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 K = ºC Always use absolute temperature (Kelvin) when working with gases.

STP Standard Temperature & Pressure 0°C 273 K 1 atm101.3 kPa -OR- STP

V = volume = how much space a gas occupies Units –L, mL, cm 3 – 1000 mL = 1 L, 1 mL = 1 cm 3 n = moles = how much gas there is R = ideal gas constant = (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↓ V 1 = V 2 T 1 T 2 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 240 K, 33 °C

Boyle’s Law P↓ V ↑ & P↑ V ↓ P  1/V (pressure is inversely proportional to volume) P 1 V 1 = P 2 V 2 –T and n = constant Ex: Pressure: 0.98 atm  0.92 atm Volume: ? mL  8.0 L P V 7.5 L

AVOGADRO’S LAW V  n  V  n  V  n (direct) V 1 = V 2 n 1 n 2 –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 2.3moles

Gay-Lussac’s Law P 1 = P 2 T 1 T 2 –V & n constant Direct relationship P  T  P  T  P T

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? min 85 K, °C

COMBINED IDEAL GAS LAW P 1 V 1 = P 2 V 2 n 1 T 1 n 2 T 2 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 P 1 V 1 = P 2 V 2 T 1 T 2

Ideal Gas Law (“Pivnert”) PV = nRT R = ideal gas constant = (L*atm) (mol*K) = 8.31 (L*kPa) (mol*K)

Ideal Gas Law (“Pivnert”) PV=nRT R = The Ideal Gas Constant (memorize) R = (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. P total = P gas 1 + P gas 2 + P­ gas 3 + … Example: Find the total pressure for a mixture that contains three gases. The partial pressure of nitrogen is kPa, helium is KPa, and oxygen is kPa kPa