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Gases

Gases. Chapter 5. Gas Properties. Four properties determine the physical behavior of any gas: Amount of gas Gas pressure Gas volume Gas temperature. Gas pressure. Gas molecules exert a force on the walls of their container when they collide with it. Gas pressure.

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Gases

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  1. Gases Chapter 5

  2. Gas Properties • Four properties determine the physical behavior of any gas: • Amount of gas • Gas pressure • Gas volume • Gas temperature

  3. Gas pressure • Gas molecules exert a force on the walls of their container when they collide with it

  4. Gas pressure • Gas pressure can support a column of liquid • Pliquid = g•h•d • g = acceleration due to the force of gravity (constant) • h = height of the liquid column • d = density of the liquid

  5. Atmospheric pressure • Torricelli barometer • In the closed tube, the liquid falls until the pressure exerted by the column of liquid just balances the pressure exerted by the atmosphere. • Patmosphere = Pliquid = ghd • Patmosphere liquid height Standard atmospheric pressure (1 atm) is 760 mm Hg

  6. Units for pressure • In this course we usually convert to atm

  7. Gas pressure • Pliquid = g•h•d • Pressure exerted by a column of liquid is proportional to the height of the column and the density of the liquid • Container shape and volume do not affect pressure

  8. Example • A barometer filled with perchloroethylene (d = 1.62 g/cm3) has a liquid height of 6.38 m. What is this pressure in mm Hg (d = 13.6 g/cm3)? • P = ghd = g hpce dpce = g hHg dHg • hpce dpce = hHg dHg • hHg = hpce d pce = (6.38 m)(1.62 g/cm3) = 0.760 m dHg 13.6 g/cm3 • hHg = 760 mm Hg

  9. Gas pressure • A manometer compares the pressure of a gas in a container to the atmospheric pressure

  10. Gas Laws: Boyle • In 1662, Robert Boyle discovered the first of the simple gas laws • PV = constant For a fixed amount of gas at constant temperature, gas pressure and gas volume are inversely proportional

  11. Gas Laws: Charles • In 1787, Jacques Charles discovered a relationship between gas volume and gas temperature: • relationship between volume and temperature is always linear • all gases reach V = 0 at same temperature, –273.15 °C volume (mL) • this temperature is ABSOLUTE ZERO temperature (°C)

  12. A temperature scale for gases:the Kelvin scale • A new temperature scale was invented: the Kelvin or absolute temperature scale • K = °C + 273.15 • Zero Kelvins = absolute zero

  13. Gas laws: Charles • Using the Kelvin scale, Charles’ results is • For a fixed amount of gas at constant pressure, gas volume and gas temperature are directly proportional • A similar relationship was found for pressure and temperature:

  14. Standard conditions for gases • Certain conditions of pressure and temperature have been chosen as standard conditions for gases • Standard temperature is 273.15 K (0 °C) • Standard pressure is exactly 1 atm (760 mm Hg) • These conditions are referred to as STP (standard temperature and pressure)

  15. Gas laws: Avogadro • In 1811, Avogadro proposed that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. • At constant temperature and pressure, gas volume is directly proportional to the number of moles of gas • Standard molar volume: at STP, one mole of gas occupies 22.4 L

  16. Putting it all together:Ideal Gas Equation • Combining Boyle’s Law, Charles’ Law, and Avogadro’s Law give one equation that includes all four gas variables: • R is the ideal or universal gas constant • R = 0.08206 atm L/mol K

  17. Using the Ideal Gas Equation • Ideal gas equation may be expressed two ways: • One set of conditions: ideal gas law • Two sets of conditions: general gas equation

  18. Ideal Gas Equation and molar mass • Solving for molar mass (M)

  19. Ideal Gas Equation and gas density

  20. Gas density • Gas density depends directly on pressure and inversely on temperature • Gas density is directly proportional to molar mass

  21. Mixtures of Gases • Ideal gas law applies to pure gases and to mixtures • In a gas mixture, each gas occupies the entire container volume, at its own pressure • The pressure contributed by a gas in a mixture is the partial pressure of that gas • Ptotal = PA + PB(Dalton’s Law of Partial Pressures)

  22. Mixtures of Gases • When a gas is collected over water, it is always “wet” (mixed with water vapor). • Ptotal = Pbarometric = Pgas + Pwater vapor • Example: If 35.5 mL of H2 are collected over water at 26 °C and a barometric pressure of 755 mm Hg, what is the pressure of the H2 gas? The water vapor pressure at 26 °C is 25.2 mm Hg.

  23. Gas mixtures • The mole fraction represents the contribution of each gas to the total number of moles. • XA = mole fraction of A

  24. Gas Mixtures • For gas mixtures, Each gas occupies the entire container. The volume fraction describes the % composition by volume. mole fraction equals pressure fraction equals volume fraction

  25. P2 = P1 and T2 = T1 Gases in Chemical Reactions • To convert gas volume into moles for stoichiometry, use the ideal gas equation: • If both substances in the problem are gases, at the same T and P, gas volume ratios = mole ratios.

  26. A Model for Gas Behavior • Gas laws describe what gases do, but not why. • Kinetic Molecular Theory of Gases (KMT) is the model that explains gas behavior. • developed by Maxwell & Boltzmann in the mid-1800s • based on the concept of an ideal or perfect gas

  27. Ideal gas • Composed of tiny particles in constant, random, straight-line motion • Gas molecules are point masses, so gas volume is just the empty space between the molecules • Molecules collide with each other and with the walls of their container • The molecules are completely independent of each other, with no attractive or repulsive forces between them. • Individual molecules may gain or lose energy during collisions, but the total energy of the gas sample depends only on the absolute temperature.

  28. Molecular collisions and pressure • Force of molecular collisions depends on • collision frequency • molecule kinetic energy, ek • ek depends on molecule mass m and molecule speed u • molecules move at various speeds in all directions

  29. Molecular speed • Molecules move at various speeds • Imagine 3 cars going 40 mph, 50 mph, and 60 mph • Mean speed = u = (40 + 50 + 60) ÷ 3 = 50 mph • Mean square speed (average of speeds squared) u2 = (402 + 502 + 602) ÷ 3 = 2567 m2/hr2 • Root mean square speed urms = √2567 m2/hr2 = 50.7 mph

  30. Distribution of molecule speeds

  31. The basic equation of KMT • Combining collision frequency, molecule kinetic energy, and the distribution of molecule speeds gives the basic equation of KMT • P = gas pressure and V = gas volume • N = number of molecules • m = molecule mass • u2 = mean square molecule speed (average of speeds squared)

  32. Combine the Equations ofKMT and Ideal Gas If n = 1, N = NA and PV = RT Avogadro’s number

  33. Combine the Equations ofKMT and Ideal Gas NA x m (Avogadro’s number x mass of one molecule) = mass of one mole of molecules (molar mass M)

  34. Combine the Equations ofKMT and Ideal Gas We can calculate the root mean square speed from temperature and molar mass

  35. Calculating root mean square speed • To calculate root mean square speed from temperature and molar mass: • Units must agree! • Speed is in m/s, so • R must be 8.3145 J/mol K • M must be in kg per mole, because Joule = kg m2 / s2 • Speed is inversely related to molar mass: light molecules are faster, heavy molecules are slower

  36. Interpreting temperature • Combine the KMT and ideal gas equations again Again assume n=1, so N = NA and PV = RT

  37. Interpreting temperature • Absolute (Kelvin) temperature is directly proportional to average molecular kinetic energy • At T = 0, ek = 0

  38. Diffusion and Effusion • Diffusion (a) is migration or mixing due to random molecular motion • Effusion (b) is escape of gas molecules through a tiny hole

  39. Rates of diffusion/effusion • The rate of diffusion or effusion is directly proportional to molecular speed: • The rates of diffusion/effusion of two different gases are inversely proportional to the square roots of their molar masses (Graham’s Law)

  40. Using Graham’s Law • Graham’s Law applies to relative rates, speeds, amounts of gas effused in a given time, or distances traveled in a given time.

  41. Using Graham’s Law with times • Graham’s law can be confusing when applied to times rate = amount of gas (n) time (t)

  42. Use common sensewith Graham’s Law • When you compare two gases, the lighter gas • escapes at a greater rate • has a greater root mean square speed • can effuse a larger amount in a given time • can travel farther in a given time • needs less time for a given amount to escape or travel • Make sure your answer reflects this reality!

  43. Reality Check • Ideal gas moleculesReal gas molecules • constant, random, same straight-line motion • point masses are NOT points – molecules have volume; Vreal gas > Videal gas • independent of each other areNOT independent – molecules are attracted to each other, so Preal gas < Pideal gas • gain / lose energy during same (some energy may be collisions, but total energy absorbed in molecular depends only on T (ek))

  44. Real gas corrections • For a real gas, • a corrects for attractions between gas molecules, which tend to decrease the force and/or frequency of collisions (so Preal < Pideal) • b corrects for the actual volume of each gas molecule, which increases the amount of space the gas occupies (so Vreal > Videal) • The values of a and b depend on the type of gas

  45. An equation for real gases:the van der Waals equation Add correction to Preal to make it equal to Pideal, because intermolecular attractions decrease real pressure Subtract correction to Vreal to make it equal to Videal, because molecular volume increases real volume

  46. When do I needthe van der Waals equation? • Deviations from ideality become significant when • molecules are close together (high pressure) • molecules are slow (low temperature) • At low pressure and high temperature, real gases tend to behave ideally • At high pressure and low temperature, real gases do not tend to behave ideally } non-ideal conditions

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