ap chemistry chapter 10

7/25/2019 AP Chemistry Chapter 10

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Chapter 10

Gases


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Barometers and Standard

Atmospheric Pressure


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Atmospheric Pressure Standard atmospheric

pressuredefined as the

pressure sufficient to support a

mercury column of 760mm

(units of mmHg, or torr!


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pressuredefined as thepressure sufficient to support amercury column of 760mm

(units of mmHg, or torr! Another unit "as introduced to

simplify thin#s, the atmosphere(1 atm$ 760 mm%#!


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pressuredefined as the

pressure sufficient to support a

mercury column of 760mm

(units of mmHg, or torr!

Another unit "as introduced to

simplify thin#s, the atmosphere

(1 atm$ 760 mm%#!

1 atm $ 760 mm%# $ 760 torr $

101!&' kPa(pa#e '6'!


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STP

standard temperature and pressure

Standard temperature 0C or 273 K

Standard pressure 1 atm (or equia!ent"


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Pressure varies

inversely with volumeVolume varies inversely

with pressure

The volume of a sample of gas is inverselyproportional to its pressure, if temperature

remains constant.


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#o$!e%s &a'


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Boyle)s *a"+ Pressure -olume

(.i#ure 10!6 (a pa#e '6&

P V

PV


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#o$!e%s &a' Pressure)*o!ume +e!ationships

A sample of air occupies 73.3 mL at 98.7 atm and 0 C.

What volume will the air occupy at 4.02 atm and 0 C?

1,00 m&


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#o$!e%s &a' Pressure)*o!ume +e!ationships

A sample of helium occupies 535 mL at 988 mmHg and

25C. If the sample is transferred to a 1.05-L flask at25 C, what will be the gas pressure in the flask?

-03 mm Hg


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Efects o temperature on agas

Volume varies directly withTemperature

The volume of a quantity of gas,

held at constant pressure, variesdirectly with the Kelvin

temperature.


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Charles)s *a"

a


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Charles *a"+ -olume and /emperature

(.i#ure 10! Pa#e '66


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Char!es% &a' and ./so!ute ero

trapo!ation to

ero o!ume gies

a temperature o4

)273C or 0 K


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A sample of oxygen gas occupies a volume of 2.10 L at 25 C.

What volume will this sample occupy at 150 C? Assume no

change in p!essu!e."

Char!es%s &a' Temperature)*o!ume +e!ationships

256, &


17/87

A sample of oxygen gas occupies a volume of 2.10 L at 25 C.

At what Celsius tempe!atu!e will the volume of oxygen

occupy 0.#50 L? Assume no change in p!essu!e."

Char!es%s &a' Temperature)*o!ume +e!ationships

)17C


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Pressure s5 Temperature

Pressure aries direct!$ 'ith Temperature

84 the temperature o4 a 4ied o!ume o4 gasdou/!es its pressure dou/!es5


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Pressure s5 Temperature

/he pressure eerted 2y a#as is directly related to theKe!intemperature!

- is constant!


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Pressure 3s! /emperature


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amp!e

A #as has a pressure of 64 torr at 1'5C! hat is the

temperature in Celsius if the pressure increases to 1!0 atm

Pi$ 64 torr Pf$ 1!0 atm 760 torr $ 1140 torr 1 atm

/i$ 1'5C 8 '7&

$ 401 9 T4 $ 9


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So!ution

T2 $ 401 9 1140 torr $ 70:9

64 torr

70:9 ; '7& $ 4&65C


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Com/ined 9as &a' Pro/!em

. samp!e o4 he!ium gas has a o!ume o4 051,0 &: a

pressure o4 05,00 atm and a temperature o4 26C5

;hat is the ne' temperature(C" o4 the gas at a

o!ume o4 6050 m& and a pressure o4 3520 atm/he olecular

ass of a -olatile *i@uid?! 8t is due BBBB5

Attempt the pre;la2 for >/he olecular

ass of a -olatile *i@uid?! 8t is due BBBB5

$!o%lem& A volatile liquid is placed in a flas whose volume is !"#.# ml


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$!o%lem&A volatile liquid is placed in a flas whose volume is !"#.# ml

and allowed to boil until all of the liquid is gone, and only vapor fills the

flas at a temperature of $##.#o% and &'( mm )g pressure. *f the mass

of the flas before and after the e+periment was $.'&!g and $".!& g,

what is the molar mass of the liquid

-756 gAmo!


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C ! ! t th d it i A& 4


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Ca!cu!ate the densit$ in gA& o4

2gas at STP5

15=3 gA&

alton)s *a" of Partial Pressure


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alton)s *a" of Partial Pressure /he total pressure in a container is the sum of the partial

pressures of all the #ases in the container!

=n a #aseous miture, a #as)s partia! pressureis the one the#as "ould eert if it "ere 2y itself in the container!

Ptotal$ P1 8 P' 8 P& Ptotal$ 100 9Pa 8 '0 9Pa 8 '00 9Pa $ --0 KPa


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A B

/otal $ 6!0 atm

P * *miture P

. '!0 atm 1!0 * '!0 atm

# 4!0 atm 1!0 * 4!0 atm

T'o 150 & containers: . and #: contain gases

'ith 250 atm and =50 atm: respectie!$5 #oth

gases are 4orced into Container #5 @ind the tota!

pressure o4 the gas miture in #5

1!0 *

alton)s *a" Pro2lem


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alton s *a" Pro2lem .ir contains o$gen: nitrogen: car/on dioide: and

trace amounts o4 other gases5 ;hat is the partia!

pressure o4 o$gen at standard conditions i4 thepartia! pressure o4 nitrogen: car/on dioide: andother gases are 7651 KPa: 050= KPa: and 056= KParespectie!$dry? oy#en

#as at S/P (P"ater$ '&! torr at 'oC

PD'$ P/; P"ater$ 7!0 torr ; '&! torr $ 7&4!' torr

@ind the mo!ar mass o4 an unkno'n gas i4 a 0 1 g samp!e o4


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@ind the mo!ar mass o4 an unkno'n gas i4 a 051 g samp!e o4

the gas is co!!ected oer 'ater and equa!ied to a pressure o4

7,157 torr and a o!ume o4 6050 m& at a temperature o4 2,C 5


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@ind the mo!ar mass o4 an unkno'n gas i4 a 0 1 g samp!e o4


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@ind the mo!ar mass o4 an unkno'n gas i4 a 051 g samp!e o4

the gas is co!!ected oer 'ater and equa!ied to a pressure o4

7,157 torr and a o!ume o4 6050 m& at a temperature o4 2,C 5

== gAmo!


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%ome"or

o the AP sample pro2lem (1::: /est

@uestion K in note2oo! =t "ill 2e

included as part of your home"or!

on)t for#et the pre;la2 and la2 summary

for >/he olecular ass of a -olatile

*i@uid?!


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Gas iffusion and Jffusion

9rahamEs &a' #o3erns the rate of effusion and diffusion of #as molecules!

FStinkG or FieG


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FStinkG or FieG

a

e oo ean @uare pee


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@ p

.i#! 10!17 Pa#e '


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NETNETD-JJE/

To use 9raham%s &a': /oth gases must /e at same temperature5

di44usiondi44usion partic!e moement4rom

high to !o' concentration

e44usione44usion di44usion o4 gas

partic!es

through an opening

@or gases: rates o4 di44usion I e44usion o/e$ 9raham%s !a'

more massie > s!o'J !ess massie > 4ast


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Gas iffusion and Jffusion

9rahamEs &a' #o3erns the rate of effusion and diffusion of #as molecules!


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etermine the relati3e rate of diffusion

for rypton and 2romine!

1.381=

9r

diffuses 1!&1 times faster than Br'!

Kr

Br

Br

Kr

m

m

v

v 2

2

=

A

B

B

A

m

m

v

v=

g/mol83.80

g/mol159.80=

Graham)s *a"

/he li#htest #as is >Gas A? and the hea3ier #as is >Gas B?!

3AI3B?!

9r,35,0

Br76560=

D

%1


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A molecule of oy#en #as has an a3era#e speed of 1'!&mIs at a #i3en temp and pressure! hat is the a3era#espeed of hydro#en molecules at the same conditions

A

B

B

A

mm

vv =

2

2

2

2

H

O

O

H

m

m

v

v=

g/mol2.02g/mol32.00

m/s12.3vH =1

Graham)s *a"

3.980m/s12.3

vH =

1

m/s49.0vH =1

D1-5666=

%150076=

D

%1


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An unno"n #as diffuses 4!0 times faster than D'!

.ind its molar mass!

Am

g/mol32.0016=

A

B

B

A

m

m

v

v =

A

O

O

A

m

m

v

v2

2

=

Amg/mol32.004.0=

16

g/mol32.00m

A

=

1

=

Amg/mol32.004.0

g/mol2.0=

Graham)s *a"

/he li#htest #as is >Gas A? and the hea3ier #as is >Gas B?!

/he ratio >3AI3B? is 4!0!

S@uare 2oth

sides to #et rid

of the s@uare

root si#n!

D1-5666=

%'250

'i i ( l l )h'i ti ( l l )h


73/87

/heory de3eloped to eplain #as 2eha3ior!

/heory of mo3in# molecules!

Assumptions+

F Gases consist of a lar#e num2er of molecules in constant

random motion!

F -olume of indi3idual molecules ne#li#i2le compared to3olume of container!

F =ntermolecular forces (forces 2et"een #as molecules

ne#li#i2le!

F Jner#y can 2e transferred 2et"een molecules, 2ut totalinetic ener#y is constant at constant temperature!

F A3era#e inetic ener#y of molecules is proportional to

temperature!

'inetic (olecula! )heo!y'inetic (olecula! )heo!y

'i i ( l l )h'i ti ( l l )h


74/87

9inetic molecular theory #i3es us anunderstandin# of pressure and

temperature on the molecular le3el!

Pressure of a #as results from the

num2er of collisions per unit time on the

"alls of container!

a#nitude of pressure #i3en 2y ho"

often and ho" hard the molecules

strie!

Gas molecules ha3e an a3era#e ineticener#y!

Jach molecule has a different ener#y!


'i ti ( l l )h'i ti ( l l )h


75/87

/here is a spread ofindi3idual ener#ies

of #as molecules

in any sample of

#as!


As the temperature

increases, the a3era#e

inetic ener#y of the#as molecules

increases



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As inetic energy increases, the velocity of the gasmolecules increases.

2 0oot mean square speed, u, is the speed of a gas

molecules having the certain average inetic energy.

2 Average inetic energy, , is related to root meansquare speed, u:

11$mu=


a



77/87

As inetic energy increases, the velocity of the gasmolecules increases.

2 0oot mean square speed, u, is the speed of a gas

molecules having the certain average inetic energy.

2 Average inetic energy, , is related to root meansquare speed, u:

11$mu=


a

)ow does this theory e+plain /oyles Law


78/87

As the volume of a container of gas increases atconstant temperature, the gas molecules have to travel

further to hit the walls of the container. 3here are

fewer collisions by the gas molecules with the walls

of the container. 3herefore, pressure decreases.*f temperature increases at constant volume, the average

inetic energy of the gas molecules increases.

3herefore, there are more collisions with the

container walls and the pressure increases.

)ow does this theory e+plain /oyles Law

)ow does this theory e+plain %harles Law


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*f temperature increases at constant volume, the averageinetic energy of the gas molecules increases and

they speed up. 3herefore, there are more frequent

and more forceful collisions with the container walls

by the gas molecules and the pressure increases.

)ow does this theory e+plain %harles Law

Ideal Gases vs. Real GasesIdeal Gases vs. Real Gases


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An idea! gasis an >ima#inary #as? made

up of particles "ith ne#li#i2le particle

3olume and ne#li#i2le attracti3e forces!

Ideal Gases vs. Real GasesIdeal Gases vs. Real Gases


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8n a F+ea! 9asG the mo!ecu!es o4 a gas dohae o!ume and the mo!ecu!es do attract

each other5

There4ore an$thing that makes gas partic!es

more !ike!$ to stick together or sta$ c!ose to

one another make them /ehae !ess idea!!$5

-eal ases& /eviations f!om +eal ehavio!


82/87

2 As the volume %ecomes

smalle!* the molecules get

close! togethe!* an+ a

g!eate! f!action of theoccupie+ space is actually

ta,en up %y gas molecules.

2 )he!efo!e* the highe! the

p!essu!e* the less the gas!esem%les an i+eal gas.


As the p!essu!e on a gas inc!eases* the molecules a!e fo!ce+

into a smalle! volume.



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2 )he smalle! the +istance %etween gas

molecules* the mo!e li,ely att!active

fo!ces will +evelop %etween the

molecules.

2 As tempe!atu!e inc!eases* the gas

molecules move faste! an+ a!efu!the! apa!t.

2 Also* highe! tempe!atu!es mean

mo!e ene!gy availa%le to %!ea,

inte!molecula! fo!ces.2 )he!efo!e* the highe! the

tempe!atu!e* the mo!e i+eal the gas.


0eal Gases and *deal /ehavior


84/87

2 A !eal gas typically exhi%its %ehavio! closest toi+eal gas3 %ehavio! at low p!essu!es an+ high

tempe!atu!es.

0eal Gases and *deal /ehavior

-eal ases& )he van +e! Waals e4uation


85/87

We a++ two te!ms to the i+eal gas e4uation one to co!!ect fo!

volume of molecules an+ the othe! to co!!ect fo!inte!molecula! att!actions

)he co!!ection te!ms gene!ate the van +e! Waals e4uation&

whe!e aan+ ba!e empi!ical constants.

-eal ases& )he van +e! Waals e4uation

1

1

V

an

nbV

nRT

P =

( ) nRTnbVV

anP =

+1

1

aco!!ects fo! the effect of molecula! att!actions van +e!

Waals fo!ces"* an+ bco!!ects fo! the molecula! volume

0eal Gases: 3he van der 4aals equation


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We a++ two te!ms to the i+eal gas e4uation one to co!!ect fo!

volume of molecules an+ the othe! to co!!ect fo! inte!molecula!

att!actions

)he co!!ection te!ms gene!ate the van +e! Waals e4uation&

2 ou will not %e !e4ui!e+ to solve this e4uation %ut you shoul+ou will not %e !e4ui!e+ to solve this e4uation %ut you shoul+,now its fo!m an+ which va!ia%les nee+ to %e co!!ecte+.,now its fo!m an+ which va!ia%les nee+ to %e co!!ecte+.

0eal Gases: 3he van der 4aals equation

( ) nRTnbVV

anP =

+1

1

aco!!ects fo! the effect of molecula! att!actions van +e!

Waals fo!ces"* an+ bco!!ects fo! the molecula! volume


87/87

ap chemistry chapter 10

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