Chap06 soln

Physical Chemistry

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6 Physical transformations of pure substances Solutions to exercises Discussion questions E6.1(b) Refer to Fig. 6.8. The white lines represent the regions of superheating and supercooling. The chemical potentials along these lines are higher than the chemical potentials of the stable phases represented by the colored lines. Though thermodynamically unstable, these so-called metastable phases may persist for a long time if the system remains undisturbed, but will eventually transform into the thermo- dynamically stable phase having the lower chemical potential. Transformation to the condensed phases usually requires nucleation centers. In the absence of such centers, the metastable regions are said to be kinetically stable. E6.2(b) At 298 K and 1.0 atm, the sample of carbon dioxide is a gas. (a) After heating to 320 K at constant pressure, the system is still gaseous. (b) Isothermal compression at 320 K to 100 atm pressure brings the sample into the supercritical region. The sample is now not much different in appearance from ordinary carbon dioxide, but some of its properties are (see Box 6.1). (c) After cooling the sample to 210 K at constant pressure, the carbon dioxide sample solidifies. (d) Upon reducing the pressure to 1.0 atm at 210 K, the sample vapourizes (sublimes); and finally (e) upon heating to 298 K at 1.0 atm, the system has resumed its initial conditions in the gaseous state. Note the lack of a sharp gas to liquid transition in steps (b) and (c). This process illustrates the continuity of the gaseous and liquid states. E6.3(b) First-order phase transitions show discontinuities in the first derivative of the Gibbs energy with respect to temperature. They are recognized by finite discontinuities in plots of H , U , S , and V against temperature and by an infinite discontinuity in C p . Second-order phase transitions show discontinuities in the second derivatives of the Gibbs energy with respect to temperature, but the first derivatives are continuous. The second-order transitions are recognized by kinks in plots of H , U , S , and V against temperature, but most easily by a finite discontinuity in a plot of C p against temperature. A λ -transition shows characteristics of both first and second-order transitions and, hence, is difficult to classify by the Ehrenfest scheme. It resembles a first-order transition in a plot of C p against T , but appears to be a higher-order transition with respect to other properties. See the book by H. E. Stanley listed under Further reading for more details. Numerical exercises E6.4(b) Assume vapour is a perfect gas and vap H is independent of temperature ln p p = + vap H R 1 T 1 T 1 T = 1 T + R vap H ln p p = 1 293 . 2 K + 8 . 314 J K 1 mol 1 32 . 7 × 10 3 J mol 1 × ln 58 . 0 66 . 0 = 3 . 378 × 10 3 K 1 T = 1 3 . 37 8 × 10 3 K 1 = 296 K = 23 C
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88 INSTRUCTOR S MANUAL E6.5(b) d p d T = S m V m fus S = V m d p d T V m p T assuming fus S and V m independent of temperature.
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