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32W MW (kg/mol) T (K)P (torr)P (Pa)A (m 2 ) /4N/VdN/dt (s -1 ) dN/dt (g/hr) 0.1838545004.986640.0000011801.07E+221.923E+182.113 dN/dt = A /4 N/V Density - # molecules are available for collision (m -3 ):N/V = PN A /(RT) = {8RT/( M)} 1/2 19.32Tungsten effusion – MW = 0.18385 kg/mol Given: T = 4500 K - dN/dt = 2.113 g/hour - A = 1.00 mm 2. find P W at 4500K? Convert all units to SI and find /4 Find N/V from effusion equation Solve for P – which will represent Tungsten vapor pressure For Friday do 19.28 and 19.31

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

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

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

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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 Real Gases: Z = PV m /RT 1 Z is a measure of nonideality of gas If … PV m = RT then … Z = PV m /RT = 1 Z is called the compressibility factor Real Gases: Z = 1 + B/V m + C/V m 2 + D/V m 3 + … Virial Equation: power series with respect to V B, C, etc. are dependent on T as well as gas.

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Van der Waals Equation P meas = P real < P id V real < V id = V meas Ideal V = volume of container will V real be less or more than that? Ideal P = assumes no molecular interactions Do gas molecules attract or repel? How will this effect P meas ?

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Van der Waals Equation (P + a/V m 2 )(V m - b) = RT P meas = P real < P id V real < V id = V meas a = f(intermolecular forces) units = atm cm 6 mol -2 b = molecular volume units = cm 3 mol -1 P vdw = RT/(V m – b) – a/V m 2 (P + n 2 a/V 2 )(V - nb) = nRT

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Z P (atm) ideal real VdW RK CH 4 gas at 300K

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Z P atm He Ne Ar Kr Xe Rel Value Gas MW (kg/mol)ab He 0.004 3.41E+0423.65 Ne 0.020 2.09E+0516.97 Ar 0.040 1.34E+0632.21 Kr 0.084 2.29E+0639.58 Xe 0.131 4.11E+0651.24

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Van der Waals Equation (P + a/V m 2 )(V m - b) = RT a = f(intermolecular forces) units = atm cm 6 mol -2 b = molecular volume units = cm 3 mol -1 P vdw = RT/(V m – b) – a/V m 2 (P + n 2 a/V 2 )(V - nb) = nRT Critical Values – Experimentally determined from phase diagrams (Chapter 6) P c, T c, and V c are constant and unique to each gas. b = RT c /(8P c ) a = 27R 2 T c 2 /(64P c 2 )

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Partial derivatives dP/dT = nR/V (P + a/V m 2 )(V m - b) = RT PV = nRT & P = nRT/V P vdw = RT/(V m – b) – a/V m 2 dP/dT = R/(V m -b) = nR/(V-nb)

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

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