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dN / dt = A • <v>/4 • N/V

dN / dt = A • <v>/4 • N/V. Density - # molecules are available for collision (m -3 ): N/V = PN A /(RT) <v> = {8RT /( p M )} 1/2. 19.32 Tungsten effusion – MW = 0.18385 kg/ mol

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dN / dt = A • <v>/4 • N/V

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  1. dN/dt = A • <v>/4 • N/V Density - # molecules are available for collision (m-3): N/V = PNA/(RT) <v> = {8RT/(pM)}1/2 19.32 Tungsten effusion – MW = 0.18385 kg/mol Given: T = 4500 K - dN/dt = 2.113 g/hour - A = 1.00 mm2. find PW at 4500K? Convert all units to SI and find <v>/4 Find N/V from effusion equation Solve for P – which will represent Tungsten vapor pressure For Friday do 19.28 and 19.31

  2. Chemical Systems System vs. surroundings The state of a system is defined by indicating the values of the measurable properties of the system. Properties of a system …. intensive extensive independent of amountdependent on amount P and T V, n, & all forms of energy E, U, H, S, G …. etc. extensive per mole molar volume (V, V/n or Vm) molar enthalpy or Hm

  3. T is a measure of how much kinetic energy the particles of a system have. translational energy, etr = 3kT/2 or Etr = 3nRT/2 Heat, q, is the transfer of energy from one system to another due to a difference in temperature. A B C A B C TA > TB = TC TA = TB = TC

  4. Equations of state ….. PV = nRT or PVm = RT Partial derivatives: (dP/dT)n,V = nR/V (dV/dT)n,P = ? nR/P (dP/dV)n,T = ? -nRTV-2 or -nRT/V2 PV = nRT P = nRT/V = nRTV-1

  5. Kinetic Molecular Theory (KMT) Assume: 1. gas particles have mass but no volume 2. particles in constant, random motion 3. no attractive/repulsive forces 4. conservation of energy at every collision If … PVm= RT then … Z =PVm/RT = 1 Z is called the compressibility factor Real Gases: Z = PVm/RT  1 Z is a measure of nonideality of gas Real Gases: Z = 1 + B/Vm + C/Vm2 + D/Vm3 + … Virial Equation: power series with respect to V B, C, etc. are dependent on T as well as gas.

  6. Van derWaals Equation Ideal — V = volume of container will Vreal be less or more than that? Vreal < Vid = Vmeas Pmeas = Preal < Pid Ideal — P = assumes no molecular interactions Do gas molecules attract or repel? How will this effect Pmeas?

  7. Van derWaals Equation (P + a/Vm2)(Vm - b) = RT Pvdw = RT/(Vm – b) – a/Vm2 Pmeas = Preal < Pid Vreal < Vid = Vmeas (P + n2a/V2)(V - nb) = nRT a = f(intermolecular forces) units = atm cm6mol-2 b = molecular volume units = cm3 mol-1

  8. CH4 gas at 300K ideal VdW RK Z real P (atm)

  9. Z P atm Rel Value He Ne Ar Kr Xe

  10. Van derWaals Equation (P + a/Vm2)(Vm - b) = RT Pvdw = RT/(Vm – b) – a/Vm2 (P + n2a/V2)(V - nb) = nRT Critical Values – Experimentally determined from phase diagrams (Chapter 6) Pc, Tc, and Vc are constant and unique to each gas. b = RTc/(8Pc) a = 27R2Tc2/(64Pc2) a = f(intermolecular forces) units = atm cm6mol-2 b = molecular volume units = cm3 mol-1

  11. PV = nRT & P = nRT/V Partial derivatives ― dP/dT = nR/V (P + a/Vm2)(Vm - b) = RT Pvdw = RT/(Vm – b) – a/Vm2 dP/dT = R/(Vm-b) = nR/(V-nb)

  12. Partial derivatives ― dP/dT = nR/V P, T, V (dx/dy)z • (dy/dz)x • (dz/dx)y = -1 The cyclic rule for partial derivatives (chain rule) (dP/dT)V • (dT/dV)P • (dV/dP)T = -1 a = 1/V • (dV/dT)P(expansion coefficient) k = -1/V • (dV/dP)T(isothermal compressibility) (dP/dT)V = - (dV/dT)P /(dV/dP)T = a/k

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