Gas Laws


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Gas Laws

  1. 1. Gas Laws February 10 th & 11 th , 2010 Ms. Komperda
  2. 2. The Kinetic Molecular Theory is a set of statements that describe the behavior of gases <ul><ul><li>Gases are made up of a large number of small particles </li></ul></ul><ul><ul><li>These particles are in constant random motion </li></ul></ul><ul><ul><li>The speed (kinetic energy) that these particles travel at is directly related to their temperature </li></ul></ul><ul><ul><li>The particles collide with each other and the walls of the container frequently </li></ul></ul><ul><ul><li>Pressure is a measurement of how often these molecules hit the walls of the container </li></ul></ul>
  3. 3. Ideal vs Real Gases <ul><li>It is easier to describe the behavior of ideal gases. To do this we assume some things about gases that may not be true </li></ul><ul><ul><li>The particles in ideal gases: </li></ul></ul><ul><ul><ul><li>Take up no space </li></ul></ul></ul><ul><ul><ul><li>Never attract or repel each other </li></ul></ul></ul><ul><li>Real gases actually do take up space and can attract or repel. </li></ul><ul><ul><li>At HIGH TEMPERATURE and LOW PRESSURE real gases behave like ideal gases </li></ul></ul><ul><ul><li>Why? </li></ul></ul>
  4. 4. Properties of Gases <ul><li>Chemists do not simply observe gases, they measure their properties. These are the properties we measure: </li></ul><ul><li>V = volume of the gas (L) </li></ul><ul><li>T = temperature (K) </li></ul><ul><ul><li>ALL temperatures MUST be in Kelvin!!! No Exceptions! </li></ul></ul><ul><li>n = amount (moles) </li></ul><ul><li>P = pressure (atmospheres) </li></ul>
  5. 5. Pressure <ul><li>Pressure is the force exerted over a certain area </li></ul><ul><li>Because gases have mass they exert pressure </li></ul><ul><li>Pressure of air is measured with a BAROMETER (developed by Torricelli in 1643) </li></ul><ul><li>Hg rises in tube until force of Hg (down) balances the force of atmosphere (pushing up). (Just like a straw in a soft drink) </li></ul>
  6. 6. Pressure <ul><li>Column height measures Pressure of atmosphere </li></ul><ul><li>1 standard atmosphere (atm) * </li></ul><ul><li>= 760 mm Hg (or torr) * </li></ul><ul><li>= 14.7 pounds/in2 (psi) </li></ul><ul><li>= 101.3 kPa (kiloPascal) </li></ul><ul><li>= about 34 feet of water! </li></ul><ul><li>* Memorize these! </li></ul>
  7. 7. Pressure Conversions = 0.9182 atm = 0.625 atm 475 mm Hg x 93.01 kPa x
  8. 8. Boyle’s Law <ul><li>P 1 V 1 = P 2 V 2 </li></ul><ul><li>This means Pressure and Volume are INVERSELY PROPORTIONAL if moles and temperature are constant (do not change). For example, P goes up as V goes down. </li></ul>Robert Boyle (1627-1691). Son of Earl of Cork, Ireland.
  9. 9. Boyles Law Graph P V
  10. 10. Boyle’s Law <ul><li>A bicycle pump is a good example of Boyle’s law. </li></ul><ul><li>As the volume of the air trapped in the pump is reduced, its pressure goes up, and air is forced into the tire. </li></ul>
  11. 11. Charles’s Law <ul><li>If n and P are constant, then </li></ul><ul><li>V and T are DIRECTLY proportional. </li></ul><ul><li>V1 V2 </li></ul><ul><li>T1 T2 </li></ul><ul><li>If one temperature goes up, the volume goes up! </li></ul>Jacques Charles (1746-1823). Isolated boron and studied gases. Balloonist. =
  12. 12. Charles Law Graph T V
  13. 13. Charles’s Law <ul><li>Think about what happens to your bike tires in the winter </li></ul><ul><li>As the temperature decreases the tires deflate </li></ul><ul><li>This also happens if you take a balloon outside on a cold day </li></ul>
  14. 14. Gay-Lussac’s Law <ul><li>If n and V are constant , then </li></ul><ul><li>P and T are DIRECTLY proportional. </li></ul><ul><li>P 1 P 2 </li></ul><ul><li>= </li></ul><ul><li>T 1 T 2 </li></ul><ul><li>If one temperature goes up, the pressure goes up! </li></ul>Joseph Louis Gay-Lussac (1778-1850)
  15. 15. Gay-Lussac’s Graph T P
  16. 16. <ul><li>The good news is that you don’t have to remember all three gas laws! Since they are all related to each other, we can combine them into a single equation. </li></ul><ul><li>P 1 V 1 P 2 V 2 </li></ul><ul><li>= </li></ul><ul><li>T 1 T 2 </li></ul>Combined Gas Law No, it’s not related to R2D2
  17. 17. <ul><li>If you should only need one of the other gas laws, you can cover up the item that is constant and you will get that gas law! </li></ul><ul><li> </li></ul><ul><li>= </li></ul>Combined Gas Law P 1 V 1 T 1 P 2 V 2 T 2 Boyle’s Law Charles’ Law Gay-Lussac’s Law
  18. 18. <ul><li>A sample of helium gas has a volume of 0.180 L, a pressure of 0.800 atm and a temperature of 29°C. What is the new temperature (°C) of the gas at a volume of 90.0 mL and a pressure of 3.20 atm? </li></ul><ul><li>Notice how this problem still has TWO sets of conditions- before and after </li></ul>Combined Gas Law Problem List what you know: P 1 = 0.800 atm V 1 = .180 L T 1 = 302 K P 2 = 3.20 atm V 2 = .090 L T 2 = ??
  19. 19. <ul><li>P 1 = 0.800 atm V 1 = .180 L T 1 = 302 K </li></ul><ul><li>P 2 = 3.20 atm V 2 = 0.090 L T 2 = ?? </li></ul><ul><li>P 1 V 1 P 2 V 2 Cross multiply to get rid of the fraction: P 1 V 1 T 2 = P 2 V 2 T 1 </li></ul><ul><li>T 1 = T 2 </li></ul><ul><li>Solve for T 2 T 2 = P 2 V 2 T 1 = 3.20 atm x 0.090 L x 302 K </li></ul><ul><li> P 1 V 1 0.800 atm x .180 L </li></ul><ul><li>T 2 = 604 K - 273 = 331 °C </li></ul>Calculations T 2 = 604 K
  20. 20. <ul><li>Brings together all gas properties, including moles. </li></ul><ul><li>What is the difference between a real and an ideal gas? </li></ul>Ideal Gas Law PV = nRT
  21. 21. <ul><li>P = Pressure </li></ul><ul><li>V = Volume </li></ul><ul><li>T = Temperature </li></ul><ul><li>n = number of moles </li></ul><ul><li>R is a constant, called the Ideal Gas Constant </li></ul><ul><li>R = 0.08206 </li></ul>Using the Ideal Gas Law L * atm mol * K
  22. 22. <ul><li>How much N 2 is required to fill a small room with a volume of 27,000 L to 745 mm Hg at 25 o C? </li></ul><ul><li>List knowns (change units if needed) </li></ul><ul><li>V = 27,000 L </li></ul><ul><li>T = 25 o C + 273 = 298 K </li></ul><ul><li>P = 745 mm Hg * (1 atm/760 mm Hg) = 0.98 atm </li></ul><ul><li>And we always know R, 0.08206 L*atm / mol*K </li></ul>Ideal Gas Calculation
  23. 23. <ul><li>Rearrange the equation and solve for the unknown </li></ul><ul><li>PV = n RT </li></ul>Ideal Gas Calculation RT RT n = 1082 mol How many grams of N 2 is this? 1082 mol * (28 g/ 1mol) = 30,296 g!
  24. 24. <ul><li>What is the </li></ul><ul><li>total pressure in </li></ul><ul><li>the cylinder? </li></ul><ul><li>P total in gas mixture = P 1 + P 2 + ... </li></ul><ul><li>Dalton’s Law: total P is sum of PARTIAL pressures. </li></ul>Dalton’s Law of Partial Pressure
  25. 25. Diffusion <ul><li>Think about a time you were in a room with somebody wearing too much perfume… </li></ul><ul><li>Why don’t you smell it immediately? </li></ul><ul><li>What about people across the room? </li></ul><ul><ul><li>This is because the smell spreads out. </li></ul></ul><ul><li>This rapid dispersion of particles from high concentration to low concentration is DIFFUSION in action! </li></ul>
  26. 26. <ul><li>Think about when a nail makes a small puncture in a tire and the air escapes? Isn’t that diffusion too? </li></ul><ul><ul><li>When this happens, we are looking at EFFUSION, or the motion of a gas through a small opening </li></ul></ul><ul><li>Since the opening is small, gas particles have to “wait in line” for other particles to pass through. </li></ul><ul><ul><li>Like a grocery checkout, it’s first come, first served. </li></ul></ul><ul><ul><li>Lighter particles travel faster and escape more often than more massive particles. </li></ul></ul><ul><ul><ul><li>Difference between having a full cart (heavy and slow) and 10 items or less (light and fast) </li></ul></ul></ul>Effusion
  27. 27. <ul><li>Graham’s law governs effusion and diffusion of gas molecules. </li></ul>Rates of Effusion & Diffusion Thomas Graham, 1805-1869. Professor in Glasgow and London. Rate of effusion is inversely proportional to molar mass. High mass = low speed Low mass = high speed