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Gases

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Subtopics

•

Physical characteristics of gases• Formula and Unit

• Instruments

•Gases Law (Boyle, harles, !"ogadro and!monton#

• Ideal Gas $%uation

•&alton Partial Pressure

• 'inetic olecular )heory of Gases

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Physicalcharacteristics

of gases

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• Gases assume the volume and shape of their containers.

• Gases are the most compressible state of matter.

• Gases will mix evenly and completely when confined to

the same container.

• Gases have much lower densities than liquids and solids.

5.1

Physical Characteristics of Gases

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Sea level 1 atm

4 miles 0.5 atm

10 miles 0.2 atm

5.$

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Instruments

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 s P  (h increases V  decreases

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P  α 1#V 

P  x V  ! constant

P 1 x V 1 ! P $ x V $

5.+

,oyle/s 0aw

Constant temperature

Constant amount of )as

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  sample of chlorine )as occupies a volume of 2& m0

at a pressure of %$& mm). 3hat is the pressure of

the )as (in mm) if the volume is reduced at constant

temperature to 152 m04

P 1 x V 1 ! P $ x V $

P 1 ! %$& mm)

V 1 ! 2& m0

P $ ! 4

V $ ! 152 m0

P $ !P 1 x V 1

V $

%$& mm) x 2& m0152 m0

! ! 22&' mm)

5.+

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ariation of )as volume with temperature

at constant pressure.

5.+

V  α T 

V  ! constant x T 

V 1#T 1 ! V $#T $ T  (6 ! t  ('C 7 $%+.15 

Charles/ 8

Gay90ussac/s

0aw

:emperature must be

in 6elvin

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  sample of carbon monoxide )as occupies

+.$' 0 at 1$5 'C. t what temperature will the

)as occupy a volume of 1.52 0 if the pressure

remains constant4

V 1 ! +.$' 0

T 1 ! +;.15 6

V $ ! 1.52 0

T $ ! 4

T $ !V $ x T 1

V 1

1.52 0 x +;.15 6+.$' 0

! ! 1$ 6

5.+

V 1#T 1 ! V $#T $

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 vo)adro/s 0aw

V  α

 number of moles (n

V  ! constant x n

V 1#n1 ! V $#n$

5.+

Constant temperatureConstant pressure

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 mmonia burns in oxy)en to form nitric oxide ("

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P*+*  P-+-

n*)* n-)-

V 1#T 1 ! V $#T $

P 1 x V 1 ! P $ x V $

V 1#

n1 !

V $#

n$

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 r)on is an inert )as used in li)htbulbs to

retard the vapori=ation of the filament.

certain li)htbulb containin) ar)on at 1.$' atmand 1; 'C is heated to ;5 'C at constant

volume. 3hat is the final pressure of ar)on in

the li)htbulb (in atm4

P 1

T 1

P 2 

T 2 !

P 1 ! 1.$' atm

T 1 = $1 6

P 2  ! 4

T 2  = +5; 6

P 2  ! P 

1 x

T 2 

T 1

! 1.$' atm x +5; 6$1 6

! 1.2; atm

5.2

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Ideal Gas

$%uation

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>deal Gas ?quation

5.2

Charles/ law@ V  α T   (at constant n and P 

 vo)adro/s law@ α n  (at constant P  and T 

,oyle/s law@ α (at constant n and T 1P 

V  α nT 

P 

V  ! constant x ! R nT 

P 

nT 

P R 

 is the gas constant

PV  ! nRT 

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:he conditions ' 'C and 1 atm are called standard

temperature and pressure (STP).

PV = nRT 

R =

PV 

nT  !

(1 atm($$.2120

(1 mol($%+.15 6

R  ! '.';$'5% 0 A atm # (mol A 6

5.2

?xperiments show that at B:P* 1 mole of an ideal)as occupies $$.212 0.

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3hat is the volume (in liters occupied by 2.; ) of Cl

at B:P4

PV = nRT 

V =nRT 

P 

T  ! ' 'C ! $%+.15 6

P = 1 atm

n ! 2.; ) x1 mol Cl

+&.25 ) Cl! 1.+% mol

V  !1 atm

1.+% mol x '.';$1 x $%+.15 60AatmmolA6

V  ! +'.& 0

5.2

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&alton.s Laws of

Partial Pressure

lt / 0 f P ti l P

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alton/s 0aw of Partial Pressures

V  and T  

areconstant

P 1 P $ P total = P 1 7 P $

5.&

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Consider a case in which two )ases*  and ,* are in a

container of volume .

P   !n AD:

V 

P , !n

BD:

V 

n  is the number of moles of 

n, is the number of moles of ,

P : ! P   7 P ,  X   !n 

n  7 n, X , !

n,

n  7 n,

P   ! X   P : P , ! X , P :

P i  ! X 

i  P :

5.&

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  sample of natural )as contains ;.$2 moles of C2*

'.2$1 moles of C$&* and '.11& moles of C+;. >f the

total pressure of the )ases is 1.+% atm* what is the

partial pressure of propane (C+;4

P i  ! X 

i  P :

 X propane !'.11&

;.$2 7 '.2$1 7 '.11&

P : ! 1.+% atm

! '.'1+$

P propane ! '.'1+$ x 1.+% atm ! '.'1;1 atm

5.&

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Pi ni/)

  +

P i  ! X i  P :

0i ni  n)