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Chapter 14

Chapter 14 . The behavior of gases. Reviewing what we know about gases…. What do we know about… Kinetic energy? Distance between molecules? Density? Compressibility? Compressibility: how much the volume of matter decreases under pressure. Pressure.

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Chapter 14

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  1. Chapter 14 The behavior of gases

  2. Reviewing what we know about gases… • What do we know about… • Kinetic energy? • Distance between molecules? • Density? • Compressibility? • Compressibility: how much the volume of matter decreases under pressure.

  3. Pressure • Based on: The number and magnitude of the collisions with the container walls • How do you increase pressure? • Amount of gas • Volume of container • Temperature

  4. Assignment: using the reading on pages 414-417 fill in the following chart…

  5. Gas Laws -mathematical relationships (__________) between Volume, Temp, Pressure and quantity of gas (i.e. # of moles = n) Note: x  y__________________________________ x  1/y___________________________________

  6. Boyle's Law States that the ________ of a gas _______________ with the ___________ at constant Temperature. i.e. P  1/V => PV  1 => PV = k k is different for each gas under different circumstances. But for the same gas: if you change P, V changes, such that __________________________________

  7. P1V1 = k P2V2 = k P3V3 = k …. so _________Boyle’s Law Units: ANY, as long as you’re consistent.

  8. Boyle’s Law problems:

  9. Charles’s Law Jacques Charles (1787) noticed that as you ________ the _______ of a gas, the _______ also increases proportionately. (why?) i.e. V  T If you cool a gas enough, then according to Kinetic Theory, an ideal gas should reach zero volume (theoretically), but not for real gases. Gas particles condense close enough to become liquid, then solid, with a finite Volume.

  10. Graph of Volume vs Temperature: This is ____________________________________! Lord ______ took advantage of this knowledge and decided to start a third Temperature scale with this as the starting point. Note that when you extend the graph for any gas, they all terminate at a Temp. of _______ for zero Volume.

  11. The lowest possible temperature is known as ________________ = -273oC (~ -460oF) We use Absolute Zero as the starting point of the new temperature scale called the Kelvin scale. (K) So_____________and ______________ Which leads to:K = oC + 273

  12. Charles Law:the __________ of a gas at constant pressure ___________with the ___________ (in Kelvin) http://physics.gac.edu/~mellema/Aapt2001/Charles'%20Law.htm

  13. So, let’s plot V vs T(K) and see what we get. The slope… rise over run… is V/T… is a constant k i.e.V  T => V 1 => V = k(constant) T T SoCharles Law

  14. Charles Laws Problems:

  15. Gay-Lussac's Law Gay-Lussac’s Law: “the Pressure of a fixed mass of a gas, held at constant Volume, varies directly (proportionately) with the Kelvin Temperature.” Joseph Gay-Lussac (1802) noticed that as you _________________of a fixed Volume of a gas, the ____________________.

  16. i.e. P  T  P 1  P = k T T So: Gay-Lussac’s Law

  17. Gay-Lussac’s Problems:

  18. Combined gas law: Summary of Eqns: Boyle’s Law P1V1 = P2V2 Charles’s V1 = V2 T1 T2 Gay-Lussac’s P1 = P2 T1 T2

  19. All 3 eqns are connected to each other & we can combine them all into 1 eqn. (=?) We get a combination of all 3 eqns called the: Combined gas law. Anything that is held constant, simply gets cancelled out of the eqn.

  20. Ideal Gas Law So far, we have formulas that tell us what happens to a gas when you change certain factors:- P, V & T (n is constant) Now lets look at a gas in absolute terms where no variables are changing. Ideal Gas Law: the mathematical relationship between _____________________AND the ________________ of a gas. * Based on the concept of an ideal gas… which is not a real gas… remember?

  21. So, Ideal Gas Law is: PV = nRT where T is in K, V is in L REMEMBER there are several different values of R, depending on what units of Pressure you use

  22. Instead of using k,there is a special constant called theIdeal Gas Constant (R) If P is in kPa, R = 8.314 L.kPa/mol.K atm, R = 0.0821 L.atm/mol.K

  23. Examples • At 34.0˚C, the pressure inside a nitrogen-filled tennis ball with a volume of 148mL is 212kPa. How many moles of gas are inside the ball?

  24. A helium filled balloon contains 0.16 mol He at 101kPa and a temperature of 23 ˚C. What is the volume of the gas in the balloon?

  25. Exceptions to Ideal gas law Real Gases:act like Ideal gases in most circumstances, except.. Consider a gas at high pressure, or at low T, what happens to Volume? Real gases stop acting like ideal gases… so the ideal gas law does NOT apply iff the gas is at a very low temperature (near 0 K) or very high pressure (near 60,000 kPa)

  26. Dalton’s Law of Partial Pressures The # of gas molecules directly affects the pressure of the gas. ____________________________________________________________________________________________ In a mixture of gases that is confined in a fixed volume, each gas provides its own pressure contributing to the total. Each individual gas’s pressure is known as their “Partial Pressure”

  27. Two separate gases, (O2 & N2 ) each in separate containers, have an individual pressure of 0.12 atm’s They are transferred to a third container. The new pressure of the gases when combined is ____________.

  28. Dalton’s Law of Partial Pressuresstates that: “the total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.” i.e. PT = P1 + P2 + P3 +… e.g. PATM = PO2 + PN2 + PCO2 +... = 101.3 kPa ∴ To get the total pressure of a gas mixture, solve for the individual pressures then add them

  29. Diffusion: the gradual mixing of 2 gases due to their spontaneous random motion. Effusion & Diffusion

  30. Effusion: process where the molecules of a gas confined in a container, randomly pass through a tiny opening in the container. Effusion

  31. Recall that KE = ½ mv2and that 2 gases at the same Temp. have the same Kinetic Energy. So Gas A Gas B @ same T. KE(A) = KE(B) If gas B is a lighter molecule (mB is lower) then vB must be higher for KE to remain the same. The whole point: Lighter, less dense gases travel faster at the same Temperatures.

  32. Graham’s Law of Effusion __________________________________________ ____________________________________________ Graham’s Law of Effusion“states that the rates of effusion (r or v) of gases (at same T & P ) are inversely proportional to the square root of their Molar Masses” We could prove it, but lets not  Graham’s Law… rate of effusion of Gas 2 (v2) =  M1 rate of effusion of Gas 1 (v1)  M2

  33. Gases e Finito !

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