Gases

Kinetic Molecular Theory

• 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.

C. Johannesson

Temperature= how fast the molecules are moving

ºF

ºC

K

-459 32 212

-273 0 100

0 273 373

32FC 95 K = ºC + 273

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

STP

Standard Temperature & PressureStandard Temperature & Pressure

0°C 273 K

1 atm 101.3 kPa-OR-

STP

V = volume = how much space a gas occupies

Units– L, mL, cm3

– 1000 mL = 1 L, 1 mL = 1 cm3

n = moles = how much gas there is

R = ideal gas constant • = 0.0821 (L*atm) (mol*K) • = 8.31 (L*kPa) (mol*K)

BASIC GAS LAWS

Charles’ Law

• T V (temperature is directly proportional to volume)• T ↑ V↑ & T↓ V↓

• V1 = V2

T1 T2 T is always in K– P and n = constant

• Ex) A 25 L balloon is released into the air on a warm afternoon (42º C). The next morning the balloon is recovered on the ground. It is a very cold morning and the balloon has shrunk to 22 L. What is the temperature?

V

T

CharlesLaw.exe

240 K, 33 °C

Boyle’s Law• P↓ V ↑ & P↑ V ↓• P 1/V (pressure is inversely proportional to volume)

• P1V1 = P2V2– T and n = constant

Ex: Pressure: 0.98 atm 0.92 atmVolume: ? mL 8.0 L

P

V

Boyle'sLaw.exe

7.5 L

AVOGADRO’S LAW• Vn Vn • V n (direct)

• V1 = V2

n1 n2

– T & P Constant

EX: A 3 liter sample of gas contains 3 moles. How much gas will there be, in order for the sample to be 2.3 liters? P & T do not change

Avogadro'sLaw.exe

2.3moles

Gay-Lussac’s Law

• P1 = P2

T1 T2

– V & n constant

• Direct relationship

• PT PT

P

T

Gay-Lussac'sLaw.exe

Example: A can of Dust Off is sitting next to my computer at 25°C and 3.5 atm. I flip the can over and spray some air out. The room has a pressure of 1.0 atm. What is the temperature of the air as it escapes the container?

http://www.youtube.com/watch?v=4qe1Ueifekg2.06 min

85 K, - 188 °C

COMBINED IDEAL GAS LAW

• P1V1 = P2V2

n1T1 n2T2

• If P, V, n, or T are constant then they cancel out of the equation.

• n usually constant (unless you add or remove gas), so

• P1V1 = P2V2

T1 T2

Ideal Gas Law (“Pivnert”)• PV = nRT

• R = ideal gas constant • = 0.0821 (L*atm)

(mol*K)

• = 8.31 (L*kPa)

(mol*K)

Ideal Gas Law (“Pivnert”)

PV=nRT R = The Ideal Gas Constant (memorize)R = 0.0821 (L*atm) (mol*K) R = 8.31 (L*kPa) (mol*K)* Choose which R to used based on the units of your pressure. If you have mmHg change it to atm.* V has to be in Liters, n in Moles, T in Kelvin, P can be in atm or kPa

P V = n R T (atm) (L) = (moles) (L*atm/mol*K) (K)(kPa) (L) = (moles) (L*kPa/mol*K) (K)

Dalton’s Law of Partial Pressure• The total pressure of a mixture of gases is

equal to the sum of the partial pressures of the component gases.

• Ptotal = Pgas 1 + Pgas 2 + P gas 3 + …

• Example: Find the total pressure for a mixture that contains three gases. The partial pressure of nitrogen is 15.75 kPa, helium is 47.25 KPa, and oxygen is 18.43 kPa.

81.43 kPa