Chapter16_B - Chapter 16 - Section B - Non-Numerical...

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Chapter 16 - Section B - Non-Numerical Solutions 16.1 The potential is displayed as follows. Note that K is used in place of k as a parameter to avoid confusion with Boltzmann’s constant. Combination of the potential with Eq. (16.10) yields on piecewise integration the following expression for B : B = 2 3 π N A d 3 ± 1 + ( K 3 1 ) ( 1 e ξ/ kT ) ( l 3 K 3 ) ( e ±/ kT 1 From this expression, dB dT = 1 kT 2 ± ( K 3 1 e ξ/ kT + ( l 3 K 3 e ±/ kT ² according to which dB / dT = 0 for T →∞ and also for an intermediate temperature T m : T m = ± + ξ k ln ³ ξ ± ´ K 3 1 l 3 K 3 µ¶ That T m corresponds to a maximum is readily shown by examination of the second derivative d 2 B / dT 2 . 16.2 The table is shown below. Here, contributions to U (long range) are found from Eq. (16.3) [for U (el)], Eq. (16.4) [for U (ind)], and Eq. (16.5) [for U (disp)]. Note the following: 1. As also seen in Table 16.2, the magnitude of the dispersion interaction in all cases is substantial. 2. U (el), hence f (el), is identically zero unless both species in a molecular pair have non-zero permanent dipole moments. 3. As seen for several of the examples, the fractional contribution of induction forces can be sub- stantial for unlike molecular pairs. Roughly: f (ind) is larger, the greater the difference in polarity of the interacting species. 721
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Molecular Pair C 6 / 10 78 Jm 6 f (el) f (ind) f (disp) f (el)/ f (disp) CH 4 /C 7 H 16 49.8 0 0 1.000 0 CH 4 /CHCl 3 34.3 0 0.008 0.992 0 CH 4 /(CH 3 ) 2 CO 24.9 0 0.088 0.912 0 CH 4 /CH 3 CN 22.1 0 0.188 0.812 0 C 7 H 16 /CHCl 3 161.9 0 0.008 0.992 0 C 7 H 16 /(CH 3 ) 2 CO 119.1 0 0.096 0.904 0 C 7 H 16 /CH 3 CN 106.1 0 0.205 0.795 0 CHCl 3 /(CH 3 ) 2 CO 95.0 0.143 0.087 0.770 0.186 CHCl 3 /CH 3 CN 98.3 0.263 0.151 0.586 0.450 (CH 3 ) 2 CO/CH 3 CN 270.3
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This note was uploaded on 04/18/2011 for the course CEM 497 taught by Professor Ku during the Spring '11 term at Punjab Engineering College.

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Chapter16_B - Chapter 16 - Section B - Non-Numerical...

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