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Chemistry 100

Chemistry 100. Gases and Gas Laws. The Definition of a Gas. Gas - a substance that is characterised by widely separated molecules in rapid motion. Mixtures of gases are uniform. Gases will expand to fill containers. Examples of Gaseous Substances.

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Chemistry 100

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  1. Chemistry 100 Gases and Gas Laws

  2. The Definition of a Gas Gas - a substance that is characterised by widely separated molecules in rapid motion. Mixtures of gases are uniform. Gases will expand to fill containers.

  3. Examples of Gaseous Substances • Common gases O2 and N2, the major components of "air" • Other gases F2, Cl2, H2 gaseous diatomic molecules • H2 and He are the ‘lighter than air’ gases • N2O (laughing gas)

  4. Three States of Matter Solids Liquids Gases

  5. Gases (cont’d) Most molecular compounds are solids or liquids at room temperature, but they can be converted to a gas relatively easily Important exception  ionic solids (e.g., NaCl) can't be easily coverted to gases

  6. Gases and Vapours • What is the difference between a gas and a vapour? • Gases  normally in the gaseous state at 25°C and 1 atm pressure • A vapour is the gaseous form of any substance that is normally in the liquid or solid state at normal temperatures and pressures

  7. The Definition of Pressure • The pressure of a gas is best defined as the forces exerted by gas on the walls of the container • Define P = force/area • The SI unit of pressure is the Pascal 1 Pa = N/m2 = (kg m/s2)/m2

  8. The Measurement of Pressure • How do we measure gas pressure? • Barometer - invented by Torricelli • Gas pressure conversion factors • 1 atm = 760 mm Hg = 760 Torr • 1 atm = 101.325 kpa = 1.01325 bar

  9. The Barometer

  10. The Gas Laws • Four variables were sufficient to fully describe the state of a gas • Pressure (P) • Volume (V) • Temperature (T) • The amount of the gas in moles (n)

  11. Boyle's Law • The gas volume/pressure relationship • The volume occupied by the gas is inversely proportional to the pressure • V  1/P • Temperature and the amount of the gas are fixed • V = k1/ P or PV = k1 • k1 is a proportionality constant

  12. Boyle's Law

  13. Charles and Gay-Lussac's Law • Defines the gas volume/temperature relationship • V  T (constant pressure and amount of gas) • Note T represents the temperature on Lord Kelvin's temperature Scale V = k2 T k2 proportionality constant

  14. Charles and Gay-Lussac's Law

  15. An Aside • The Kelvin temperature scale - • Lord Kelvin recognised the significance of the intercept in the volume/temperature relationship • All temperature (°C) vs. volume plots extrapolated to 0 volume at -273.15°C • Kelvin - absolute 0 • all thermal motion ceases

  16. The Kelvin Temperature Scale • Relating Kelvin scale and the Celcius scale • T (K) = [ tc (°C) + 273.15°C] K/°C • Freezing point of water: tc = 0 °C; T = 273.15 K • Boiling point of water: tc = 100 °C; T = 373.15 K • Room temperature: tc = 25 °C; T = 298 K • NOTE tc = C; T (K) = K NO DEGREE SIGN

  17. Amonton’s Law • The pressure/temperature relationship • For a given quantity of gas at a fixed volume, P  T P = k3 T P1 = k3T1 P2 = k3T2 P1 / T1 = P2 / T2 Amonton's law

  18. Amonton’s Law V1 V2 V3 P / atm V4 t = -273.15C t / C

  19. Avogadro’s Law • The volume of a gas at constant T and P is directly proportional to the number of moles of gas V = k4 n => n = number of moles of gas

  20. Avogadro’s Law

  21. The Ideal Gas Equation of State • We have four relationships V  1/P; Boyle’s law V  T; Charles’ and Gay-Lussac's law V  n; Avogadro’s law P  T; Amonton’s law

  22. Ideal Gas Equation of State • We combine these relationships into a single fundamental equation of state  the ideal gas equation PV = nRT R is the universal gas constant R = 0.082057 L atm / (K mol) = 8.314 J / (K mol)

  23. The Definition of an Ideal Gas • An ideal gas is a gas that obeys totally the ideal gas law over its entire P-V-T range • Ideal gases - molecules have negligible intermolecular attractive forces • Occupy a negligible volume compared to the container volume

  24. Standard Temperature and Pressure • Define: STP (Standard Temperature and Pressure) • Temperature  0.00 °C = 273.15 K • Pressure  1.000 atm • The volume occupied by 1.000 mole of an ideal gas at STP is 22.41 L!

  25. Gas Density Calculations A simple expression for calculating the molar mass of an unknown gas. Molar mass and gas density M = (dRT) / P d = the gas density

  26. Partial Pressures 2 1 2 2 1 1 2 1 2 2 1 1 1 2 Let's consider two ideal gases (gas 1 and gas 2) in a container of volume V.

  27. Dalton's Law of Partial Pressure • In a gaseous mixture, • each gas exerts the same pressure as if it was alone and occupied the same volume. • the partial pressure of each gas, Pi, is related to the total pressure by Pi = Xi PT • Xi is the mole fraction of gas i.

  28. Partial Pressures (cont’d) The pressure exerted by the gases is the sum of the partial pressures of the individual gases Let P1 and P2 be the partial pressures of gas 1 and 2, respectively. PT = P1 + P2 = nT (RT/V), PT = n1 (RT/V) + n2 (RT / V)

  29. The Mole Fraction • The mole fraction is defined as follows • For a two component mixture n1 = moles of substance 1 n2 = moles of substance 2 nT = n1 + n2 X1 = n1 / nT; X2 = n2 / nT

  30. Gas Collection Over Water

  31. Gas Collection Over Water Many gas measurements are carried out over water. Water vapour is collected with the gas. PT = Pgas + PH2O

  32. Kinetic Molecular Theory of Gases Macroscopic (i.e., large quantity) behaviour of gases. The kinetic molecular theory of gases attempts to explain the behaviour of gases on a molecular level.

  33. Kinetic Theory of Gases Gases consist of molecules widely separated in space. Volume of molecules is negligible compared to total gas volume. Gas molecules are in constant, rapid, straight-line motion. Collisions are elastic. Average kinetic energy (K.E.) of molecules depends on absolute temperature (T) only. Attractive forces between molecules are negligible.

  34. Kinetic Theory of Gases

  35. Gas Laws Explanations • Gas pressure results from collisions of gas molecules with the container walls. • Pressure depends on • the number of collisions per unit time • how hard gas molecules strike the container wall!

  36. Avogadro’s Law • More collisions of gas with container wall. • V  n at constant P, T. • Let's increase the amount of gas in the container (T, P constant)

  37. Boyle's Law • More collisions of the gas molecules with • the container wall and P increases. (V  1/P) Let's decrease the volume of the container (constant n and T).

  38. Charles’ and Gay-Lussac’s Law Low Temp. High Temp. The molecules must move faster T must increase. Let container volume increase (P, n are held constant).

  39. Molecular Speeds K.E. = 1/2 M U2 M = the molar mass of the gas U2 =the mean square speed of the gas • This speed is an average speed (some will always be fast, some slow).

  40. The Mean Square Speed • Kinetic Molecular Theory of Gases allows us to relate macroscopic measurements to molecular quantities • P, V are related to the molar mass and mean square seed, U2 P V = 1/3 n M U2 = n R T

  41. The Root Mean Square Speed 1/3 MU2 = RT U2 = 3RT / M (U2)1/2 = urms = (3RT/M)1/2 urms = the root mean square speed

  42. The Root Mean Square Speed

  43. The Mean Free Path Gas molecules encounter collisions with other gas molecules and with the walls of the container Define the mean free path as the average distance between successive molecular collisions

  44. The Mean Free Path

  45. The Mean Free Path As the pressure of the gas increases, the mean free path decreases, i.e., the higher the pressure, the greater the number of collisions encountered by a gas molecule.

  46. Diffusion Diffusion - gradual mixing of gas molecules caused by kinetic properties. Graham's Law  Under constant T, P, the diffusion rates for gaseous substances are inversely proportional to the square roots of their molar masses.

  47. Graham’s Law r1/r2 = (M2 / M1)1/2 • r1 and r2 are the diffusion rates of gases 1 and 2. • M1 and M2 are the molar masses of gas 1 and gas 2, respectively.

  48. Effusion Effusion - the process by which a gas under pressure goes (escapes) from one compartment of a container to another by passing through a small opening.

  49. Effusion

  50. The Effusion Equation • Graham’s Law - estimate the ratio of the effusion times for two different gases. t1/t2 = (M1 / M2)1/2 • t1 and t2 are the effusion times of gases 1 and 2. • M1 and M2 are the molar masses of gas 1 and gas 2, respectively.

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