P a n a rt v p b n b rt v n a is the number of moles

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P A = n A RT V P B = n B RT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B X A = n A n A + n B X B = n B n A + n B P A = X A P T P B = X B P T P i = X i P T mole fraction (X i ) = n i n T
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27 A sample of natural gas contains 8.24 moles of CH 4 , 0.421 moles of C 2 H 6 , and 0.116 moles of C 3 H 8 . If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C 3 H 8 )? P i = X i P T X propane = 0.116 8.24 + 0.421 + 0.116 P T = 1.37 atm = 0.0132 P propane = 0.0132 x 1.37 atm = 0.0181 atm
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28 2KClO 3 ( s ) 2KCl ( s ) + 3O 2 ( g ) P T = P O + P H O 2 2 Collecting a Gas over Water
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29 Vapor of Water and Temperature
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30 Chemistry in Action: Scuba Diving and the Gas Laws P V Depth (ft) Pressure (atm) 0 1 33 2 66 3
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31 Units of Pressure 1 pascal (Pa) = 1 N/m 2 1 atm = 760 mmHg = 760 torr 1 atm = 101,325 Pa Pressure = Force Area ( force = mass x acceleration) 1 N = 1 kg m/s 2
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32 Kinetic Molecular Theory of Gases 1. A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points ; that is, they possess mass but have negligible volume. 2. Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic. 3. Gas molecules exert neither attractive nor repulsive forces on one another. 4. The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy KE = ½ mu 2 = CT
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33 Kinetic theory of gases and … Compressibility of Gases Boyle’s Law P α collision rate with wall Collision rate α number density Number density α 1/ V P α 1/ V Charles’ Law P α collision rate with wall Collision rate α average kinetic energy of gas molecules Average kinetic energy α T P α T
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34 Kinetic theory of gases and … Avogadro’s Law P α collision rate with wall Collision rate α number density Number density α n P α n Dalton’s Law of Partial Pressures Molecules do not attract or repel one another P exerted by one type of molecule is unaffected by the presence of another gas P total = Σ P i
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35 Apparatus for Studying Molecular Speed Distribution
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36 The distribution of speeds for nitrogen gas molecules at three different temperatures The distribution of speeds of three different gases at the same temperature u rms = 3 RT M
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