Behavior of Gases

Example of Importance of Gases

Airbags fill with N 2 gas in an accident. Gas is generated by the decomposition of sodium azide Gas molecules save your life! 2 NaN 3 ---> 2 Na + 3 N 2

Kinetic Molecular Theory (KMT)  Particles in an

ideal gas

…  have no volume.

 have elastic collisions.  are in constant, random, straight-line motion.

 don’t attract or repel each other.

 have an avg. KE directly related to Kelvin temperature.

Real Gases  Particles in a

REAL gas

… 

have their own volume



attract each other

 Gas behavior is

most ideal

… 

at low pressures



at high temperatures



when very small in size



when nonpolar

PLIGHT

Characteristics of Gases

 Gases expand to fill any container uniformly.



Are in random motion, have no attraction

 Gases have very low densities.



Particles have no volume = lots of empty space

Characteristics of Gases

 There is a lot of “free” space in a gas.

 Gases can be compressed.

 no volume = lots of empty space

 Gases undergo diffusion & effusion.

 Are always in random motion  Smaller and lighter gas particles do this faster

Gas Pressure

pressure



force area

Which shoes create the most pressure?



What Causes Pressure?

 http://www.chm.davidson.edu/vce/kineticm oleculartheory/Pressure.html

Factors Affecting Gas Pressure 

Number of Moles

(Amount of gas)  As # of particles increase, the number of collisions with the container wall increases.



Volume

 Smaller the volume, the greater the pressure exerted on the container.



Temperature

 As temp. increases, KE increases, this increases frequency of collisions making pressure increase.

Measuring Gas Pressure 

Barometer

 measures atmospheric pressure  (developed by Torricelli in 1643) Aneroid Barometer Mercury Barometer



Standard Pressure (Sea Level)

101.3 kPa (kilopascal) 1 atm 760 mm Hg (also called torr)

You may be asked to convert between units of pressure!

Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in soft drink) Column height measures pressure of atmosphere 1 standard atmosphere (atm) = 760 mm Hg (or torr)

Measuring Gas Pressure 

Manometer

 measures contained gas pressure U-tube Manometer

The Gas Laws

Working with Formulas

Temperature

 Always use absolute temperature (Kelvin) when working with gases.

ºC -273 K 0 0 273 100 373

K = ºC + 273

Gas properties can be modeled using math.

Model depends on:  V = volume of the gas (L)  T = temperature (K) 

ALL temperatures MUST be in Kelvin!!!

 n = amount (moles)  P = pressure (atmospheres or kPa)

STP Standard Temperature & Pressure 0 °C 1 atm -OR 273 K 101.325 kPa 760 mmHg

Boyle’s Law

Robert Boyle (1627-1691). Son of Earl of Cork, Ireland .

 The pressure and volume of a gas are inversely related  at constant mass & temp

P

PV = k

V

Boyle’s Law

 Since P x V is always a constant: P 1 x V 1 = P 2 x V 2

l

Pressure and Volume Relationship

http://www.chm.david

son.edu/vce/kineticm oleculartheory/PV.htm

If Mass and Temp are Constant

Boyle’s Law

Balloon in a Vacuum

Charles’ Law

Jacques Charles (1746-1823). Isolated boron and studied gases. Balloonist .

 The volume and absolute temperature (K) of a gas are directly related  at constant mass & pressure

V V



k T T

Charles’ Law

 Since V/T is always a constant: V 1 T 1 = V 2 T 2

If Mass and Pressure are Constant

Charles’ Law

Pour Liquid Nitrogen on Balloon!!

http://group.chem.iastate.edu/Greenbowe/sections/projectfolder/flas hfiles/gaslaw/charles_law.html

http://www.pinnaclescience.com/demo.htm

P

Gay Lussac’s Law

 The pressure and absolute temperature (K) of a gas are directly related  at constant mass & volume

P T



k T

Gay – Lussac’s Law

 Since P/T is always a constant: P T 1 1 = P T 2 2

 

Pressure and Temperature Relationship

http://www.chm.davidson.edu/vce/kineticmoleculartheory /PT.html

Review of 3 Gas Laws

Summary of Changing Variables http://www.mhhe.com/physsci/chemistry/es sentialchemistry/flash/gasesv6.swf

Combined Gas Law (on Ref Table)

The good news is that you don’t have to remember all three gas laws! We can combine them into a single equation.

If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law!

P 1 V 1 = T 1 P 2 V 2 T 2 P 1 V 1 T 2 = P 2 V 2 T 1

Example

A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29 °C. What is the new temperature ( °C) of the gas at a volume of .090 L and a pressure of 3.20 atm?

Set up Data Table P 1 = 0.800 atm V 1 P 2 = 3.20 atm V 2 = .180 L T = .090 L T 1 2 = 302 K = ??

Gas Law Problems

 A gas occupies 473 ml at 36 °C. Find its volume at 94 °C.

CHARLES’ LAW

GIVEN:

T



V

 V 1 = 473 ml T 1 = 36 °C = 309K V 2 = ?

T 2 = 94 °C = 367K WORK: P 1 V 1 T 2 = P 2 V 2 T 1 (473 ml )(367 K)=V 2 (309 K)

V 2 = 562 ml

Gas Law Problems  A gas occupies 100. mL at 150. kPa. Find its volume at 200. kPa.

BOYLE’S LAW

GIVEN:

P



V

 V 1 = 100. mL P 1 = 150. kPa V 2 = ?

P 2 = 200. kPa WORK: P 1 V 1 T 2 = P 2 V 2 T 1 (150.kPa)(100.mL)=(200.kPa)V 2

V 2 = 75.0 mL

 Gas Law Problems °C. Find its volume at STP. GIVEN:

P



COMBINED GAS LAW T



V

 WORK: V 1 = 7.84 ml P 1 = 71.8 kPa T 1 = 25 °C = 298 K V 2 = ?

P 2 = 101.325 kPa T 2 = 273 K P 1 V 1 T 2 = P 2 V 2 T 1 (71.8 kPa)(7.84 ml)(273 K) =(101.325 kPa) V 2 (298 K)

V 2 = 5.09 ml

 Gas Law Problems A gas’ pressure is 765 torr at 23°C. At what temperature will the pressure be 560. torr? GIVEN:

P



GAY LUSSAC’S LAW T

 WORK: P 1 = 765 torr T 1 = 23 °C = 296K P 2 = 560. torr T 2 = ?

P 1 V 1 T 2 = P 2 V 2 T 1 (765 torr)T 2 = (560. torr)(309K)

T 2 = 226 K = -47 °C

Dalton’s Law of Partial Pressures  P total = P 1 +P 2 +….

 Total pressure of a mixture of gases in a container is the

sum

of the individual pressures (

partial pressures

) of each gas, as if each took up the total space alone.

 This is often useful when gases are collected “over water”

Dalton’s Law of Partial Pressures  The total pressure of a mixture of gases equals the sum of the partial pressures of the individual gases.

P total

= P

1

+ P

2

+ ...

P atm P H2O = P H2 +

 Dalton’s Law 22.5

°C. Find the pressure of the dry gas if the atmospheric pressure is 94.4 kPa.

The total pressure in the collection bottle is equal to atmospheric pressure and is a mixture of H 2 and water vapor.

GIVEN: P H2 = ?

P P total H2O = 94.4 kPa = 2.72 kPa Look up water-vapor pressure on for 22.5

° C.

WORK: P total = P H2 + P H2O 94.4 kPa = P H2 + 2.72 kPa P H2 = 91.7 kPa Sig Figs: Round to least number of decimal places.

 Dalton’s Law A gas is collected over water at a temp of 35.0

°C when the barometric pressure is 742.0 torr. What is the partial pressure of the dry gas? The total pressure in the collection bottle is equal to barometric

DALTON’S LAW

GIVEN: P gas = ?

P P total H2O = 742.0 torr = 42.2 torr Look up water-vapor pressure for 35.0

° C.

WORK: P total = P gas + P H2O 742.0 torr = P H2 + 42.2 torr P gas = 699.8 torr Sig Figs: Round to least number of decimal places.

Graham’s Law



Diffusion

 Spreading of gas molecules throughout a container until evenly distributed.



Effusion

 Passing of gas molecules through a tiny opening in a container

Graham’s Law



Speed of diffusion/effusion

 Kinetic energy is determined by the temperature of the gas.

 At the same temp & KE, heavier molecules move more slowly.

Avogadro’s Principle

 Equal volumes of gases contain equal numbers of moles  at constant temp & pressure  true for any gas

Equal volumes of gases at the same T and P have the same number of molecules.

V V n



k n