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Gas laws

Gas laws. Relationships between variables in the behaviour of gases. Learning objectives. Describe physical basis for pressure in a gas Describe the basic features of the kinetic theory Distinguish among and convert common units of pressure

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Gas laws

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  1. Gas laws Relationships between variables in the behaviour of gases

  2. Learning objectives • Describe physical basis for pressure in a gas • Describe the basic features of the kinetic theory • Distinguish among and convert common units of pressure • Apply gas laws to simple problems in predicting conditions of a gas • Apply ideal gas law to simple stoichiometry problems in gases

  3. Gas: no interactions • Not rigid • Completely fills container • Compressible • Low density • Energetic molecules

  4. Kinetic theory and car tires – a case for atoms • Molecules have energy • Energy increases with T • Pressure is caused by energetic molecules striking tire wall • Pumping up tire increases number of molecules • More molecules – higher pressure • Higher temperature – higher pressure

  5. Kinetic theory of gases • Gases consist of small atoms or molecules in constant random motion • Volume occupied by molecules is negligible • Molecules are independent of each other – no interactions • Collisions are perfectly elastic (no energy loss) • Average energy is proportional to the temperature

  6. Under pressure: the atmosphere • Gases exert pressure by virtue of motion • Gravity makes the air density higher near the earth’s surface • Pressure decreases with elevation

  7. Atmospheric pressure • Pressure is force per unit area • The weight of the air supports a column of mercury 760 mm high • Barometer is used for measuring atmospheric pressure • Atmospheric pressure changes with the weather

  8. The atmosphere is layered • Troposphere • Where the weather happens • Stratosphere • Where the ozone is • Mesosphere • Ionosphere • The brutal strength of solar radiation ionizes all the components – permits transmission of radio signals around the earth without need of mirrors

  9. Units of pressure • Atmosphere • Atmospheric pressure = 1 atm • mm (or cm, or in) of mercury • Atmospheric pressure = 760 mm (76 cm/29.9 in) Hg • Pascal is SI unit for pressure • Atmospheric pressure = 101 000 Pa (N/m2) • Pounds/square inch • Atmospheric pressure = 14.7 lb/in2 • Torr • Atmospheric pressure = 760 torr • Bar • Atmospheric pressure = 1.01 bar

  10. Standard temperature and pressure (STP) • Standard conditions allow direct comparison of properties of different substances • Standard temperature is 273 K (0ºC) • Standard pressure is 760 mm Hg or 1 atmosphere • At STP, 1 mole of any ideal gas occupies 22.414 L

  11. Pressure changes (units) • Convert 0.50 atm into a) mm Hg b) Pa

  12. Gas laws: experience in math form • The properties of gases can be described by a number of simple laws • The laws establish quantitative relationships between different variables • They are largely intuitively obvious and familiar

  13. The four variables • Pressure (P) • Volume (V) • Temperature (T in Kelvin) • Number of molecules (n in moles)

  14. Variables and constants • In the elementary gas laws two of the four variables are kept constant • Each law describes how one variable reacts to changes in another variable • All the simple laws can be integrated into one combined gas law

  15. Boyle’s law • The first experimental gas law • Pressure increases, volume decreases (T, n constant)

  16. Boyle’s law problems • Initial conditions: P1 and V1 • Final conditions: P2 and V2 • Four variables: three given, one unknown • Rearrange equation: • Units are not important provided same on both sides

  17. Tank contains 12 L of gas at 4,500 mm Hg. What is volume when pressure = 750 mm Hg?

  18. Charles’ Law • As temperature increases, volume increases (P, n constant) • Temperature must be measured in Kelvin

  19. Absolute zero • Gay-Lussac observed V changed by 1/273 of value at 0ºC • Plotted as V = kT (T = ºC + 273): • V = 0 at T = 0 • Does the gas actually occupy zero volume? • No, at lower T the law is not followed

  20. Do’s and don’ts with Charles’ law

  21. Combined gas law • Fold together Boyle and Charles: • Given five of the variables, find the sixth • Units must be consistent • Temperature in Kelvin

  22. Example of combined gas law • Gas at 27ºC and 2 atm pressure occupies 2 L. What is new volume if pressure becomes 4 atm and temperature is raised to 127ºC?

  23. Gay-Lussac and law of combining volumes • When gases react at constant temperature and pressure, they combine in volumes that are related to each other as ratios of small whole numbers • His experiments with hydrogen and oxygen had implications for the understanding of the atom and the structures of simple molecules

  24. Avogadro’s Law • As the number of moles of gas increases, so does the volume (P, T constant)

  25. Dalton’s law of partial pressures • A mixture of gases exerts a pressure as if all the gases were independent of one another • Total pressure is the sum of the pressures exerted by each one • P = p1 + p2 + p3 + …

  26. Calculations with partial pressures

  27. Molar gas volume • The molar volume of a gas is the volume occupied by 1 mole. At STP (standard temperature 273 K, and pressure 1 atm) one mole of gas occupies 22.4 L • Gas density is easily obtained from the molar mass and molar volume – d = m/V

  28. Ideal Gas Law • The particles of an ideal gas have mass but no volume - a fair approximation at low pressures • Collisions between the gas molecules are perfectly “elastic” – like superhard billiard balls. Reasonable for smaller molecules or noble gases • R is the ideal gas constant = 0.0821 L-atmK-1mol-1 • Gases deviate from ideal behaviour as • pressure increases – closer proximity of molecules • molecules are more polar – stronger interactions

  29. Calculations with the ideal gas law

  30. Chemical equations with gases • Reactions with solids involve masses • Reactions with gases involve volumes

  31. Stoichiometry with the ideal gas law

  32. Gas laws and crash safety • The airbag represents a fascinating study of chemistry applied in a very practical area • Airbags have reduced serious injuries and fatalities by a significant margin compared with seat belts only • Chemistry plays a crucial role in the performance of the airbag

  33. Timing is everything • The airbag must deploy within about 40 ms of the impact • The airbag must not deploy unless there is an impact • Inflation depends upon a rapid chemical reaction generating a quantity of gas • The bag, once inflated, must then deflate at the point of impact with the driver to prevent injury

  34. Chemistry is involved at many points • Chemical reaction to produce gas (nitrogen) • Strong N≡N bond provides driving force • Reaction kinetics determine rate – must be fast • Gas laws provide inflation – P proportional to T

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