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  1. Gases Ch. 10 in Textbook

  2. Intro: Bonds vs. IMFs • When separating an ionic solid, BONDS must be broken to separate the ions (strong) • When separating molecules in a molecular solid, INTERMOLECULAR FORCES (IMFs) must be broken to separate the molecules (weak) • The behavior of gases is governed by IMFs, not bonds

  3. Properties of Gases • rapidly diffuse to fill container, homogeneously mixing • shape and volume defined by container • low density, molecules very spread out • high kinetic energy • possess vibrational, translational, and rotational motions • high entropy • high compressibility HW: 10.2

  4. Pressure • force/area (N/m2) • atmospheric pressure = pushing force of 1 m2 column of air on surface of Earth due to gravity • standard atmospheric pressure (at sea level): 1 atm = 760 mmHg = 760 torr = 1.01325 x 105 Pa = 101.325 kPa mercury barometer from textbook HW: 10.8 (a)-(c)

  5. Manometers • similar to barometer, good for low pressure gases • (a) closed-tube manometer • (b) open-tube manometer when atmospheric pressure is greater than that of the gas • (c) open-tube manometer when atmospheric pressure is lower than that of the gas from textbook

  6. Example Calculation #0 • You are given an open-end manometer. If the atmospheric pressure is 0.975 atm and the height of the mercury is 67 mm higher on the end open to the atmosphere, what is the pressure of the enclosed gas in atm? HW: 10.14

  7. Boyle’s Law • the volume of a gas is indirectly related to its pressure (at const. temperature) • V = constant x 1/P or PV = constant • ex) decrease volume of syringe, pressure of gas increases


  9. Amonton’s Law • the pressure of a gas is directly related to its absolute temperature (at constant volume) • P = constant x T or P/T = constant • ex) pressure of tires increase as friction from the road heats them up


  11. Charles’s Law • the volume of a gas is directly proportional to its absolute temperature (at constant pressure) • V = constant x T or V/T = constant • ex) a balloon expands as it is heated

  12. HW: 10.16

  13. Gay-Lussac’s Law • when gases react with one another, the volume ratios in which they react are simple, whole numbers • implies that atoms/molecules are reacting in whole-number ratios

  14. from textbook

  15. Avogadro’s Law • interpreted Gay-Lussac’s Law on a molecular level using Dalton’s atomic theory • the volume of a gas is directly related to the number of gas molecules • V = constant x nor V/n = constant

  16. Avogadro’s Hypothesis • equal volumes of (different) gases at the same temperature and pressure contain an equal number of molecules (but not necessarily the same masses) HW: 10.19

  17. Ideal Gas Law • combine all gas laws and we get: V = constant x n x T P • rearranging and designating R as our gas constant, we get: PV = nRT • known as the ideal gas equation because it describes a theoretical gas that is accurately described by this equation • used to describe a gas under unchanging conditions

  18. The Gas Constant • many possible values, but we will use R= 0.0821 L•atm/mol•K or R= 62.4 L•torr/mol•K • this means that you must always convert volume to liters, pressure to atmospheres or torr, and temperature to Kelvin

  19. Example Calculation #1 • Nitrogen gas fills a syringe at 28.5 °C. The pressure equals 111.3 kPa when the syringe expands to 35.6 mL. How many grams of nitrogen are present? HW: 10.24 (c) & (d), 10.30 (a)

  20. Molar Volume • the volume of 1.000 mol of gas at standard temperature and pressure • STP= 1.000 atm and 273 K

  21. Example Calculation #2 • Calculate the molar volume at STP. HW: 10.22

  22. Combined Gas Law • used to describe a gas under changing conditions • P1V1 = P2V2 T1 T2 • remember to keep temperature in Kelvin, other units don’t matter so long as they are CONSISTENT • if one variable remains constant, remove it from both sides of the equation

  23. Example Calculation #3 • A gas at STP is heated to a temperature of 88.0 °C, pressure of 768 torr, and a volume of 56.7 mL. What was the original volume of the gas? HW: 10.18, 10.32 (a) & (b)

  24. Gas Density and Molar Mass • we want to find the density of the gas in g/L • if we rearrange the ideal gas equation, we can at least get mol/L: n/V = P/RT • we can convert moles to grams by multiplying by the molar mass M • to maintain the equation, we have to do this to both sides of the equation pure carbon dioxide

  25. nM/V = PM/RT or d = PM/RT • we can also find the molar mass of an unknown gas by rearranging: M = dRT/P

  26. Example Calculation #4 • What is the density of carbon dioxide at 766.6 torr and 56.1 °C? HW: 10.36, 10.38

  27. Ignore • volumes of gases in chemical reactions

  28. Dalton’s Law of Partial Pressures • the total pressure of a mixture of gases is the sum of the pressures of the individual gases • in other words, each gas exerts its own pressure, independently of the other gases and there are no interactions between different gases • Ptotal = PA + PB + PC + ….


  30. we can REMIX! the ideal gas law as follows: Ptotal = (nA + nB + nC + …)RT/V • similarly we can use the molefraction tofind the partial pressure of a gas given the total pressure • mole fraction, XA = nA/ntotal (no units) • PA = XA Ptotal


  32. Example Calculation #5 • 2.00 g of oxygen and 2.00 g of nitrogen are mixed in a 2.0 L vessel at 25.0 °C. What is the total pressure of the vessel and the partial pressure of each gas component? HW: 10.54

  33. Gas Collection • a gas produced in a chemical reaction can be collected over water by a displacement method • once the gas is collected, the container must be lowered or raised to equalize outside and inside pressures (water levels equalize) • because water vaporizes (even at room temp.) we must include this in our calcs

  34. Ptotal = Pgas + Pwater • Pwater can be looked up in Appendix B for various temperatures


  36. Kinetic-Molecular Theory (KMT) • visual and mathematical model of how an ideal gas behaves according to the ideal gas equation • anytime we describe the motion or collisions of a gas, we are using KMT • there are 5 assumptions

  37. many molecules in continuous, random motions • molecular volume is negligible compared to container volume • attractive and repulsive forces between molecules are negligible • KE is transferred during collisions, but the avg. KE does not (at const. temp.) • avg. KE is proportional to the absolute temp. HW: 10.60

  38. Root-Mean-Square Speed, urms • KE per molecule = ½mv2 • each molecule in a gas has its own KE, but the avg. KE remains the same at a given temp. • the rms speed, u, is thespeed of a molecule that possesses avg. KE (center of curve) • notice how the distribution of speeds changes with increasing temperature from textbook

  39. from textbook • where k = 1.38 x 10-23 J/K (Boltzmann’s constant) and m = mass of molecule in kg or where R = 8.31 J/mol•K and M = molar mass in kg/mol • final unit: m/s (don’t worry about it)

  40. based on formula, at the same temp, the more massive the molecule the more slowly it moves compared to a less massive molecule which moves more quickly • see CD-ROM for example

  41. Example Calculation #6 • What is the rms speed of an oxygen molecule at room temperature? HW: 10.62

  42. Graham’s Law of Effusion from textbook • effusion is the escaping of a gas molecule through a tiny hole • the faster the rms speed, the more likely that the gas molecule will escape • thus, the larger the molecule, the slower it moves and the less likely it is to effuse • ex) helium balloon vs. air balloon

  43. Example Calculation #7 • By what factor does fluorine gas effuse faster than chlorine gas? HW: 10.66

  44. Diffusion • the natural spreading of a gas to fill a space • smaller molecules diffuse faster than larger molecules • however, collisions limit the diffusion rate • mean free path = the avg. distance traveled between collisions

  45. Real Gases • unlike an ideal gas, real gases are not described perfectly by the ideal gas law • real gases have a significant volume (relative to the container volume) and significant attractions or repulsions for one another



  48. real gases are most ideal at a higher temperatures and a lower pressures from textbook HW: 10.67

  49. van der Waals Equation • makes corrections for “real” gases • P = _nRT_ – n2a V – nbV2 • where a and b are van der waals constants for different substances • nb is the correction for volume • n2a/V2 is the correction for attractions

  50. rearranged to its more “familiar” form: (P + n2a) (V – nb) = nRT V2