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- 1. Chapter 14 The Behavior of Gases
- 2. Section 14.1 The Properties of Gases <ul><li>OBJECTIVES: </li></ul><ul><ul><li>Explain why gases are easier to compress than solids or liquids are. </li></ul></ul>
- 3. Section 14.1 The Properties of Gases <ul><li>OBJECTIVES: </li></ul><ul><ul><li>Describe the three factors that affect gas pressure. </li></ul></ul>
- 4. Compressibility <ul><li>Gases can expand to fill its container, unlike solids or liquids </li></ul><ul><li>The reverse is also true: </li></ul><ul><ul><li>They are easily compressed , or squeezed into a smaller volume </li></ul></ul><ul><ul><li>Compressibility is a measure of how much the volume of matter decreases under pressure </li></ul></ul>
- 5. Compressibility <ul><li>This is the idea behind placing “air bags” in automobiles </li></ul><ul><ul><li>In an accident, the air compresses more than the steering wheel or dash when you strike it </li></ul></ul><ul><ul><li>The impact forces the gas particles closer together, because there is a lot of empty space between them </li></ul></ul>
- 6. Compressibility <ul><li>At room temperature, the distance between particles is about 10x the diameter of the particle </li></ul><ul><ul><li>Fig. 14.2, page 414 </li></ul></ul><ul><li>This empty space makes gases good insulators (example: windows, coats) </li></ul><ul><li>How does the volume of the particles in a gas compare to the overall volume of the gas? </li></ul>
- 7. Variables that describe a Gas <ul><li>The four variables and their common units: </li></ul><ul><ul><li>1. pressure (P) in kilopascals </li></ul></ul><ul><ul><li>2. volume (V) in Liters </li></ul></ul><ul><ul><li>3. temperature (T) in Kelvin </li></ul></ul><ul><ul><li>4. amount (n) in moles </li></ul></ul><ul><li>The amount of gas , volume , and temperature are factors that affect gas pressure. </li></ul>
- 8. 1. Amount of Gas <ul><li>When we inflate a balloon, we are adding gas molecules. </li></ul><ul><li>Increasing the number of gas particles increases the number of collisions </li></ul><ul><ul><li>thus, the pressure increases </li></ul></ul><ul><li>If temperature is constant, then doubling the number of particles doubles the pressure </li></ul>
- 9. Pressure and the number of molecules are directly related <ul><li>More molecules means more collisions, and… </li></ul><ul><li>Fewer molecules means fewer collisions. </li></ul><ul><li>Gases naturally move from areas of high pressure to low pressure , because there is empty space to move into – a spray can is example. </li></ul>
- 10. Common use? <ul><li>A practical application is Aerosol (spray) cans </li></ul><ul><ul><li>gas moves from higher pressure to lower pressure </li></ul></ul><ul><ul><li>a propellant forces the product out </li></ul></ul><ul><ul><li>whipped cream, hair spray, paint </li></ul></ul><ul><li>Fig. 14.5, page 416 </li></ul><ul><li>Is the can really ever “empty”? </li></ul>
- 11. 2. Volume of Gas <ul><li>In a smaller container, the molecules have less room to move. </li></ul><ul><li>The particles hit the sides of the container more often. </li></ul><ul><li>As volume decreases, pressure increases. (think of a syringe) </li></ul><ul><ul><li>Thus, volume and pressure are inversely related to each other </li></ul></ul>
- 12. 3. Temperature of Gas <ul><li>Raising the temperature of a gas increases the pressure, if the volume is held constant. (Temp. and Pres. are directly related ) </li></ul><ul><ul><li>The molecules hit the walls harder, and more frequently! </li></ul></ul><ul><li>Fig. 14.7, page 417 </li></ul><ul><li>Should you throw an aerosol can into a fire? What could happen? </li></ul><ul><li>When should your automobile tire pressure be checked? </li></ul>
- 14. Section 14.2 The Gas Laws <ul><li>OBJECTIVES: </li></ul><ul><ul><li>Describe the relationships among the temperature, pressure, and volume of a gas. </li></ul></ul>
- 15. Section 14.2 The Gas Laws <ul><li>OBJECTIVES: </li></ul><ul><ul><li>Use the combined gas law to solve problems. </li></ul></ul>
- 16. The Gas Laws are mathematical <ul><li>The gas laws will describe HOW gases behave. </li></ul><ul><ul><li>Gas behavior can be predicted by the theory. </li></ul></ul><ul><li>The amount of change can be calculated with mathematical equations. </li></ul><ul><li>You need to know both of these: the theory , and the math </li></ul>
- 17. Robert Boyle (1627-1691) <ul><li>Boyle was born into an aristocratic Irish family </li></ul><ul><li>Became interested in medicine and the new science of Galileo and studied chemistry. </li></ul><ul><li>A founder and an influential fellow of the Royal Society of London </li></ul><ul><li>Wrote extensively on science, philosophy, and theology. </li></ul>
- 18. #1. Boyle’s Law - 1662 <ul><li>Pressure x Volume = a constant </li></ul><ul><li>Equation: P 1 V 1 = P 2 V 2 ( T = constant) </li></ul>Gas pressure is inversely proportional to the volume , when temperature is held constant.
- 19. Graph of Boyle’s Law – page 418 Boyle’s Law says the pressure is inverse to the volume. Note that when the volume goes up, the pressure goes down
- 20. - Page 419
- 21. Jacques Charles (1746-1823) <ul><li>French Physicist </li></ul><ul><li>Part of a scientific balloon flight on Dec. 1, 1783 – was one of three passengers in the second balloon ascension that carried humans </li></ul><ul><li>This is how his interest in gases started </li></ul><ul><li>It was a hydrogen filled balloon – good thing they were careful! </li></ul>
- 22. #2. Charles’s Law - 1787 <ul><li>The volume of a fixed mass of gas is directly proportional to the Kelvin temperature, when pressure is held constant. </li></ul><ul><li>This extrapolates to zero volume at a temperature of zero Kelvin . </li></ul>
- 23. Converting Celsius to Kelvin <ul><li>Gas law problems involving temperature will always require that the temperature be in Kelvin . (Remember that no degree sign is shown with the kelvin scale.) </li></ul><ul><ul><li>Reason? There will never be a zero volume, since we have never reached absolute zero. </li></ul></ul>Kelvin = C + 273 °C = Kelvin - 273 and
- 24. - Page 421
- 25. Joseph Louis Gay-Lussac (1778 – 1850) <ul><li>French chemist and physicist </li></ul><ul><li>Known for his studies on the physical properties of gases. </li></ul><ul><li>In 1804 he made balloon ascensions to study magnetic forces and to observe the composition and temperature of the air at different altitudes. </li></ul>
- 26. #3. Gay-Lussac’s Law - 1802 <ul><li>The pressure and Kelvin temperature of a gas are directly proportional, provided that the volume remains constant. </li></ul><ul><li>How does a pressure cooker affect the time needed to cook food? (Note page 422) </li></ul><ul><li>Sample Problem 14.3, page 423 </li></ul>
- 27. #4. The Combined Gas Law The combined gas law expresses the relationship between pressure, volume and temperature of a fixed amount of gas. Sample Problem 14.4, page 424
- 28. <ul><li>The combined gas law contains all the other gas laws! </li></ul><ul><li>If the temperature remains constant... </li></ul>P 1 V 1 T 1 x = P 2 V 2 T 2 x Boyle’s Law
- 29. <ul><li>The combined gas law contains all the other gas laws! </li></ul><ul><li>If the pressure remains constant... </li></ul>P 1 V 1 T 1 x = P 2 V 2 T 2 x Charles’s Law
- 30. <ul><li>The combined gas law contains all the other gas laws! </li></ul><ul><li>If the volume remains constant... </li></ul>P 1 V 1 T 1 x = P 2 V 2 T 2 x Gay-Lussac’s Law
- 31. Section 14.3 Ideal Gases <ul><li>OBJECTIVES: </li></ul><ul><ul><li>Compute the value of an unknown using the ideal gas law. </li></ul></ul>
- 32. Section 14.3 Ideal Gases <ul><li>OBJECTIVES: </li></ul><ul><ul><li>Compare and contrast real an ideal gases. </li></ul></ul>
- 33. 5. The Ideal Gas Law #1 <ul><li>Equation: P x V = n x R x T </li></ul><ul><li>P ressure times V olume equals the number of moles ( n ) times the Ideal Gas Constant ( R ) times the T emperature in Kelvin. </li></ul><ul><li>R = 8.31 (L x kPa) / (mol x K) </li></ul><ul><li>The other units must match the value of the constant , in order to cancel out. </li></ul><ul><li>The value of R could change, if other units of measurement are used for the other values (namely pressure changes) </li></ul>
- 34. <ul><li>We now have a new way to count moles (the amount of matter), by measuring T, P, and V. We aren’t restricted to only STP conditions: </li></ul><ul><li>P x V </li></ul><ul><li>R x T </li></ul>The Ideal Gas Law n =
- 35. Ideal Gases <ul><li>We are going to assume the gases behave “ideally”- in other words, they obey the Gas Laws under all conditions of temperature and pressure </li></ul><ul><li>An ideal gas does not really exist , but it makes the math easier and is a close approximation. </li></ul><ul><li>Particles have no volume? Wrong! </li></ul><ul><li>No attractive forces? Wrong! </li></ul>
- 36. Ideal Gases <ul><li>There are no gases for which this is true (acting “ideal”); however, </li></ul><ul><li>Real gases behave this way at a) high temperature , and b) low pressure. </li></ul><ul><ul><li>Because at these conditions, a gas will stay a gas </li></ul></ul><ul><ul><li>Sample Problem </li></ul></ul>
- 37. #6. Ideal Gas Law 2 <ul><li>Equation: P x V = m x R x T M </li></ul><ul><li>Allows LOTS of calculations, and some new items are: </li></ul><ul><li>m = mass, in grams </li></ul><ul><li>M = molar mass, in g/mol </li></ul><ul><li>Molar mass = m R T P V </li></ul>
- 38. Density <ul><li>Density is mass divided by volume </li></ul><ul><li>m </li></ul><ul><li>V </li></ul><ul><li>so, </li></ul><ul><li>m M P </li></ul><ul><li>V R T </li></ul>D = D = =
- 39. Real Gases and Ideal Gases
- 40. Ideal Gases don’t exist, because: <ul><li>Molecules do take up space </li></ul><ul><li>There are attractive forces between particles </li></ul><ul><ul><li>- otherwise there would be no liquids formed </li></ul></ul>
- 41. Real Gases behave like Ideal Gases... <ul><li>When the molecules are far apart. </li></ul><ul><li>The molecules do not take up as big a percentage of the space </li></ul><ul><ul><li>We can ignore the particle volume. </li></ul></ul><ul><li>This is at low pressure </li></ul>
- 42. Real Gases behave like Ideal Gases… <ul><li>When molecules are moving fast </li></ul><ul><ul><li>This is at high temperature </li></ul></ul><ul><li>Collisions are harder and faster. </li></ul><ul><li>Molecules are not next to each other very long. </li></ul><ul><li>Attractive forces can’t play a role. </li></ul>
- 43. Section 14.4 Gases: Mixtures and Movements <ul><li>OBJECTIVES: </li></ul><ul><ul><li>Relate the total pressure of a mixture of gases to the partial pressures of the component gases. </li></ul></ul>
- 44. Section 14.4 Gases: Mixtures and Movements <ul><li>OBJECTIVES: </li></ul><ul><ul><li>Explain how the molar mass of a gas affects the rate at which the gas diffuses and effuses. </li></ul></ul>
- 45. #7 Dalton’s Law of Partial Pressures <ul><li>For a mixture of gases in a container, </li></ul><ul><ul><li>P Total = P 1 + P 2 + P 3 + . . . </li></ul></ul><ul><li>P 1 represents the “ partial pressure”, or the contribution by that gas. </li></ul><ul><li>Dalton’s Law is particularly useful in calculating the pressure of gases collected over water. </li></ul>
- 46. Collecting a gas over water Connected to gas generator
- 47. <ul><li>If the first three containers are all put into the fourth, we can find the pressure in that container by adding up the pressure in the first 3: </li></ul>2 atm + 1 atm + 3 atm = 6 atm 1 2 3 4
- 48. Diffusion is: <ul><li>Effusion: Gas escaping through a tiny hole in a container. </li></ul><ul><li>Both of these depend on the molar mass of the particle , which determines the speed. </li></ul><ul><li>Molecules moving from areas of high concentration to low concentration. </li></ul><ul><ul><li>Example: perfume molecules spreading across the room. </li></ul></ul>
- 49. <ul><li>Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing. </li></ul><ul><li>Molecules move from areas of high concentration to low concentration. </li></ul>
- 50. <ul><li>Effusion : a gas escapes through a tiny hole in its container </li></ul><ul><li>-Think of a nail in your car tire… </li></ul>Diffusion and effusion are explained by the next gas law: Graham’s
- 51. 8. Graham’s Law <ul><li>The rate of effusion and diffusion is inversely proportional to the square root of the molar mass of the molecules. </li></ul><ul><li>Derived from: Kinetic energy = 1/2 mv 2 </li></ul><ul><li>m = the molar mass, and v = the velocity. </li></ul>Rate A Mass B Rate B Mass A =
- 52. <ul><li>With effusion and diffusion, the type of particle is important: </li></ul><ul><ul><li>Gases of lower molar mass diffuse and effuse faster than gases of higher molar mass. </li></ul></ul><ul><li>Helium effuses and diffuses faster than nitrogen – thus, helium escapes from a balloon quicker than many other gases </li></ul>Graham’s Law
- 53. End of Chapter 14

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