1 / 23

20 B Week II Chapters 9 -10)

• Macroscopic Pressure •Microscopic pressure( the kinetic theory of gases: no potential energy) • Real Gases: van der Waals Equation of State London Dispersion Forces: Lennard-Jones V(R ) and physical bonds Chapter 10 • 3 Phases of Matter: Solid, Liquid and Gas of a

josh
Download Presentation

20 B Week II Chapters 9 -10)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. • Macroscopic Pressure •Microscopic pressure( the kinetic theory of gases: no potential energy) • Real Gases: van der Waals Equation of State London Dispersion Forces: Lennard-Jones V(R ) and physical bonds Chapter 10 • 3 Phases of Matter: Solid, Liquid and Gas of a single component system( just one type of molecule, no solutions) Phase Transitions: A(s) A(g) Sublimation/Deposition A(s) A(l) Melting/Freezing A(l) A(g) Evaporation/Condensation 20 B Week II Chapters 9 -10)

  2. For a fixed mass( of gas, e.g., Air) how does the Volume occupied by the gas change when the gas is cooled or heated? Lets do an experiment! • Define a Thermodynamic Temperature scale to make a thermometer( to measure T) Assumes we know nothing about the Boltzmann distribution so T is a parameter • Charles’ Law V/T = const

  3. Quantifying the temperature scale requires some material Property that changes if the material is heated or cooled. The thermal expansion coefficient = (1/V)(V/T) assume fractional rate of change of V with respect to T is ideal. The temperature scale should be material independent (Universal) appears to be Universal for low pressure gases Over the T range where water freezes and boils, Charles observed that = (1/V)(V/T) ~const for low pressure gases. = (1/V)(V/T)=(1/V0){V-V0}/{T-T0} V0 and T0, are the initial volume and Temperature, thermometer material and V and T, , are the final volume and Temperature, respectively!

  4. The Experiment: we need 3 T’s to be accurate The material for the experiment is air 20±? Room Temp! Assigned values

  5. = (1/V0){V-V0}/{T-T0} Thermal expansion Let V0 be the gas Volume at T0 = 0 The Freezing point of water! T = (1/{(V/V0) – 1} Re-arrange to V=V0 T} If T has units of °C (Celsius), the boiling point of water must be set to 100 °C! All measurements are for air at low pressure

  6. Fitting the V vs T the equation to the data, we can extrapolate to absolute zero! V0= 1.5 L V=V0 T} solve for T at V=0 gives T=C V0= 1.0 L

  7. However, the mass of gas is fixed! So V can approach zero but cannot be zero! V=V0 T} so as V goes to zero T goes to The absolute T=0 K T=C V0= 1.5 L V0= 1.0 L

  8. In terms of an absolute temperature T=-273.15 C= 0 K (Kelvin) V~T since as V approaches 0, T  0 V = TConst. This is most useful form of Charles’ Law V~ N (the number of gas atoms/Molecules) (Since the more molecules the greater the volume) V~1/P from Boyle’s Law Therefore V~ NT/P or V=kNT/P: PV=kNT The is Ideal or Perfect Gas Law where k = Boltzmann Constant : PV=kNT

  9. PV=kNT: The Idea Gas Law! Appliedtwo different gases, e.g., N2 and O2 (Or even better! The Law describing the behavior of a Theoretically Perfect/Ideal Gas)! Can be used for all gases at Low Pressure and high enough temperature ~ ultrahigh vacuum ultralow pressures! ~ very small hole or area A. If P=PO2 + PN2(partial pressures) P=NO2kT/V + NN2kT/V P = (NO2 + NN2 )kT/V=NkT/V N=NO2 + NN2 which is true Effusion Cell

  10. Partial Pressures add. P= P1 + P2 + P3 + etc + = Fig. 9-9, p. 377

  11. When dealing with the behavior of large numbers N~NA NA=6.022 x 1023 mole-1 then we must average over the behavior of the individual atom/molecule in the system For example. If i is the total energy of the ith atom/molecule, Kinetic + Potential, then the average energy per atom/molecule is <>= (1 + 2 + 3 ………. + N )/N=∑i/N This is the behavior we observe and is the domain of Statistical Mechanics: the science that describes the behavior of a system with large numbers of atoms/molecules based on the behavior of individual atoms/molecules, e.g., Gases!

  12. The Kinetic Theory of Gases uses this idea to describe the Behavior of an ideal gas! Think about this for a min! The average behavior can be determined by watching one particle for a very long time(infinitely long in principle), or a large number of particles (infinitely large in principle) for a short time, i.e., snapshot or an instant <(vx)2

  13. The Kinetic Theory Nanoscopic theory of gas pressure watch the average behavior of one particle and describe the behavior of a system with a large number of particles L

  14. The Kinetic Theory Nanoscopic theory of gas pressure watch the average behavior of one particle and describe the behavior of a system with a large number of particles - FA =F = ma=d(mv)/dt mv = linear momentum (mv)=(mvx)f - (mvx)i (mv)=-mvx - mvx=-2mvx t=2L/vx L

  15. The Kinetic Theory Microscopic pressure one particle at a time V=AL -FA = F = ma=d(mv)/dt force atom/molecule mv = linear momentum (mv)=(mvx)f - (mvx)i (mv)=-mvx - mvx=-2mvx t=2L/vx L • FA =F = ma=d(mv)/dt ~ -2mvx/(2L/vx)= - m(vx)2/L • FA=2m(vx)2/L; <FA>=m<(vx)2>/L average force on the wall • Px=P= N<FA>/A=Nm<(vx)2>/AL=(N/V) m<(vx)2>

  16. Motion in all directions x,y, and z are equally likely: <vx>=<vy>=<vz> v2 = (vx)2 + (vy)2 +(vz)2 =u2 then < v2 >=<u2>=<(vx)2 + (vy)2 +(vz)2>=3<(vx)2> or <(vx)2> = <u 2 >/3 The average of speed in all directions must be the same <(vx)2>=<(vy)2>=<(vz)2> for the random motion of an atom/molecule P= (N/V) m<(vx)2>= (N/3V) m< u2 > but <KE>= (m/2)< u2 > So P=(N/V)<KE>(2/3) recall that PV=NkTso <KE>=(3/2)kT Since <>=<PE> + <KE> = <KE> for a prefect gas, that is a gas described by PV=NkT Fig. 9-11, p. 379

  17. Partial Pressures add. P= P1 + P2 + P3 + etc + = Fig. 9-9, p. 377

  18. • Macroscopic Pressure •Microscopic pressure( the kinetic theory of gases: no potential energy) • Real Gases: van der Waals Equation of State London Dispersion Forces: Lennard-Jones V(R ) and physical bonds Chapter 10 • 3 Phases of Matter: Solid, Liquid and Gas of a single component system( just one type of molecule, no solutions) Phase Transitions: A(s) A(g) Sublimation/Deposition A(s) A(l) Melting/Freezing A(l) A(g) Evaporation/Condensation 20 B Week II Chapters 9 -10)

  19. <V(R )> = 0 For R Very Large Density N/V is low Therefore P=(N/V)kT is low A A R Fig. 9-18, p. 392

  20. Real Gases and Intermolecular Forces Lennard-Jones Potential V(R ) = 4{(R/)12 -(R/)6} kT >>  Ar+ Ar  well depth ~ Ze or Mass but it’s the # of e

  21. Real Gases and Intermolecular Forces Lennard-Jones Potential V(R ) = 4{(R/)12 -(R/)6} ~ hard sphere diameter • well depth Bond Dissociation D0= h

  22. The London Dispersion or Induced Dipole Induced Dipole forces Weakest of the Physical Bonds but is always present!

More Related