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Exploring Gas Laws & Properties of Matter

Dive into the fundamental principles of gas laws and properties of matter including density, compressibility, and thermal expansion. Understand the Kinetic Molecular Theory and how it relates to gases, liquids, and solids. Explore key concepts like pressure, volume, and temperature relationships in the gas laws. Discover how to apply Boyle's Law, Charles' Law, and the Ideal Gas Law in various scenarios. Learn about Dalton's Law of Partial Pressures and Graham's Law of Effusion. Expand your knowledge of chemistry with real-world applications and problem-solving exercises.

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Exploring Gas Laws & Properties of Matter

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  1. Chapter 13-14Kinetic Molecular Theory and the Gas Laws Chemistry Sleevi

  2. Properties of Matter • Density – mass per unit volume • Shape – dependence on container • Compressibility – change in volume with change in pressure • Thermal expansion – change in volume with change in temperature

  3. Properties of Matter

  4. Properties of Matter

  5. Gases, Liquids, and Solids State of a substance: kinetic energy vs strength of the interactions between the particles.

  6. Kinetic Molecular Theory • Description of gas particles: • Move randomly & rapidly • Small compared to space between them • No attractive forces • Kinetic energy increases with temperature • Collisions are elastic

  7. Characteristics of a Gas

  8. An Ideal Gas • KMT: • volume of particles negligible compared to distances between the particles • no attractive forces between particles • Real gases differ most from an ideal gas at low temperatures and high pressures.

  9. Pressure of a Gas • Measured with barometer (invented by Torricelli in 17th C) • Pressure due to collisions of particles with objects • Pressure is force per unit area (pounds per square inch) • Standard atmosphere = pressure needed to support a 760 mm column of mercury 1 atm = 760 mm Hg

  10. How a Hg Barometer Works

  11. Other Pressure Units 1 atm = 760 mm Hg = 760 torr = 14.7 psi = 101 kPa = 1.01 bar = 29.9 in Hg

  12. Converting Pressure Units • Examples • Convert 455 torr to atm • Convert 250 kPa to mm Hg

  13. STP • Standard Temperature & Pressure • 0oC • 1 atm

  14. Kinetic Energy & Temperature

  15. The Gas Laws • Mathematical relationships between pressure, volume, temperature and quantity of a gas • Studied by Boyle (17th C), Charles, Gay-Lussac, Avogadro (18th C)

  16. Boyle’s Law • For a fixed amount of gas at constant temperature, pressure is inversely proportional to volume. As pressure increases, volume decreases. PV = constant P1V1=P2V2

  17. Boyle’s Law Pressure Volume

  18. Boyle’s Law • If the volume of a cylinder of gas is halved, the pressure of the gas inside the cylinder doubles. P1V1 = P2V2 initial conditionsnew conditions

  19. Boyle’s Law Example Gas Laws Worksheet #1

  20. Charles’ Law For a fixed amount of gas, the volume of a gas is directly proportional to its temperature at constant pressure.

  21. Charles’ Law Volume Temperature -273oC

  22. Temperature Scales Celsius the difference between the melting point and boiling point of water subdivided into 100 degrees. Fahrenheit  the difference between the melting point and boiling point of water subdivided into 180 degrees

  23. Celsius vs Fahrenheit oC = 5/9(oF-32) oF = 9/5(oC) + 32 -40oC = -40oF 20oC = 68oF 30oC = 86oF

  24. Kelvin Temperature Scale • Based on work of Charles • Increment on Kelvin scale same as increment on Celsius scale • Scale begins at zero (absolute zero) K = oC + 273 oC = K – 273 Gas Laws always use T in K!

  25. Charles’s Law • If the temperature of the cylinder is doubled, the volume of the gas inside the cylinder doubles. V1 V2 = T1 T2 initial conditions new conditions

  26. Charles’s Law

  27. Charles’ Law Example: • Calculate the final volume when a 75.0 mL sample of gas is heated from 5oC to 60oC at constant pressure. • convert T to Kelvin • volume can be any volume units as long as they match

  28. Charles’ Law Example Gas Laws Worksheet #6

  29. Gay-Lussac’s Law For a fixed quantity of a gas, the pressure of a gas is directly proportional to its temperature (at constant volume) P1 P2 = T1 T2

  30. Gay-Lussac’s Law Example Gas Laws Worksheet #9

  31. Combined Gas Law • Combines relationships of P, V and T • As each parameter is held constant, reduces to the individual law. P1V1 P2V2 = T1 T2

  32. Combined Gas Law • Example Gas Laws Worksheet #11

  33. Gas Laws

  34. The Ideal Gas Law PV = nRT P = pressure in atm V = volume in L n = number of moles R = ideal gas constant = 0.0821 L atm mol K T = temperature (in Kelvin)

  35. Ideal Gas Law • What is the volume of 0.413 mol of hydrogen gas at a temperature of 20oC and a pressure of 1200 torr? • convert T to Kelvin • convert P to atm

  36. Ideal Gas Law • Calculate molar mass (molecular weight = MW) • Using the ideal gas law, calculate the number of moles • MW = sample mass (in g)/# moles

  37. Dalton’s Law of Partial Pressures Total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the gases in the mixture For a mixture of three gases A, B, and C: Ptotal = PA + PB + PC partial pressures of A, B, and C

  38. Dalton’s Law of Partial Pressures Example: A sample of exhaled air contains four gases with the following partial pressures: N2 (563 mm Hg), O2 (118 mm Hg), CO2 (30 mm Hg), and H2O (50 mm Hg). What is the total pressure of the sample? Ptotal = PN2 + PO2 +PCO2 + PH2O Ptotal = 563 mm Hg + 118 mm Hg + 30 mm Hg + 50 mm Hg Ptotal = 761 mm Hg Answer

  39. Graham’s Law Diffusion • Tendency of molecules to move toward areas of lower concentration Effusion • A gas escapes through a tiny hole in a container

  40. Graham’s Law • Rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass. • Relationship between mass, velocity and KE KE = ½ mv2

  41. Graham’s Law • Relationship between mass, velocity and KE KE = ½ mv2 • Two objects with different masses have same KE, how do their velocities compare?

  42. Graham’s Law =

  43. Liquids • Particles have kinetic energy • Particles are attracted to one another • Definite volume • Reduced space between molecules (vs gases) • Increased density (vs gases) • Condensed state of matter

  44. Liquids • Vaporization • Conversion of liquid to a gas • Evaporation • Conversion of liquid to a gas BELOW the bp • Evaporative Cooling • Higher KE particles leave; lower KE particles left behind

  45. Liquids • Vapor pressure • Measure of the force exerted by a gas above a liquid • More gas molecules above the liquid, higher vapor pressure • More volatile gas, higher vapor pressure • Increases with increasing temperature

  46. Liquids

  47. Liquids • Measuring vapor pressure • Manometer

  48. Liquids • Boiling Point • Temperature at which vapor pressure = external pressure on the liquid • Normal Boiling Point • Boiling point of a liquid at 1 atm • Boiling is a cooling process; higher KE particles leave the liquid leaving lower KE • Steam worse than boiling liquid (higher potential energy)

  49. Solids • Crystal Structure – arrangement of the particles within the solid • Unit cell – smallest group of particles within a crystal that retains the geometric shape of the crystal

  50. Solids Crystal Systems: • Cubic • Tetragonal • Orthorhombic • Monoclinic • Triclinic • Hexagonal • Rhombohedral

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