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Partial Pressure and Graham's Law

The first edition of this book was previously published by Pearson Education, Inc. It was The second edition, version 10 is copyright ©2020 by Howard DeVoe. This work is licensed under a Creative Commons Attribution 40 International License: https://creativecommons org/licenses/by/4 0/ The book was typeset using the LATEX typesetting system and the memoir class. Most of the figures were produced with PSTricks, a related software program. The fonts are Adobe Times, MathTime, and Computer Modern Typewriter. A Solutions Manual is available at the Web site linked below. I thank the Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland for hosting the Web site for this book:

Figures (10)

An illustration of Dalton's law using the gases of air at sea level
Figure 9.9 In 1783, the first (a) hydrogen-filled balloon flight, (b) manned hot air balloon flight, and (c) manned hydrogen-filled balloon flight occurred. When the hydrogen-filled balloon depicted in (a) landed, the frightened villagers of Gonesse reportedly destroyed it with pitchforks and knives. The launch of the latter was reportedly viewed by 400,000 people in Paris.
Figure 9.10 The effect of temperature on gas pressure: When the hot plate is off, the pressure of the gas in the sphere is relatively low. As the gas is heated, the pressure of the gas in the sphere increases.
Figure 9.11 For a constant volume and amount of air, the pressure and temperature are directly proportional, provided the temperature is in kelvin. (Measurements cannot be made at lower temperatures because of the condensation of the gas.) When this line is extrapolated to lower pressures, it reaches a pressure of 0 at –273 °C, which is 0 on the kelvin scale and the lowest possible temperature, called absolute zero.
Figure 9.12 The volume and temperature are linearly related for 1 mole of methane gas at a constant pressure of 1 atm. If the temperature is in kelvin, volume and temperature are directly proportional. The line stops at 111 K because methane liquefies at this temperature; when extrapolated, it intersects the graph’s origin, representing a temperature of absolute zero.
Figure 9.13 When a gas occupies a smaller volume, it exerts a higher pressure; when it occupies a larger volume, it exerts a lower pressure (assuming the amount of gas and the temperature do not change). Since P and V are inversely proportional, a graph of 1P1P vs. V is linear.
Figure 9.14 The relationship between pressure and volume is inversely proportional. (a) The graph of P vs. V is a hyperbola, whereas (b) the graph of (1P)(1P) vs. V is linear.
Figure 9.15 Breathing occurs because expanding and contracting lung volume creates small pressure differences between your lungs and your surroundings, causing air to be drawn into and forced out of your lungs.
Figure 9.16 Scuba divers use compressed air to breathe while underwater. (credit: modification of work by Mark Goodchild)
Figure 9.17 Scuba divers, whether at the Great Barrier Reef or in the Caribbean, must be aware of buoyancy, pressure equalization, and the amount of time they spend underwater, to avoid the risks associated with pressurized gases in the body. (credit: Kyle Taylor)

Key Points

  • The partial pressure of a substance in a real gas mixture is in general different from the pressure of the pure substance at the same T and V , because the intermolecular interactions are different.
  • Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.
  • If there is a liquid junction between electrolyte solutions of different composition, slow diffusion of ions through the junction is inevitable.
  • In the case of an ideal gas mixture, Hi is also independent of p, because the molar enthalpy of an ideal gas depends only on T .
  • At the outlet of the nozzle, it has returned to atmospheric pressure and is expelled into the atmosphere.
  • Vapor-pressure lowering In a binary two-phase system in which a solution of volatile solvent A and nonvolatile solute B is in equilibrium with gaseous A, the vapor pressure of the solution is equal to the system pressure p.

Terms

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