The Gas Laws

Kinetic Molecular Theory (KMT) Kinetic Molecular Theory of gases attempts to explain the properties of gases such as pressure, temperature, or volume, by looking at what they are made up of and how they move

Kinetic Molecular Theory (KMT) Kinetic refers to motion The energy an object has because of its motion is called kinetic energy Example: A ball rolling down a hill has kinetic energy

Kinetic Molecular Theory (KMT) There are three main components to kinetic theory: Perfectly elastic collisions, no energy is gained or lost when gas molecules collide Gas molecules take up no space they are so small Gas molecules are in constant, linear, random motion

Kinetic Molecular Theory (KMT) How does Kinetic Theory explain Gas Pressure? Gas Pressure results from fast moving gas particles colliding with the sides of a container More Collisions = Higher Pressure

Kinetic Molecular Theory (KMT) How does Temperature relate to Kinetic Theory? Temperature is a measure of the average kinetic energy of all the particles in a gas Higher Energy = Higher Temperature

Kinetic Molecular Theory (KMT) Through KMT, several Laws were developed to help calculate the changes in pressure, temperature, and volume of gases. There are 6 Basic Laws: 1. Boyle’s Law 2. Charles’ Law 3. Gay-Lussac’s Law 4. Avogadro’s Law 5. Ideal Gas Law – volume liters only 6. Dalton’s Law Combined Gas Law

Units used to describe gas samples: Volume Liter (L) Milliliter (mL) 1000 mL = 1L Temperature Kelvin ONLY K = ºC + 273 Pressure Atmosphere (atm) Kilopascale (kPa) Torr (torr) mm of mercury (mm Hg) 1 atm = 101.3 kPa 1 atm = 760 mm Hg 1 atm = 760 torr Standard Temperature and Pressure (STP) Standard Temperature = 273K Standard Pressure = 1 atm

Boyle’s Law Boyle’s Law – at constant temperature, the volume of the gas increases as the pressure decreases. (and the volume of the gas decreases and the pressure increases). They are inversely related V↑ P↓ Volume L P1V1 = P2V2 If you squeeze a gas sample, you make its volume smaller. Pressure (kPa)

↕ Same temperature Moveable piston Now . . . a container where the volume can change (syringe) Moveable piston ↕ Same temperature Volume is 100 mL at 25°C Volume is 50 mL at 25°C In which system is the pressure higher? (Which has the greater number of collisions with the walls and each other?) Boyle’s Law video example

P1V1 = P2V2 Boyle’s Law Example 2.00 L of a gas is at 740.0 mmHg pressure. What is its volume at 760.0 mmHg pressure? P1V1 = P2V2 2.00L x 740.0 mmHg = 760.0 mm Hg x V2 2.00L x 740.0 mmHg = 760.0 mm Hg x V2 760.0 mm Hg 760.0 mmHg 1.95 L = V2

Charles’ Law Charles’ Law – at a constant pressure, the volume of a gas increases as the temperature of the gas increases (and the volume decreases when the temperature decreases). They are directly related. increase the speed of the particles collide more often and with more force causing the walls of a flexible container expand. Think of hot air balloons! V1 V2 T1 T2 = Volume L Temperature (K) Charles’ Law Video Example

V1 = V2 T1 T2 4.40L = V2 323K 298K (298K) x 4.40L = V2 (298K) Charles’ Law Example: 4.40 L of a gas is collected at 50.0°C. What will be its volume upon cooling to 25.0°C? First you must convert temperatures from Celsius to Kelvin. Temperature must always be in Kelvin K = 273 + °C T1 = 273 + 50.0°C = 323K T2 = 273 + 25.0°C = 298K V1 = V2 T1 T2 4.40L = V2 323K 298K (298K) x 4.40L = V2 (298K) 323K 298K V2 = 4.06L

Gay-Lussac’s Law Gay-Lussac’s Law – at a constant volume, the pressure of a gas increases as the temperature of the gas increases (and the pressure decreases when the temperature decreases). They are directly related. P1 P2 T1 T2 Pressure (atm) = Temperature (K) Gay-Lussac’s Law Video Example

A B Steel cylinder (2L) contains 500 molecules of O2 at 400 K In which system do the O2 molecules have the highest average kinetic energy (temperature)? In which system will the particles collide with the container walls with the greatest force and the most often? In which system is the pressure higher? B B B

Example: In a rigid container a gas has a pressure of 1. 3 atm at 25°C Example: In a rigid container a gas has a pressure of 1.3 atm at 25°C. What is the pressure of the gas if it is heated to 45°C? First you must convert temperatures from Celsius to Kelvin. Temperature must always be in Kelvin K = 273 + °C T1 = 273 + 25.0°C = 298K T2 = 273 + 45.0°C = 318K P1 P2 T1 T2 1.3 atm = P2 298K 318K (318K) X 1 1.3 atm = P2 298K 318K X (318K) 1 P2 = 1.39 atm 1.4 atm (2 sig figs)

Unit Conversions Practice Convert 56.0 mL to L .056L Convert 65.6 g H2O to moles H2O 65.6g x 1mole H2O 18.02 g 3.64 mole H2O Convert 788 torr to atm 788 x 1 atm 760 torr 1.04 atm

Note that all temperatures must be in Kelvin! Combined Gas Law A combination of Boyle’s, Charles’, and Gay-Lussac’s Laws P1V1 P2V2 T1 T2 = Note that all temperatures must be in Kelvin!

Example: A gas occupies 2.0 L at 2.5 atm and 25ºC. What is it’s volume if the temperature is increased to 33ºC and the pressure is decreased to 1.5 atm? P1V1 P2V2 T1 T2 P1 = 2.5 atm V1 = 2.0L T1 = 25 + 273 = 298K P2 = 1.5 atm V2 = ? T2 = 33 + 273 = 306K (2.5 atm)(2.0L) (306K) = V2 (298K) (1.5 tm) V2 = 3.4 L

Example: A gas occupies 4.5 L at 1.3 atm and 35ºC. What is the final temperature if the final volume of the gas is 3.2 L with a pressure of 1.5 atm? P1V1 = P2V2 T1 T2 P1 = 1.3 atm V1 = 4.5L T1 = 35 + 273 = 308K P2 = 1.5 atm V2 = 3.2L T2 = ?K (1.5 atm)(3.2L) (308K) = T2 (4.5L) (1.3 atm) T2 = 250K

Avogadro’s Law (Hypothesis pg 320) Avogadro’s Law – equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. H2 O2 CO2 1 mole of ANY gas takes up a volume of 22.4 L at STP. This is called Molar Volume 22.4L = 1 mole of gas at STP Memorize this!

One mole of ANY gas takes up a volume of 22.4 L at STP. Avogadro’s Law: One mole of ANY gas takes up a volume of 22.4 L at STP. So how many molecules of any gas are there in 22.4 L at STP? 6.022 x 1023

Avogadro’s Law: At STP, 1.0 L of Helium gas contains the same number of atoms as: 2.0 L of Kr 1.0 L of Ne 0.5 L of Rn 1.5 L of Ar Therefore equal _______________ of gas contain equal numbers of __________ or ______________________. volumes atoms molecules

Ideal Gases Gases whose behavior can be predicted by the kinetic molecular theory are called ideal, or perfect, gases. No gases are truly ideal because no gas totally obeys all of the gas laws. An ideal gas is an imaginary gas that is perfect and does follow everything perfectly. We assume that all gases behave like ideal gases so there is an ideal gas law

Ideal Gas Law P = pressure in atmospheres (atm) PV = nRT P = pressure in atmospheres (atm) V = volume in Liters (L) n = # of moles T = temperature in Kelvin (K) R =.08206 L·atm/mol·K

Ideal Gas Law Example: How many moles of oxygen will occupy a volume of 2.50 L at 1.20 atm and 25°C? PV = nRT n = PV RT n = (1.20)(2.50) (.08206) (298K) n = .123 moles of oxygen

Ideal Gas Law Example: What volume will 12.4 grams of O2 gas occupy at 756 torr and 17°C? PV = nRT V = nRT P P = 756 torr 1 X 1 atm 760.0 torr P = .995 atm n = 12.4g 1 x 1 mol 32.00g n = .388 mol V = (.388)(.08206) (290.0K) .995 atm V = 9.28L

What is STP. STP stands for standard temperature and pressure What is STP? STP stands for standard temperature and pressure. Standard temperature is always 273K. Standard pressure is always 1.00 atm. Examples using STP: At 1.80 atm of pressure and 30.0 °C temperature, a gas occupies a volume of 65.5 mL. What will be the volume of the same gas at STP? Which gas law should we use? Combined Gas Law P1V1 = P2V2 T1 T2 (1.80 atm) (65.5 mL) = (1.00 atm) V2 (303K) 273K (1.80 atm) (65.5 mL) (273K) = V2 (303K) (1.00 atm) V2 = 106 mL

One More Law!! Dalton’s Law of Partial Pressures - In a mixture of gases, each gas exerts a certain pressure as if it were alone. The pressure of each one of these gases is called the partial pressure. The total pressure of a mixture of gases is the sum of all of the partial pressures. Ptotal = P1 + P2 + P3 ……. Pair = PO2 + PN2 + Par + PH2O + PCO2

Ptotal = P1 + P2 + P3 PTOTAL = 179 kPa Example: What is the total pressure of a mixture of gases made up of CO2, O2, and H2 if the partial pressures are 22.3 kPa, 44.7 kPa, and 112 kPa, respectively? Ptotal = P1 + P2 + P3 PTOTAL = 22.3kPa + 44.7 kPa + 112 kPa = PTOTAL = 179 kPa

YouTube - MythBusters - Fun With Gas

Gas Stoichiometry 0.100 mol H2 1 mol N2 22.4 L N2 = .747 L N2 1 Example 1: One mole of any gas at STP occupies a volume of ___________ L . How do you write this as a conversion factor?  22.4 L 1 mol 1mol 22.4L For the following reaction: N2(g) +3H2 (g) 2NH3(g) What volume of nitrogen gas at STP would be required to react with 0.100 mol of hydrogen gas in the reaction above? 22.4 0.100 mol H2 1 mol N2 22.4 L N2 = .747 L N2 1 3 mol H2 1 mol N2

Gas Stoichiometry N2(g) +3H2 (g) 2NH3(g)    What volume of nitrogen gas at STP would be required to react with 0.100 grams of hydrogen gas in the reaction above? 22.4 L N2 0.100 g H2 1 mol H2 1 mol N2 3 mol H2 1 2.02 g H2 1 mol N2 = .370 L N2

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