainer would "ave varying volu%esdepending on t"e conditions.

# /ases are capable of e panding orcan be easily co%pressed.


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D'#C* 6/ & /

/'# C&6 ' D'#C* 'D - 3 C &C*(#C(P C 7&* & L'#8

1. 7(L '2. P*'## *'

3. !' P'*&! *'


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7(L ' () & /

7(L ' 9 a%ount of space occupied

Conventional unit in c"e%istry liters

Derived #. . unit in c"e%istry 9 % 3

1 liter : 1;;; %L : 1;;; c% 3 : 1 d% 3

1 liter : ;.;;1 % 3

Conversion factors8


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P*'## *' () & /

P*'## *' 9 a%ount of force per unitareaConventional unit in c"e%istry at%

Derived #. . unit in c"e%istry 9 Pa

1 at% : 1;1325 Pa : 1.;1325 bar

1 at% :


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P*'## *' () & /

P*'## *'

a%ount of force per unit

area$ &verage force e erted by agas on t"e walls of t"e

container $ %easured using abaro%eter or a %ano%eter


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!' P'*&! *'

!' P'*&! *' >uantitative description of t"e

average inetic energy of %olecules

Conventional unit in c"e%istry Kelvin

K :(

C ? 2


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D'&L /

D'&L /

$ Perfect gas

$ ndividual gas %olecules do not

attract repel nor react wit" one anot"er $ energy and %o%entu% duringcollisions wit" ot"er gas %olecules are

conserved$ gases e "ibit t"is be"avior at lowpressures and "ig" te%peratures


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D'&L / & (D'L

)or general c"e%istry purposes allcalculations assu%e t"at gases "aveideal c"aracteristics unless statedot"erwise.


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D'&L / '> &! (6

)or an ideal gas its %acroscopicvariables are related by t"e e$uation

+"ereP : pressure in at%

7 : volu%e in liters

n : nu%ber of %oles of gases

* : gas constant : ;.; 21 @LEat%AB@%ol EKA

! : te%perature in Kelvin scale

P 7 : n * !


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&L!'*6&! 7' D'&L/ '> &! (6

+"ereP : pressure in at%

gas : %olar %ass of gas in gB%ol

d : density of gas in gBL

* : gas constant : ;.; 21 @LEat%AB@%ol EKA

! : te% erature in Kelvin scale

P gas : d * !


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#!P C(6D ! (6#

#!&6D&*D !' P'*&! *' &6DP*'## *'

! : 2


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#!&6D&*D (L&* 7(L '

7(L ' of 1 %ole of anyideal gas in #!P Conditions

@1 at% and 2


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'F& PL'

2.;; %oles of an ideal gas "as apressure of 5.2; at% at 45; K.Co%pute for t"e volu%e and %olar%ass of t"is ideal gas if t"e %ass oft"e gas was found to be 4. gra%s.


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'F& PL'Co%plete t"e table below for gaseous

6 2( 4 @ 6 2( 4 : G2.;2 gB%olA

105(F)390 K 1.15 L(E)

(D)0.783(C)488 mL673 mm

Hg

(B)(A)43.1 oC4.98 L1.77 atm

gramsnTVP


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#!( C, ( '!*- involving gases

%ass %olar

substance of gra%sn =

( )Kliters gasDat% gasD

!*7Pn =

1. substance

3. solute in solHn

5. ideal gas

( ) ( )litersnDsolInsolI 7n =

)or%ula to solve fort"e nu%ber of %oles!ype of reactant


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/ L&+#8

1. oyleHs Law2. C"arlesHs Law

3. /ay LussacHs Law

4. &vogadroHs Law

5. Co%bined /as Law

=. DaltonHs Law of Partial Pressures


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%as la"s

1. oyleHs law 9 at constant ! t"evolu%e of a gas is inverselyproportional to t"e applied pressure.

V &'(P)

or

P17

1 : P

27

2


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%as la"s

2. C"arlesHs law 9 at constant P volu%eis directly proportional to te%perature

7 !

or

2

2

1

1!7

!7

=


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Deri*ation of the el*in scale

&bsolute scale 9 Kelvin scale

&bsolute ero 9 te%perature at w"ic"t"ere is ero volu%e @( K : 2


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%as la"s

3. /ay LussacHs law 9 at constant 7pressure is directly proportional tote%perature

P Tor

2

2

1

1!P

!P

=


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%as la"s

4. Co%bined gas law e$uation 9co%bination of t"e t"ree previous gaslaws as long as no gas escapes t"econtainer @constant n or %oles of gasA

2

22

1

11

!7P

!7P =


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'F& PL'

/aseous 6, 3 at 2;; oC e erts apressure of 3.45 at% in a 3 .G literballoon. f t"e te%perature was

decreased to 15;o

C and t"e pressurewas relieved to 2.;; at% calculatet"e volu%e of t"e balloon containing6, 3.


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%as la"s

5. &vogadroHs law 9 at constantte%perature and pressure t"e nu%berof particles of a gas is directlyproportional to its volu%e

7 n

or

2

2

1

1

n7

n7 =


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%as la"s

=. DaltonHs law of Partial pressures 9 atconstant te%perature and volu%e t"epressure of a gas is directly

proportional to its nu%ber of %oles

P n

or

2

2

1

1

nP

nP =

n321total.....PPPPP +++=


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0O!E .+ CTIO-

(L' )*&C! (6 @ A %ole fraction ofof a co%ponent in a %i ture can bedescribed by t"e e$uation8

111+++== 3211

total

11 nnn

nn

nM

1=+++= 111321n MMMM

n a %i ture t"e %olefractions add up to 1


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P +TI ! P+ESSU+ES

P&*! &L P*'## *' pressure e erted by a gas in a%i ture of gases

Depends on its %ole fraction in t"e%i ture

( )'total' 2PP =


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% S CO!!ECTED OVE+ TE+

#ince water evaporates even below itsboiling point pressure of t"e watervapor %ust be accounted w"en a gas iscollected over water.

vapor water totalgas PPP =


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% S CO!!ECTED OVE+ TE+

$' a%ple sam4le of hydro5en "ascollected 6y dis4lacement of "ater at 7819oC1 The atmos4heric 4ressure "as :;

( ) torr


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&L!'*6&! 7' #!( C, ( '!*- in/'#

7 %oles of a gas

P %oles of gas

&vogadroHs law @constant ! and PA

7olu%e ratios instead of%ole ratiosN

DaltonHs law @constant ! and 7A

Partial pressure ratiosinstead of %ole ratiosN

/ay LussacHs Law of


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/ay LussacHs Law ofCo%bining 7olu%es

!"e %ole ratios of gaseous substancesin a c"e%ical reaction can also bee pressed in t"e sa%e volu%e ratios


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'F& PL'

,ow %any liters of a%%onia arere$uired to c"ange 12.1 liters of 6(to 6 20 &ssu%e 1;;O yield and t"e

reaction was done under constant !and P.

4 6, 3@gA ? = 6( @gA 5 6 2@gA ? = , 2( @lA


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'F& PL'

n a 1.;; liter container and 2;; oC acertain a%ount of 6 2 gas would e erta pressure of ;.;3= at%. & certaina%ount of , 2 gas would e ert a

pressure of ;.12; at% in t"e sa%econtainer. +"at would be t"e finalpressure in t"e 1.;; liter container if

t"e gaseous 6 2 and , 2 wereco%bined and allowed to react tofor% gaseous 6, 30


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K NET C MOLECULAR

THEORY OF GASES



# &*- () K 6'! C


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# & - () K 6 ! C(L'C L&* !,'(*- () /'#

1. /ases are %ostly e%pty space.2. /as %olecules are in constant

c"aotic %otion.

3. Collisions are elastic @energy and%o%entu% is conservedA

4. /as pressure is caused by t"ecollisions of t"e %olecules wit"t"e walls of t"e container.


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' pression for Pressure

6 : of %oleculesu : average speed

: %ass of %olecule

7 : volu%e of container

376 uP

2=

# !"e pressure is directly proportionalto speed of t"e gas.

# Pressure is inversely proportional tovolu%e.

&verage Kinetic 'nergy of


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&verage Kinetic nergy of!ranslational otion

6 & : =.;2 1; 23

! : te%perature in K

* : .314 QB%olEK

&t 26

3*!' =

# 'nergy is directly proportional tote%perature

# 'nergy is independent of %ass at t"esa%e te%perature

&verage #peed of /ases


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# The ?inetic ener5y of the molecules is4ro4ortional to the a6solute tem4erature1The ?inetic ener5y of the molecules is4ro4ortional to the a6solute tem4erature1

# Dis4layed in a 0a="ellian distri6ution1


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: %olar %ass of gas

! : te%perature in K

* : .314 QB%olEK

3*!R =

# #peed is directly proportional to t"es$uare root of te%perature

# #peed is inversely proportional to t"es$uare root of t"e %olar %ass


54/78

*elative #peeds of /ases

== 12

2

1

2

2

1

1

2

1

!!

3*!

3*!

RR

/iven two gases t"eir relative speedscan be derived8

# #peed is directly proportional to t"es$uare root of te%perature

# #peed is inversely proportional to t"es$uare root of t"e %olar %ass


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%as la" from the 0T


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'F& PL'

Co%pare t"e speeds of ( 3 andgaseous ,Cl. +"ic" is faster0' press t"e speed of ,Cl in ter%s of

t"e speed of ( 3.( 3 9 4 .;; gB%ol ,Cl 9 3=.4= gB%ol


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REAL GASES




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*'&L /'#


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*'&L /'#

)ro% a %olecular standpointdeviations fro% t"e ideal gas lawarise because it neglects two

factors82. attractive forces between gases

3. t"e finite volu%e of gas particles


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olar 7olu%e


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olar 7olu%e

Definition 9 t"e volu%e of 1 %ole of gas

Denoted by t"e sy%bol 7 %

n

7 7

% =


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'ffect of &ttractive )orces


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ffect of &ttractive )orces

;7

77o

%

o%% &! (6#


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(!, &L / &! (6#

*edlic" Kwong e$uation of state

Peng *obinson e$uation of state

(!,'* *'&L / '> &! (6#


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(!, &L / &! (6#

Dieterici e$uation of state

7irial '$uation of state

'6D () CL#


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6D () C &

# C"apter covered8 C"apter 12

# 6e t %eeting8 !"er%odyna%ics

# > '#! (6#0000

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8th 10th Day Gases