122ch10b - 39 10.78) u= 3RT = 3RT 1/ 2 At constant T, u =...

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39 10.78) At constant T, u = (1/ ) 1/2 a) The larger the molar mass, the slower the avg. speed (at constant T). SF 6 < HBr < Cl 2 < H 2 S < CO (g/mol) 146.06 80.91 70.91 34.08 28.01 Dec , Inc speed ( u ) b) Calculate the rms speeds of CO and Cl 2 at 30 0 K. Use eqn above and make sure R, T and are in SI units (8.314 J/mol C K or kg C m 2 /s 2 C mol C K, Kelvin, kg/mol, respectively) to give SI units for u (m/s) 3 (8.314 kg C m 2 /s 2 C mol C K)(30 0 K) u CO = (-------------------------------------------) 1/2 = 516.85 m/s = 516 m/s 28.01 x 10 -3 kg/mol 3 (8.314 kg C m 2 /s 2 C mol C K)(30 0 K) u Cl 2 = (-------------------------------------------) 1/2 = 324.84 m/s = 325 m/s 70.91 x 10 -3 kg/mol As expected, the lighter CO molecules move as the greater rms speed. 10.81) u RT RT == 33 12 /
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40 10.81) (cont.) 10.82)
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41 10.82) (cont.) 10.83) a) Gases behave non -ideally at HIGH Pressure and LOW Temp (Real gases behave ideally at low P and high T) b) Real gases behave non-ideally because they have: Finite Volumes: real gas particles occupy some of the volume of the container so the volume of free space for the molecules to move in is less than the container (causes P measured > P ideal ) - Positive deviations from ideality Intermolecular Attractive Forces: Real gases have AF and attract each other - causes the measured pressure to be less than ideal (P m < P i ) - Negative deviations from ideality c) For an ideal gas, PV/RT = n, the number of moles of gas particles, which should be a constant for all pressure, volume and temperature conditions (for 1 mole of gas PV/RT = 1 or PV/nRT = 1 is equivalent). If this ratio changes with increasing pressure the gas is not behaving ideally (i.e. if PV/nRT = 1 the gas is behaving ideally, if not then it is exhibiting non-ideal behavior). If PV/nRT > 1 the gas is exhibiting a positive deviation from ideality (due to the volume of the molecules). If PV/nRT < 1 the gas is exhibiting a negative deviation from ideality (due to the IAF between molecules).
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42 10.86) The van der Waals equation is given below: n 2 a ( P + ------ ) ( V - nb ) = nRT V 2 or nRT n 2 a P = --------- - ------ V - nb V 2 causes (+) causes ( ! ) deviation deviation P m > P i P m < P i P m = measured (real) P; P i = ideal P due to vol due to IAF of molecules a: corrects for attractive forces between particles - real gas particles have AF - ideal gas particles have NO AF (a=0) b: corrects for finite molecular volume of particles - real gases occupy some vol of the container (we are interested in free vol) - ideal gas part. Have NO vol (b=0) Both tend to inc. with inc. in Mol. Wt. And structural complexity. The “a” constant depends on AF between particles and these will be discussed further in Chapter 11. V cont - nb < V cont so nRT/(V-nb) > nRT/V ideal n 2 a/V 2 accounts for fact that AF cause particles to hit walls w. less force than ideal gases, ˆ smaller P then expected for an ideal gas (negative deviation from ideality)
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43 10.88) Under these conditions this gas exhibits a negative deviation from ideality (P measured will be closer to P VDW than P ideal & P VDW < P ideal )
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This note was uploaded on 06/11/2011 for the course CHEM 122 taught by Professor Zellmer during the Spring '07 term at Ohio State.

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122ch10b - 39 10.78) u= 3RT = 3RT 1/ 2 At constant T, u =...

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