Gas Pressure

1. Gas Pressure

2. Air Pressure

3. Pressure Units • Units of pressure: atmosphere (atm) Pa (N/m2, 101,325 Pa = 1 atm) Torr (760 Torr = 1 atm) bar (1.01325 bar = 1 atm) mm Hg (760 mm Hg = 1 atm) lb/in2 (14.696 lb/in2 = 1 atm) in Hg (29.921 in Hg = 1 atm)

4. Universal Gas Behavior • Unlike solids and liquids, gas behavior is generally independent of chemical identity. • Depends on four things only: • Absolute temperature • Pressure • Volume • Amount (moles)

5. Kinetic Molecular Theory • This theory presents physical properties of gases in terms of the motion of individual molecules. • Kinetic Theory (in this class) will be based upon six assumptions: • Average Kinetic Energy  Kelvin Temperature • Gas molecules are points separated by a great distance • Particle volume is negligible compared to gas volume • Gas molecules are in rapid random motion • Gas collisions are perfectly elastic • Gas molecules experience no attraction or repulsion

6. Gas Behavior:Gases in a Box • Insert 1 mole of gas into a fixed volume container. Then: • Gas expands to fill the container. Why? • The pressure becomes whatever value the gas laws dictate for that volume, mole, and temperature combination.

7. Gas Behavior:Gases in a Piston • Insert 1 mole of gas into a piston. Then: • Gas fills the piston. Why? • The piston changes volume until the pressure inside is equal to the pressure outside. Why?

8. Understanding the Gas Laws • Two keys to understanding the gas laws: • Understand which parameters are changing • Understand which are NOT changing

9. Pressure–Volume Law (Boyle’s Law): Boyle’s Law

10. Boyle’s Law • Pressure–Volume Law (Boyle’s Law): • The volume of a fixed amount of gas maintained at constant temperature is inversely proportional to the gas pressure.

11. Charles’ Law • Temperature–Volume Law (Charles’ Law):

12. V T µ Charles’ Law • Temperature–Volume Law (Charles’ Law): • The volume of a fixed amount of gas at constant pressure is directly proportional to the Kelvin temperature of the gas.

13. Avogadro’s Law • The Volume–Amount Law (Avogadro’s Law):

14. Avogadro’s Law • The Volume–Amount Law (Avogadro’s Law): • At constant pressure and temperature, the volume of a gas is directly proportional to the number of moles of the gas present.

15. Collecting the Gas Laws • Mathematically one can combine all of the statements we’ve made about gases. • Two equivalent equations come from this: • Combined gas law • Ideal gas law

16. Combined Gas Law • Combining the law gives: • But if it equals a constant, then after any change it will still be equal to the constant: • We write it this way: • Nothing needs to be held constant now • Remember that anything that does stay constant can be cancelled.

17. Ideal Gas Law • This constant “X” is just a number. • Units of (pressure * volume) / (moles * temp) • That is, L·atm·K–1·mol–1 • Numerically, this constant has a value of R = 0.08206 L·atm·K–1·mol–1

18. Ideal Gas Law • The equation then becomes We usually write it this way instead: PV = nRT

19. STP • Standard temperature: 273.15 K • Standard pressure: 1 atm

20. Ideal gas law vs. combined gas law • Ideal gas law • Under unchanging conditions • Combined gas law • Under changing conditions

21. What is the volume of one mole of helium gas at STP? What is the volume of one mole of argon gas at STP? 22.4 L 22.4 L What is the volume of one mole of radon gas at STP? 22.4 L

22. What is the density of one mole of helium gas at STP? What is the volume of one mole of argon gas at STP? 4.003 g / 22.4 L = 0.179 g/L 39.948 g / 22.4 L = 1.78 g/L What is the volume of one mole of radon gas at STP? 222 g / 22.4 L = 9.91 g/L

23. What information would you need to calculate the molar mass of a gas? • Mass / moles (m / n) • Enough information to get mass • P,V,T to use ideal gas law to get n • What is the molar mass of a gas with a density of 1.342 g/L–1 at STP?

24. Funky questions • At what temperature do you have 0.1 moles/atm of helium in a 1 L pure helium sample? • In one mole of chlorine gas at STP, how many Kelvins are there per liter?

25. Gas-phase stoichiometry • We have a new route to moles PV=nRT • But we need to know first how two different gases behave when in the same space

26. Gas Mixtures • Two gases in the same container have the same volume—whatever the volume of the container is. • Two gases in the same container have the same temperature—whatever the temperature is inside the container.

27. Gas Mixtures • Two gases in the same container do NOT have the same pressure. • They have whatever pressure they would have if they were in the container alone. • That is, solve PV=nRT for each gas in the mixture separately.

28. Gas Mixtures • The total pressure inside the container is the sum of the pressures of the individual gases. • Dalton’s Law of Partial Pressures

29. New Density Unit: Mole Fraction • For a two-component system, the moles of components A and B can be represented by the mole fractions (XA and XB).

30. Gas Stoichiometry • In gas stoichiometry, for a constant temperature and pressure, volume is proportional to moles. • Assuming no change in temperature and pressure, calculate the volume of O2 (in liters) required for the complete combustion of 14.9 L of butane (C4H10): 2 C4H10(g) + 13 O2(g)  8 CO2(g) + 10 H2O(l)

31. Molecular Speed • It can be shown that: • So then for neon: Molar mass

32. Mean Molecular Speeds

33. Collisions • It can be shown that: • A room temp gas collides billions of times per second • The mean free path is less than 100 nm. Mean free path Collision frequency

34. Maxwell speed distribution curves.

35. Same Behavior vs. Different Behavior • Most gas behaviors are based upon comparisons of their relative energies (temperatures) • Same temperature = same behavior • Some gas behaviors are based upon comparisons of their relative speeds • Same speed = same behavior

36. Graham’s Law • Diffusion is the mixing of different gases by random molecular motion and collision.

37. Graham’s Law • Effusion is when gas molecules escape without collision, through a tiny hole into a vacuum.

38. Graham’s Law • Graham’s Law: Rate of effusion is proportional to its rms speed, vrms. • For two gases at same temperature and pressure:

39. Behavior of Real Gases • Test of ideal gasbehavior. • Z = PV/RT Compressibility factor This plot assumes room temperature.

40. Real Gases • All the assumptions of kinetic molecular theory break down when explored in sufficient detail. • Two assumptions break down first: • The volume of gas molecules is negligible • There are no attractive or repulsive forces between molecules

41. Non-negligible volumes • The volume of molecules affects pressure-volume behavior more than temperature-pressure behavior. • For a given small volume, the pressure will be higher than the ideal gas suggests..

42. Behavior of Real Gases • Test of ideal gasbehavior. Volume non-idealities seen here!

43. Non-negligible interactions • The long-range interactions of particles are attractions, not repulsions. • Thus a real gas sample takes up less space than the ideal gas law suggests, when the molecules are not crowded together. • This effect fades as molecules move faster.

44. Behavior of Real Gases • Test of ideal gasbehavior. Attractive force non-idealities seen here!

45. Behavior of Real Gases • Corrections for non-ideality require a non-ideal gas law. The van der Waals equation is one of them: Excluded Volume IntermolecularAttractions

46. Van der Waals Constants

47. Other gas laws • van der Waals: • Peng-Robinson: • Redlich-Kwong:

48. Unifying the Gas Laws • Under normal temperatures you can liquefy a gas simply by raising the pressure • Above a certain critical temperature (Tc) you cannot liquefy a gas under any pressure. The pressure and volume of that “last” liquid are Pc and Vc

49. Critical Constants

50. “Critical” adjustments • Now we stop using temperature (and pressure and volume) in the gas laws. • Instead we write the reduced temperature (TR) as a fraction of the critical temperature (Tc). • That is TR = T / Tc