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## Kinetic Theory (Gas Laws)

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**Kinetic Theory (Gas Laws)**Chapter 16**Atomic Mass Unit**• Uses Carbon-12 as standard • 1 atom of 12C masses 12.000 u 1 u = 1.66 X 10-27 kg**Review of Moles**• 1 mole = 6.022 X 1023 atoms/molecules • GMA • GMMA • What is the molar mass of nitrogen, N2? • What is the molar mass of BaCl2? • How many moles are in 132 grams of CO2? • How many atoms are in a 200 gram sample of iron?**States of Matter**They wander in random patterns quite close to one another. Can “wiggle” in place (these are the wiggle lines)**Plasma**• 4th state of matter • Ionized gases • Electrons are removed from the atoms • Positive ions remain • Present in: • Stars • Lightning • Arc welding • Most common state of matter in the universe**Plasma**A hydrogen and helium plasma such as you would find in the sun e He+ e He+ e H+ H+ e He+ e He+ e e H+ H+ e**Temperature**• Measure of the average molecular motion of a group of atoms/molecules Conversion Formulas F = 1.8 (oC) + 32 K = C + 273 C = K – 273**Absolute Zero**• All atomic and molecular motion stops • Coldest possible temperature • Never reached absolute zero • Liquid Nitrogen = 77 K (-196 oC) • Dry Ice = 216 K (-56.6 oC)**102 oF oC**-10.0 oC oF 25 oC K 177 K oC 310 oC K**102 oF 39oC**-10.0 oC 14.0 oF 25 oC 298 K 177 K -96 oC 310 oC 583 K**Kinetic Molecular Theory**• A gas is composed of small particles (molecules) that are spaced widely apart. • Compressible • Low density - about a 1000 times less dense than a liquid • The molecules of a gas are in rapid, constant motion • Pressure – the force of the molecules hitting the side of a container**All collisions are elastic**• Molecules don’t lose any energy when they collide. • Gas molecules have little/no attractive force on one another. • Too far apart • Mix thoroughly – unlike oil and water (too far apart for polar/non-polar forces to matter)**The temperature of a gas is directly proportional to average**kinetic energy of the molecules. KE = 3kT 2 k = Boltzmann’s constant = 1.38 X 10-23 J/K**Kinetic Molecular Theory: Ex 1**What is the average KE of molecules in a gas at 37oC? T = 273 + 37 = 310 K KE = 3kT 2 KE = (3/2)(1.38 X 10-23 J/K)(310 K)= 6.42 X 10-21J (this is per molecule)**Kinetic Molecular Theory: Ex 2**What is the average KE of molecules in a gas at 100 oC? ANS: 7.72 X 10-21J**P1V1 = n1RT1 P2V2 = n2RT2**Solve both equations for R R = P1V1 R = P2V2 n1T1 n2T2 P1V1 = P2V2 n1T1 n2T2**See what you can cross out (what you are not told)**• Remember to convert to Kelvin and moles if needed.**Boyle’s Law**• Boyle’s Law – The pressure and volume of a gas are inversely related • Bicycle pump example • Piston down – low volume, high pressure • Piston up – high volume, low pressure**Example:**The volume of a car’s cylinder is 475 mL at 1.05 atm. What is the volume when the cylinder is compressed and the pressure is 5.65 atm? P1V1 = P2V2 n1T1 n2T2**Collapses to:**P1V1 = P2V2 (Answer: 88.3 mL)**Example:**• A weather balloon has a volume of 40.0 liters on the surface of the earth at 1.00 atm. What will be the volume at 0.400 atm as it rises? P1V1 = P2V2 n1T1 n2T2**Barometer**• Torricelli (1643) • Height of column stayed about 760 mm (760 torr) • The higher the elevation, the lower the mercury • Weather • Rising pressure – calm weather • Dropping pressure – storm (fast moving air)**Charles Law**• Charles Law – The temperature and volume of a gas are directly related • “HOTTER = BIGGER” • Can be used to find absolute zero • Temperature must be in Kelvin**A basketball has a volume of 12.0 L when blown up at 25.00**oC. What will be the volume if it is taken outside on a day when it is only 5.00 oC? P1V1 = P2V2 n1T1 n2T2**Collapses to:**V1 = V2 T1 T2**2. If a tire contains 30.0 L of air at 10.0 oC, what volume**will it occupy when it is driven and warms up to 50.0 oC?**Guy-Lussac’s Law**Gay-Lussac’s Law = The temperature and pressure of a gas are directly related. • Temperature must be in Kelvin • Gas in a spray can has a pressure of 5.00 atm at 25.0 oC. What will be the pressure at 400.0 oC? P1V1 = P2V2 n1T1 n2T2**Avagadro’s Law**Avagadro’s Law = The volume of a gas is directly proportional to the moles present • “MORE = BIGGER” • A balloon has a volume of 1.00 L when 50.0 grams of N2 are in the balloon. What is the volume if an additional 25.0 grams of N2 are added?**Putting it all together**• Often you change more than one thing at a time. • Ex: In a car, volume, temperature, and pressure may change. 1. The volume of 0.0400 mol of a gas is 500.0 mL at 1.00 atm and 20.0 oC. What is the volume at 2.00 atm and 30.0oC?**2. The gauge pressure in a tire is 200 kPa at 10oC. After**driving, the temperature rises to 40oC. What will be the new gauge pressure? (Remember to add 101.3 kPa to the gauge pressure to get absolute pressure)**The Ideal Gas Law**• Works very well in situations close to Earth’s pressures and temperatures • Does not work for “extreme” situations (Jupiter’s atmosphere is too cold and too dense)**PV = nRT**• P = pressure in atmosphere • V = volume in Liters • n = number of moles • T = Temperature in Kelvin • R = gas constant R = 8.31 J/ mol-K**STP**Standard Temperature & Pressure • Standard Temperature = 0oC (273 K) • Standard Pressure = 1.013 X 105 N/m2 (101.3 kPa, 1 atm)**The Ideal Gas Law**Examples: • What is the volume of 1.00 mole of a gas at STP? • What is the mass of oxygen in a container at STP that has a volume of 10.0 m3? • A helium balloon has a radius of 18.0 cm. How many moles and grams of helium are needed to fill the balloon at 20oC and 1.05 atm? (V = 4/3pr3)**The Ideal Gas Law**4. Estimate the number of molecules you exhale in one breath at STP.**Three Processes**• Constant Volume (isochoric) • Vertical Line on PV diagram • No work done • Pressure cooker • Constant Pressure (isobaric) • Horizontal line on PV graph • Work done • Constant Temperature (isothermal) • Hyperbola curve on PV graph**Graham’s Law of Diffusion**• Gases mix to fill their volume evenly • Graham’s Law of Diffusion – the speed of a gas is inversely proportional to its molar mass • The larger the molar mass, the slower the gas molecule**Graham’s Law Example**At the same temperature, which moves faster, an He atom or an N2 molecule?**Calculating Average Speed**• Root-mean-square velocity vrms = 3kT m • Heavier molecules are slower • Temperature increases speed Molar mass**Average Speed: Example 1**What is the rms speed of one O2 molecule at 20oC? First we need the mass of one O2 in kilograms (32 u)(1.67 X 10-27kg) = 5.3 X 10-26 kg vrms = (3)(1.38 X 10-23 J/K)(293 K)½ (5.3 X 10-26 kg) vrms = 480 m/s (about 1000 mph)**Average Speed: Example 2**What is the rms speed of one N2 molecule at 20oC? ANS: 510 m/s (about 1100 mph)**Relative Humidity**• Vapor exists above all liquids • Even solids have a vapor pressure • Saturated vapor pressure depends on temperature • When saturated vapor pressure exceeds atmospheric pressure, boiling occurs