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The Gas Laws

The Gas Laws. Boyle, Charles, Combined , and Ideal. Kinetic Theory. Explains the states of matter in terms of molecular composition Spacing speed. According to the theory. 1. Matter composed of small particles A. chemical properties- depend on

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The Gas Laws

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  1. The Gas Laws Boyle, Charles, Combined, and Ideal

  2. Kinetic Theory • Explains the states of matter in terms of • molecular composition • Spacing • speed

  3. According to the theory... • 1. Matter composed of small particles • A. chemical properties- depend on • a. composition • b. types of elements / molecules present. • B. physical properties- depend on • a. forces that particles exert on each other • b. distance separating the particles. • 2. Particles are in constant motion. • Degree of motion depends on temperature. • 3. Total kinetic energy of colliding particles remains constant. • elastic collisions - as indiv. particles collide some gain Ek and some lose Ek. Overall Ek is constant.

  4. States of Matter

  5. Solids • appear to vibrate around a fixed point (Extremely short free mean path) • have definite shape • “ “ volume • noncompressable • very slow rate of diffusion • crystalline or amorphous in nature

  6. Liquids • particles are closer than those of gases • forces of attraction between particles stronger than those of gases, and weaker than those of solids.

  7. Gases • The Kinetic Theory was developed by studying an ideal gas, a mathematically perfect gas. [Particles are treated as 1) point masses; as having no volume, and 2) as exerting no attractive forces on each other. • Space occupied by gas depends on temperature and pressure. • When describing a quantity of a gas temperature and pressure MUST be specified.

  8. Standard Temperature 0o C 273 K Standard Pressure 760 mm Hg 760 n/m2 760 Torr 101.325 kPa 1 atm Standard Temperature & Pressure S.T.P.

  9. Properties of Gases • Particles in a gas are in rapid, constant motion. • Gas particles travel in straight-line paths. • Gas particles fill containers.

  10. Properties of Gases • Exerts Pressure increases / decreases with a rise / fall in temperature • Have Low density 1000x less dense than liquid counterpart • Undergo Diffusion spread out from area of greater to lesser concentration until uniform spacing exists

  11. Properties of Gases Less Dense • Atmosphere is denser as you move closer to Earth’s surface. • The weight of atmospheric gases at any elevation compress the gases below. Compression Very Dense

  12. At room temperature gases... • are molecular • move independently of each other • travel at high speeds

  13. At 0oC • travel at about 1000 m/sec. • Goal to goal in .11 sec • undergo elastic collisions • alters individual speeds, but not overall Ek. • collide nearly 5 BILLION times per SECOND! • have different rates of diffusion • Less concentrated - diffusion rate  • More concentrated - diffusion rate 

  14. Diffusion rate depends on... • speed of gases • size of the molecules • attractive forces that may effect the molecules • At the same temperature: • the average kinetic energy of all molecules is the same.

  15. GAS and PRESSURE • Gas molecules exert pressure by hitting against the side of its container. • Degree of pressure dependent on: • 1. # of gas particles present* • 2. volume [size] of the container* • 3. average Ek of the molecules * • [temperature] • Changing any of these conditions changes the pressure.

  16. A barometer is a device that is used to measure atmospheric pressure.

  17. GAS and PRESSURE

  18. VOLUME and PRESSURE • To test only ONE variable at a time, the following must be held constant. • 1. # of gas particles present • 2. average Ek of the molecules [temperature] Boyle’s Law animation

  19. VOLUME and PRESSURE

  20. We can see that pressure is inversely proportional to volume P 1 V PV = k P1V1 = k and P2V2 = k P1V1 = P2V2 or V1 = P2 V2 P1 Boyle’s Law

  21. How are the pressure, volume, and temperature of a gas related? • Boyle’s law states that for a given mass of gas at constant temperature, the volume of the gas varies inversely with pressure. • As pressure decreases, volume increases

  22. DALTON’S LAW of PARTIAL PRESSURE • The pressure of each gas in a mixture is called the partial pressure of that gas. • John Dalton, the English chemist who proposed the atomic theory, discovered that the pressure exerted by each gas in a mixture is independent of that exerted by other gases present.

  23. Particle Model for a Gas Collected Over Water

  24. DALTON’S LAW of PARTIAL PRESSURE • Gases produced in the laboratory are often collected over water. The gas produced by the reaction displaces the water in the reaction bottle. • Dalton’s law of partial pressures can be applied to calculate the pressures of gases collected in this way. • Water molecules at the liquid surface evaporate and mix with the gas molecules. Water vapor, like other gases, exerts a pressure known as vapor pressure.

  25. DALTON’S LAW of PARTIAL PRESSURE • Hg originally used to measure the pressure of gases • Now known to be a carcinogen • ‘Mad as a hatter’ • H2O replaced Hg • several problems exist • Density is 13.6 x greater than mercury • Much more volatile. • Evaporates much faster. • Gases to be tested polluted with water’s vapor pressure.

  26. DALTON’S LAW of PARTIAL PRESSURE • In a mixture of gases [G1, G2, G3, ...] the TOTAL pressure of the gas mixture is the SUM of the pressures of the individual gas pressures. • Total Pressure = PressureG1 + PressureG2 + Pressure G3 + ... • If one of these gases is water • Total Pressure = PressureG1 + PressureG2 + Pressure Water + ...

  27. To ‘dry out’ a gas • Total Pressure = PressureG1 + PressureG2 + Pressure Water + ... • - Pressure Water • Pressure DRY gas = PressureG1 + PressureG2 + ...

  28. Application of Dalton’s Law • A gas is collected by water displacement. It occupies 593 cm3 of space at 45 oC. The atmospheric [total] pressure is 101.1 kPa. What volume will the dry gas occupy at 45 oC and standard pressure? • V1 = 593 cm3 V2 = ? • P1[wet] = 101.1 kPa P2 = 101.325 kPa

  29. P1V1 = P2V2 [101.1kPa*][593 cm3] = [101.325 kPa] V2 • At 45 oC, PH2O = 71.9 mm Hg • Since 760 mm Hg = 101.325 kPa • 101.325 kPa = ___x___ • 760 mm Hg 71.9 mm Hg • 9.6 kPa = x • 101.1 kPa - 9.6 kPa = 91.5 kPa Pressure of the dry gas • [91.5 kPa][593 cm3] = [101.325 kPa] V2 • [91.5 kPa][593 cm3] = V2 • [101.325 kPa] • 535.5 cm3 = V2

  30. Example B • Oxygen gas from the decomposition of potassium chlorate, KClO3, was collected by water displacement. The barometric pressure and the temperature during the experiment were 731.0 torr and 20.0°C. respectively. What was the partial pressure of the oxygen collected?

  31. Solution • Given:PT = Patm = 731.0 torr • PH2O= 17.5 torr (vapor pressure of water at 20.0°C) • Patm = PO2 + PH2O

  32. Diffusion and Effusion • The constant motion of gas molecules causes them to spread out to fill any container they are in. • The gradual mixing of two or more gases due to their spontaneous, random motion is known as diffusion. • Effusion is the process whereby the molecules of a gas confined in a container randomly pass through a tiny opening in the container.

  33. Diffusion and Effusion • Click here to view diffusion animation • Click here to view effusion animation

  34. Graham’s Law of Effusion • Rates of effusion and diffusion depend on the relative velocities of gas molecules. The velocity of a gas varies inversely with the square root of its molar mass. • Recall that the average kinetic energy of the molecules in any gas depends only the temperature.

  35. Graham’s Law of Effusion • From the equation relating the kinetic energy of two different gases at the same conditions, one can derive an equation relating the rates of effuses of two gases with their molecular mass: • Average kinetic energy = temperature Ek = 1/2mv2 Molecule 1 has a Ek1= 1/2mv2 Molecule 2 has a Ek2 =1/2mv2

  36. Graham’s Law of Effusion • At the same temperature Ek1= Ek2 1/2m1v2 = 1/2m2v2 m1v2 = m2v2 m1 = v22 m2 v12 √m1 = v2  m2 v1 Or √m1 = rate of effusion of 2  m2 = rate of effusion of 1

  37. What are the relative effusion rates of krypton (Kr) and bromine (Br2)? • mKr = vBr2  mBr2vKr • 84 =  160 • .72 = vBr2 1 vKr • Therefore, Br2 diffuses slower than Kr, at about 72% of Kr’s speed.

  38. GAS and TEMPERATURE • Jacques Charles studied the effect of temperature on gases • To test only ONE variable at a time, Charles held the following constant. • 1. # of gas particles present • 2. gas pressure • From his experiments he discovered that all gases expand and contract to the same degree, with a set temperature change.

  39. GAS and TEMPERATURE • Volume changes by 1/273 of the original volume • for each degree change in temperature. • At 0oC a gas has a volume of 1 m3. If the temperature is lowered to a -2730C the gas volume would theoretically be reduced to zero! • absolute zero- the temperature at which a gas • 1] has no volume • 2] has no Ek • Gas temperatures are ALWAYS measured in KELVINS. • Charles Law animation

  40. Charles’ Law

  41. GAS and TEMPERATURE V  T V = k T V1 = k V2 = k T1 T2 • Charles’ Law • V1 = V2 T1 T2

  42. Charles’ Law • Charles’s law states that the volume of a fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant. • Temperature in Kelvin (K)

  43. Charles’ Law • As the temperature of the water increases, the volume of the balloon increases.

  44. V1 =V2 T1 T2 4.00L = V2 297K 331K Cross multiply and solve for the missing variable, V2. The answer is:

  45. Temperature and Pressure • Gay-Lussac’s Law • Joseph Louis Gay-Lussac in the early 1800's. • To test only ONE variable at a time, Gay-Lussac held the following constant. • 1. # of gas particles present • 2. volume

  46. Pressure and temperature are directly proportional to each other Temperature and Pressure

  47. P1= k P2= k T1 T2

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