Ideal Gas Laws

7/13/2019 Ideal Gas Laws

1/27

Gases (Vapors)

Gases expand to fill any containe

Therefore, gases are highly

compressible.


2/27

Kinetic Molecular Theory (of an Ideal Gas):

1. Gases are composed of molecules or atoms whose size is

compared to the average distance between them. (Most of th

the gas container is empty.)

2. Gas molecules move randomly in straight lines in all directions

speeds.

3. The forces of attraction or repulsion between gas molecules are v

or negligible (except during collisions)

4. Collisions between gas molecules are considered elastic.

5. The average kinetic energy of a molecule is proportional to the ab

temperature.


3/27

Pressure and Volume: Boyles Law

How is the pressure applied to a gas related to its volume?

Piston

Gas molecules

Lets apply pressure


4/27

Pressure and Volume: Boyles Law

How is the pressure applied to a gas related to its volume?

Piston

Gas molecules

Piston

Gas molecules

Boyles Law: P1V1= P2V2

Volume is inversely proportional to applied pressure.


5/27

The Harder we Pus

the smaller the gavolume gets!

Boyles Law: P1V1= P2V2


6/27

molecules of air

1

2

3

Where is the pressure the greatest?

We live in sea of air


7/27

Pressure: force per unit area of surface

Units

lbs per in2 (psi)

mm of Hg (torr)

atmospheres (atm)

1 atm = 760 mm of Hg =760 torr = 14.70 psi = 101.325 kPa

Pascal (Pa)

Pairs of these can be used as conversion factors.


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10/27

Temperature and Volume: Charless Law

How is the volume of a gas related to its temperature?

gas molecules

moveable mass

(constant pressure)

What happens if heat is applied to the gas?


11/27



gas molecules

moveable mass

(constant pressure)

Why did the volume change?

What happens to the average speed of the gas

molecules?


12/27



gas molecules

moveable mass

(constant pressure)

The volume of a gas is directly proportional to its Temperature

(temperature must be in Kelvin)

Charless Law: V1/T1= V2/T2


13/27

Pressure and Temperature: Gay-Lussacs Law

The pressure of a gas is directly proportional to its Temperature

(temperature must be in Kelvin)

Gay-Lussacs Law: P1/T1= P2/T2


14/27

Combined Gas Law:

T

VP

T

VP

2

22

1

11 T must be in Kelvin

Can be rearranged to:

P1V1T2= P2V2T1

A combined gas law problem can be recognized by

having two sets of conditions.

Note: if one set of parameters is unchanged that term

will cancel on each side.


15/27

A balloon contains helium gas with a volume of 2.60 L

at 25 oC and 768 mmHg. If the balloon ascends to an

altitude where the helium pressure is 590 mmHg and

the temperature is 15 oC, what is the volume of the

balloon?

What type of

problem

is this?

There are 2 sets of

conditions.


16/27

A balloon contains helium gas with a volume of 2.60 L

at 25 oC and 768 mmHg. If the balloon ascends to an

altitude where the helium pressure is 590 mmHg and

the temperature is 15 oC, what is the volume of the

balloon? P1V1T2= P2V2T1

P1=

V1=

T1=

P2=

V2=

T2=

768 torr

2.60 L

25 + 273 = 298 K

590 torr

15 + 273 = 288 K

?

12

211

2

TP

TVPV

= (768 torr)(2.60 L)(288 K)

(590 torr)(298 K)

= 3.27 L


17/27

Ideal Gases and the Ideal Gas Law:

PV = nRuT

Temperature in K*universal gas constant

number of moles of gas

volume in units to match *R units

pressure in units to match *R units

Note: there is only one set of conditions.


18/27

Ideal Gases and the Ideal Gas Law:

PV = mRT

Temperature in K*ideal gas constant

moles of gas

volume in units to match *R units

pressure in units to match *R units

Note: there is only one set of conditions.


19/27

Avogadros Law:

Equal volumes of any two gases (ideal) at the same

temperature and pressure contain the same number of

molecules (they also occupy equal volumes).

STP

Pressure 1 atm (760 mm Hg)

Temperature 0oC (273 K)

Standard

At STP one mole of ideal gas occupies 22.4 L or 22.4 m3/kg-mol


20/27

A 12.25 L cylinder contains 75.5 g of neon at 24.5 oC.

Determine the pressure in the cylinder.

What type of

problem

is this?

Only oneset of

condition


21/27

A 12.25 L cylinder contains 75.5 g of neon at 24.5 oC.

Determine the pressure in the cylinder.

PV = nRT

P =

V =

n =

R =

T =

?

12.25 L

75.5 g = mol

20.18 g

mol 3.74

62.4 Ltorr

molK

24.5 + 273 = 297.5 K

P = nRTV

= (3.74 mol)(62.4Ltorr)(297

(12.25 L) molK

= 5667.7 torr

= 5670 torr

How many atmospheres is t

at7.46torr760

atm1torr5667.7


22/27

What is the density of carbon dioxide gas at 25 oC and

725 mmHg pressure?

Density = g/L = g L

so if we can find g and L, division will work!

P =

V =

n =

R =

T =

725mmHg

62.4 L torr

molK

25 + 273 = 298 K

What do we

do now?


23/27


725 mmHg pressure?

Density = g/L = g L

so if we can find g and L division will work!

P =

V =

n =

R =

T =

725mmHg

62.4 Ltorr

molK

25 + 273 = 298 K

Two variables! Lets pick an amou

for one and calculate the other!

Lets choose 1 mol of CO2and

find the number of Liters.


24/27


725 mmHg pressure?

Density = g/L = g L

so if we can find g and L division will work!

P =

V =

n =

R =

T =

725mmHg

62.4 Ltorr

molK

25 + 273 = 298 K

1.0 mol (44.0 g)

V = nRT

P

= (1 mol) (62.4 Ltorr) (298 K)

( molK ) (725 to

=25.6 L

NOW: 1.72___________ = 44.0 g

25.6 L


25/27

A 2.50 gram sample of a solid was vaporized in a 505 mL

vessel. If the vapor pressure of the solid was 755 mmHg at

155 oC, what is the molecular weight of the solid?

molecular weight ~ molar mass = g/mol = g mol

..so if we can find grams and moles and divide....

P =

V =

n =

R =

T =

755 torr

0.505 L

...we already have grams!! Were halfway ther

62.4 Ltorr

molK

155 + 273 = 428 K

n = PV

RT

= 755 torr |0.505 L |molK_____|___| 62.4 Ltorr | 428

= 0.01428 mol

NOW: 2.50 g = g

0.01428 mol mol

175.1


26/27

So Density is g/L (g L

and

molar massis g/mol (g mol).


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Ideal Gas Laws