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## 4 Postulates of Kinetic Theory

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**Spherical molecules in constant, random straight-line**motion • “Elastic” collisions • Point masses • No interactions 4 Postulates of Kinetic Theory**Gas that obeys all 4 assumptions of the kinetic theory all**of the time. It doesn’t exist. It’s a model. Ideal Gas**Most real gases obey the kinetic theory most of the time.**Real Gas**Spherical molecules in random, straight-line motion**• “Elastic” collisions Which assumptions of the kinetic theory hold up?**Point masses**• No interactions Which assumptions of the kinetic theory break down?**When the gas molecules are close to each other.**When do the assumptions of the kinetic theory break down?**At high pressure & low temperature.**When are the gas molecules close to each other?**At low pressure & high temperature.**When are the gas molecules far apart from each other?**Good!**How do the gas molecules act when they are far apart from each other?**Have mass**• Take the shape & volume of their container • Compressible • Diffuse (spread spontaneously) • Exert Pressure What are the properties of gases?**Force/Area**Pressure**Collisions of the gas molecules with the walls of the**container. Pressure results from?**# of impacts per unit time and force of each impact**Pressure depends on? (microscopically)**# of gas molecules per unit volume**And temperature Pressure depends on? (macroscopically)**1 atm =**760 mm Hg = 760 torr = 101.3 kPa Units of Pressure?**P = 1 atm**T = 0C = 273 K STP**The volume of 1 mole of any gas at STP = 22.4 Liters**Molar Volume at STP**A measure of the avg. kinetic energy of the particles of a**substance. Temperature**Temperature**• Pressure • Volume • # of moles 4 variables needed to completely describe a gas-phase system?**For a fixed mass and temperature, the pressure-volume**product is a constant. Boyle’s Law**Volume of a gas varies inversely with the pressure.**Boyle’s Law**PV = k where k = a constant**Boyle’s Law**P1V1 = P2V2**Boyle’s Law**Hyperbola – it’s an inverse relationship!**Graph of Boyle’s Law**Volume goes to ½ the original volume**Double the pressure**Volume goes to 1/3 the original volume**Triple the pressure**Volume goes to 2 X the original volume**Halve the pressure**Volume goes to 1/4 of the original volume**Quadruple the pressure**Kelvin: 0 K means 0 speed.**Which temperature scale has a direct relationship to molecular velocity?**Kelvin: 0 K means 0 speed.**Absolute Temperature Scale**It’s a direct relationship.**Graph of Volume vs. Kelvin Temperature**V1/T1 = V2/T2**Charles’ Law Math expression of relationship between volume & Kelvin temperature**Volume of a gas varies directly with the Kelvin temperature.**Verbal expression of Charles’ Law**The volume doubles!**What happens to the volume when the Kelvin temperature is doubled?**The volume triples!**What happens to the volume when the Kelvin temperature is tripled?**The volume is halved!**What happens to the volume when the Kelvin temperature is halved?**It’s halved!**What happens to the Kelvin temperature when the volume is halved?**It’s a direct relationship.**Graph of Pressure vs. Kelvin Temperature**P1/T1 = P2/T2**Gay-Lussac’s Law Math expression for relationship between pressure & Kelvin temperature.**The pressure of a gas**varies directly with the Kelvin temperature. Verbal expression of relationship between pressure & Kelvin temperature.**The pressure is doubled.**What happens to the pressure when the Kelvin temperature is doubled?**The pressure is halved.**What happens to the pressure when the Kelvin temperature is halved?**The pressure is tripled.**What happens to the pressure when the Kelvin temperature is tripled?**The Kelvin temperature is doubled.**What happens to the Kelvin temperature when the pressure is doubled?**P1V1 = P2V2**T1 T2 Same pressure & volume units on both sides. Temperature must be in Kelvins. Combined Gas Law**Equal volumes of gases at the same temperature & pressure**have equal numbers of molecules. What is Avogadro’s Principle?**He**N2 These 2 boxes have the same: Mass c) # of molecules Density d) # of atoms**Ptot = P1 + P2 + P3 + P4 + …**What is Dalton’s Law of Partial Pressures?