Kinetic Theory and Gases

Kinetic Theory and Gases Kinetic Theory Explains how temperature and pressure affect the motion of molecules http://exploration.grc.nasa.gov/education/rocket/images/state.gif 1

Hydraulics http://library.thinkquest.org/ C007574/media/brake1.gif http://csumc.wisc.edu/cmct/parkstreet CT/locations/idealbodyshop/car.jpg http://www.hydraulic-equipmentmanufacturers.com/gifs/hydraulic-lift.jpg KE Kinetic Energy Energy of motion Depends on: Mass elocity

PE Potential Energy Stored Energy 1)Gravitational Potential Energy Energy due to height above earth ) Chemical Potential Energy Energy stored in bonds of batteries, food, gasoline, etc. Ideal Gases Particles are point masses they have no volume Particles have no mutual attraction to each other Behavior of ideal gases is a model for how real gases behave Ideal Gas calculations are simple and the results are close to those for real gases 3

Three Assumptions of Kinetic Theory 1) All matter is made of particles ) Particles are in constant motion 3) All collisions are perfectly elastic (molecules do not lose energy in collisions) At 5 o C, Oxygen Gas average speed = 443 m/s (1000 mph) Between collisions, an oxygen molecule travels 314 times its diameter There are 4.5 billion collisions each second 4

Air Pressure: Pressure the weight of air over an area Standard Pressure: average normal air pressure at sea level = 760 mmhg = 1 atm = 14.7 lbs/in = 101.3 kpa What Causes Gas Pressure? number and intensity of collisions -- speed of particles (temperature) -- concentration of particles -- mass / size of particles 5

Used to measure air pressure Barometer 760 mm The weight of a column of mercury is balanced by the weight of the air http://umpgal.gsfc.nasa.gov/www_root/homepage/uarsscience/uars_brochure/jpegs/barometer.jpg Evangelista Torricelli http://www.forestry-suppliers.com/images/00/5491_w.jpg 6

How is Pressure related to Weather? How is Pressure related to Altitude? chips chips chips chips http://www.visionlearning.com/library/ modules/mid107/image/lobject- 36-0310301035.gif http://www.met.utah.edu/jhorel/html/mesonet/l essons/pres_mtn.gif 7

Boiling P atm P atm P vap P vap P atm P vap t = 0 min t = 5 min BOILING! P vap = P atm t = 1 min Boiling The boiling point of water in Oregon is usually about <100 o C Is Oregon above or below sea level? (~974 feet above sea level) Record High : 815 mmhg Record Low: 656 mmhg 8

Try These 1 atm = 760 mmhg = 101.3 kpa.1 atm = mmhg 1596 0.8 atm = mmhg 608 798 mmhg = atm 1.05 684 mmhg = atm 0.9 750 mmhg = 99.97 kpa 790 mmhg = kpa 105.3 Demonstrations Crush the can acuum pump (shaving cream, marshmallow, balloon) Tube with cap Flask with index card Gas can Air pressure mat, glass square, well plate, soda suction Mustard container Balloon in Flask Fire Syringe Syringe/Martian Popping Thing Bernoulli bag/ball in funnell Hero s Fountain 9

Temperature Average Kinetic Energy of particles in a substance (depends on the speed and mass of particles) 100 K 100 K 73 K 500 K # of molecules 73 K 500 K Kinetic Energy Temperature Scales Water Boils Water Freezes Kelvin: Absolute temperature scale Cannot have a negative Kelvin temperature 0 K = Absolute Zero o C + 73 = K http://www.rain.org/~mkummel/stumpers/08oct99a.gif 10

Practice Problems Convert to Kelvin 3 o C = 96 K -11 o C = 6 K 3 o F = 73 K Convert to Celsius 315 K = 4 o C 77 K = 4 o C 1 o F = 100 o C STP Standard Temperature and Pressure 0 o C 1 atm 11

Diffusion What is diffusion The random movement of particles through a medium 5 Factors that Affect the Diffusion Rate of Gases 1. Mass of Particles mass, rate of diffusion. Concentration of Particles conc, rate of diffusion 3. Temperature temp, rate of diffusion 4. Air Pressure P air, rate of diffusion Presence of Another Gas Another gas, rate of diffusion 1

Lightest molecule Compare the relative rate of diffusion of H & N H N = M M N H H N = 8 H = 3.74 N H diffuses 3.74 times faster (further) than N 13

Lab 40 What is the relative rate of diffusion of NH 3 to HCl? 1 m NH 3 HCl NH 3 (g) + HCl (g) NH 4 Cl (s) NH3 HCl = M HCl M NH3 NH3 HCl = 36.5 17 = 1.5 times faster/further 14

Boyle s Law The pressure of a gas is inversely proportional to its volume (when temperature is constant) P X = k (constant) P 1 1 = P Initial Final USE COMMON UNITS FOR P AND!!! (both atm, kpa; or both L, ml, cm 3 ) P Robert Boyle 167-1691 Try This 1 P 1 You have 1000 ml of gas at 754 mmhg. Find the volume at standard pressure.? P P 1 1 = P (754 mmhg)(1000ml) = (760 mmhg) 760 mmhg 760 mmhg = 99.1 ml 15

Dalton s Law Total pressure = sum of partial pressures P total = δp gas 1 + δp gas + δp gas 3 + P air = δp N + δp O + δp HO etc. Partial Gases collected over water Gases collected over water contain water vapor P air H O P+ O total lower bottle until water levels are equal P total = δp HO + δp gas Air Pressure Use Periodic Table Pressure of dry gas 16

750 mmhg P air P total = P HO + δpgas H O apor Gas Pressure of dry gas From Periodic Table apor Pressure Chart on PT δp HO changes with water temp Ex: A sample of H is collected over water at 5 o C and the pressure is 775 mmhg. What is the pressure of the dry gas? Ptotal = δ PH + δph O 775mmHg = δph + 3. 8mmHg δp H = 751. mmhg 17

1 Example 80 ml of gas are collected over water P at o total C. The air pressure was 758 mmhg. Find the volume of dry gas at standard pressure.? Ptotal = δ P gas +δph O 758 mmhg = δpgas +19. 8mmHg δp gas = 738. mmhg P 1 Pvap Periodic Table P = 1 1 P ( 738.mmHg )(80ml) = (760mmHg) = 77. 7ml P Charles Law The volume of a gas is directly proportional to the absolute temperature (Kelvin) if the pressure is held constant 1 = T 1 T KELIN T (K) 18

Apparently, oil tank rail cars are cleaned by scouring them with steam. Unfortunately, someone shut the hatch too soon... Try This #1 If you had 100 ml of a dry gas at 30 o C, what volume would it occupy at 60 o C? 1 = T 1 T 100ml = 303K 333K = 109.9 ml 19

Try This # 350 ml of gas at 0 o C is compressed to 100 ml. What is the new temperature? 1 350ml 100 = = T 1 T 73K T = 78K ml T Graham s Law Quiz 1) He NO = M M NO He = 46 4 = 3.4 ) 3) M M H x x = 3. = = 0.5g / mol M x H DH DH =.9 =.9 DH = 43. 5cm D 15cm NH 3 0

Open vs Closed Containers Open Container Closed Container 1) Increase Temp? ) # collisions? 3) Pressure? 4) olume? 1) Increase Temp? ) # collisions? 3) Pressure? 4) olume? Guess the Gas Law 1) An eqn with and T ) An eqn with P and 3) find the pressure of the dry gas 4) = k T 5) Uses vapor pressure of water 6) P = k 7) P 8) 9) P total = δp gas 1 + δp gas 10) Inverse Proportion 11) Direct Proportion 1) M 1 = M T 13) collected over water 14) balloon in ice 15) compressed syringe 1 1