The Gas Laws Kinetic Molecular Theory KMT Kinetic

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: 1. Perfectly elastic collisions, no energy is gained or lost when gas molecules collide 2. Gas molecules take up no space they are so small 3. Gas molecules are in

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 Combined Gas Law 2. Charles’ Law 3. Gay-Lussac’s Law 4. Avogadro’s Law 5. Ideal Gas Law – volume liters only 6. Dalton’s Law

Units used to describe gas samples: Volume Temperature Pressure Liter (L) Milliliter (m. L) Kelvin ONLY 1000 m. L = 1 L K = ºC + 273 Atmosphere (atm) Kilopascale (k. Pa) Torr (torr) mm of mercury (mm Hg) 1 atm = 101. 3 k. Pa 1 atm = 760 mm Hg 1 atm = 760 torr Standard Temperature and Pressure (STP) Standard Temperature = 273 K Standard Pressure = 1 atm

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↓ V o l u m e L P 1 V 1 = P 2 V 2 If you squeeze a gas sample, you make its volume smaller. Pressure (k. Pa)

Now. . . a container where the volume can change (syringe) Moveable piston ↕ Same temperature Volume is 100 m. L at 25°C Volume is 50 m. L 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

Boyle’s Law Example 2. 00 L of a gas is at 740. 0 mm. Hg pressure. What is its volume at 760. 0 mm. Hg pressure? P 1 V 1 = P 2 V 2 2. 00 L x 740. 0 mm. Hg = 760. 0 mm Hg x V 2 760. 0 mm. Hg 760. 0 mm Hg 1. 95 L = V 2

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. • increasing the V 1 V temperature of a gas = 2 V T 1 T 2 increases the speed o l of u gas particles which m collide more often and e with more force L causing the walls of a flexible container Temperature (K) expand. Think of hot Charles’ Law Video Example air balloons!

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 V 1 = V 2 T 1 = 273 + 50. 0°C = 323 K T 1 T 2 = 273 + 25. 0°C = 298 K (298 K) 4. 40 L = V 2 (298 K) 1 323 K 298 K 1 V 2 = 4. 06 L

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. P 1 P 2 = T 1 T 2 Pressure (atm) Gay-Lussac’s Law Video Example Temperature (K)

A B Steel cylinder (2 L) contains 500 molecules of O 2 at 400 K Steel cylinder (2 L) contains 500 molecules of O 2 at 800 K 1. In which system do the O 2 molecules have the highest average kinetic energy (temperature)? B 2. In which system will the particles collide with the container walls with the greatest force and the most often? B 3. In which system is the pressure higher? B

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 P 1 P 2 T 1 = 273 + 25. 0°C = 298 K T 1 T 2 = 273 + 45. 0°C = 318 K (318 K) X 1. 3 atm = P 2 X (318 K) 1 298 K 318 K 1 P 2 = 1. 39 atm 1. 4 atm (2 sig figs)

Unit Conversions Practice Convert 56. 0 m. L to L =. 056 L Convert 65. 6 g H 2 O to moles H 2 O = 3. 64 mole H 2 O 65. 6 g 1 mole H 1 2 O 18. 02 g Convert 788 torr to atm 1 atm = 1. 04 atm 760 torr 788 torr 1

Combined Gas Law A combination of Boyle’s, Charles’, and Gay-Lussac’s Laws P 1 V 1 P 2 V 2 = T 1 T 2 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? P 1 V 1 P 2 V 2 T 1 T 2 P 1 = 2. 5 atm V 1 = 2. 0 L T 1 = 25 + 273 = 298 K P 2 = 1. 5 atm V 2 = ? T 2 = 33 + 273 = 306 K (2. 5 atm)(2. 0 L) (306 K) = V 2 (298 K) (1. 5 tm) V 2 = 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? P 1 V 1 = P 2 V 2 T 1 T 2 P 1 = 1. 3 atm V 1 = 4. 5 L T 1 = 35 + 273 = 308 K P 2 = 1. 5 atm V 2 = 3. 2 L T 2 = ? K (1. 3 atm)(4. 5 L) = (1. 5 atm)(3. 2 L) (308 k) T 2 (1. 5 atm)(3. 2 L) (308 K) = T 2 (4. 5 L) (1. 3 atm) T 2 = 250 K

What is STP? STP is the abbreviation for standard temperature and pressure. Standard temperature is 273 K Standard pressure is 1 atm You must memorize the meaning of STP.

Avogadro’s Law (Hypothesis pg 320) Avogadro’s Law – equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. H 2 O 2 CO 2 1 mole of ANY gas takes up a volume of 22. 4 L at STP. This is called Molar Volume 22. 4 L = 1 mole of gas at STP Memorize this!

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? One mole which is 6. 022 x 1023

Avogadro’s Law: At STP, 1. 0 L of Helium gas contains the same number of atoms as: A. B. C. D. 2. 0 L of Kr 1. 0 L of Ne 0. 5 L of Rn 1. 5 L of Ar volumes Therefore equal ________ of gas atoms contain equal numbers of _____ or ___________. 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 ◦ There are no intermolecular forces between the gas molecules. ◦ The volume occupied by the molecules themselves is entirely negligible relative to the volume of the container.

Ideal Gas Law PV = n. RT 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 = n. RT n = PV RT n = (1. 20)(2. 50) (. 08206) (298 K) n =. 123 moles of oxygen

Ideal Gas Law Example: What volume will 12. 4 grams of O 2 gas occupy at 756 torr and 17°C? V = n. RT PV = n. RT P P = 756 torr X 1 atm 1 760. 0 torr P =. 995 atm x 1 mol 32. 00 g n =. 388 mol V = (. 388)(. 08206) (290 K). 995 atm V = 9. 28 L n = 12. 4 g 1

What is STP? STP stands for standard temperature and pressure. Standard temperature is always 273 K. 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 m. L. What will be the volume of the same gas at STP? Which gas law should we use? Combined Gas Law P 1 V 1 = P 2 V 2 T 1 T 2 (1. 80 atm) (65. 5 m. L) = (1. 00 atm) V 2 (303 K) 273 K (1. 80 atm) (65. 5 m. L) (273 K) = V 2 (303 K) (1. 00 atm) V 2 = 106 m. L

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 = P 1 + P 2 + P 3 ……. Pair = PO + PN 2 + Par + PH O + PCO 2 2 2

Example: What is the total pressure of a mixture of gases made up of CO 2, and H 2 if the partial pressures are 22. 3 k. Pa, 44. 7 k. Pa, and 112 k. Pa, respectively? Ptotal = P 1 + P 2 + P 3 PTOTAL = 22. 3 k. Pa + 44. 7 k. Pa + 112 k. Pa = PTOTAL = 179 k. Pa

Gas Stoichiometry Example 1: One mole of any gas at STP occupies a 22. 4 volume of ______ L. How do you write this as a conversion factor? 22. 4 L OR 1 mol 1 mol 22. 4 L For the following reaction: N 2(g) +3 H 2 (g) 2 NH 3(g) What volume of nitrogen gas at STP would be required to react with excess hydrogen gas to produce. 830 L of NH 3 in the reaction above? . 830 L NH 3 1 mol N 2 1 22. 4 L N 2 22. 4 L NH 3 2 mol NH 3 1 mol N 2 =. 415 L N 2

Gas Stoichiometry N 2(g) +3 H 2 (g) 2 NH 3(g) ? L 0. 100 g What volume of nitrogen gas at STP would be required to react with 0. 100 grams of hydrogen gas in the reaction above? (Make sure the chemical equation is balanced) 0. 100 g H 2 1 mol N 2 22. 4 L N 2 1 2. 02 g H 2 3 mol H 2 =. 370 L N 2 1 mol N 2

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