Ch. 12 Behavior of Gases

Gases

• Gases expand to fill its container, unlike solids or liquids

• Easily compressible: measure of how much the volume of matter decreases under pressure

Variables that describe a gas

• Pressure (P)– Measured in kilopascals, kPa– Pressure and number of molecules are directly

related increase molecules = increase pressure

– Gases naturally move from areas of high pressure to low pressure, due to the available space to move into

Variables that describe a gas

• Volume (V)– Measured in Liters, L– Volume and pressure are inversely related• As volume decreases, the pressure increases• Smaller container = less room for movement, therefore

molecules hit sides of container more often

Variables that describe a gas

• Temperature (T)– Measured in Kelvin, K– The temperature and pressure are directly related• Increase in temp = increase in pressure• Volume must be held constant• Molecules hit the walls harder (due to increase in K.E.)

and more frequently. Think about a tire in hot weather…

Variables that describe a gas

• Amount– Measured in moles, mol– Moles and pressure are directly related• Increase in # of moles = increase in pressureEx: Inflating a balloon is adding more molecules.• Temperature must remain constant

Gas Laws

• Describe how gases behave• Change can be calculated• Know the math and the theory!!

Boyle’s Law (1662)

• Gas pressure is inversely related to volume (as volume increases, pressure decreases)

• Temperature is constant

P1V1= P2V2

Ex: The pressure of a 2.5L of gas changes from 105 kPa to 40.5 kPa.

What will be the new volume?

Charles’s Law (1787)

• Volume is directly proportional to temp. (increase volume, increase temp)• Pressure is constant

=

Ex: A sample of Nitrogen occupies a volume of 250 mL at 25oC. What volume

will the gas occupy at 95oC?

Gay-Lussac’s Law (1802)

• Pressure and temperature are directly related(Increase pressure= Increase

temperature)• Volume is constant!

Ex: A gas has a pressure of 710 kPa at 227oC. What will the pressure be at 27oC,

if the volume does not change?

Combined Gas Law

• Combines 3 gas laws: Boyle’s, Charles’, and Gay-Lussac’s • Used when it is difficult to hold any one variable (P, V, or

T) constant

=

• Can take away any variable that is constant– Take temp away = Boyle’s– Take Pressure away = Charle’s– Take Volume away = Gay-Lussac’s

Ex: 3.0 L of Hydrogen gas has a pressure of 1.5 atm at 20oC. What would the volume be if the pressure increased to 2.5 atm at 30oC?

Ideal Gas Law• Used for gases that behave “ideally”• Allows you to solve for # of moles of a contained gas when

P, V, and T are known. • Use constant R=8.31

P(pressure)- must be in kPaV (volume)- must be in Ln (# of moles)- muse be in moles of gasR- gas constantT (Temperature)- Must be in Kelvin (oC + 273= K)

Ideal Gas Law• A gas behaves “ideally” if it conforms to the gas laws

– Gases do not usually do this– Real gases only behave this way at:

1. High temps (molecules move fast)2. Low pressure (molecules are far apart)• This is because gases will stay a gas under these conditions

– Molecules are not next to each other very long so attractive forces can’t play a role b/c molecules are moving too fast

– Ideal Gases do no exist because:1. Molecules do take up space2. There are attractive forces between molecules otherwise no liquid

would form. (Molecules slow down to become liquids)

Ex: What volume will 2.0 mol of N2 occupy at 720 torr and 20oC?

Dalton’s Law of Partial Pressures

• Used for mixture of gases in a container• If you know the P exerted by each gas in a

mixture, you can calculate the total gas pressure

• It is particularly useful in calculating pressure of gases collected over water.

Ptotal = P1 + P2 + P3…*P1 represents the “partial pressure” or the contribution by the gas

Ex: Helium, Nitrogen, and Oxygen exist in a container. Calculate the total pressure of the mixture for the

following partial pressures:He = 200 kPa N= 500 kPa O= 400 kPa

Graham’s Law of Effusion• Rate of effusion and diffusion are inversely proportional to the

square root of the mm of molecules – Effusion: Gas escaping through tiny holes in a container– Diffusion: movement from area of high concentration to low

concentration (ex: perfume spreading across a room)(Both depend of the mm of the molecule, which determines speed)

= • Type of Molecule is important

– Gases with lower mm effuse/diffuse faster– Ex: Helium diffuses/effuses faster than Nitrogen from a balloon b/c

Helium moves faster due to lower mm.Big = Slow small = Fast

Ex: