BEIJING UNIVERSITY OF CHEMICAL TECHNOLOGY Example 13.6. The value of AG that we have calculated in the series of examples yieldsK=2.79x10 This yields a degree of dissociation of 0.084 at I atm,compared with 0783 calculated from Table A.2 in Example 4.4. 7.Calculate the molar heat capacity C of water vapor at 1000K,given the frequencies of the three normal modes of vibration,1595.3652,and 3756cm Translation comtributesR To Cand assuming ideal gas behavior C=C.+R. Since three angles are required to describe the orientation of a water molecule,there are three degesof ion rdmhatc(Sti1.)Theofthefirst normal mode is given by the following expression from Table 13.3. R31aKn22g R-xer =5.460J-K-1.mol (e224-1)2 where =2=(6.626x10"Js2998x10'msX1595cm100cm:m-22 (1.381x10J-K-X1000K The other two normal modes contribute 1.213 and 1.100 J.Kmol The sum of these contributions is41.03J·K·molr',compared with41l.218J·K·mofr'from Table A.2.In the statistical mechanical calculation we have assumed that water vapor is a perfect gas,and this is not quite true. TEL:010-64434903BEIJING UNIVERSITY OF CHEMICAL TECHNOLOGY TEL:010-64434903 4 Example 13.6. The value of 0 DG that we have calculated in the series of examples yields K p =2.79×10-2 . This yields a degree of dissociation of 0.084 at 1 atm, compared with 0.0783 calculated from Table A.2 in Example 4.4. 7.Calculate the molar heat capacity Cp of water vapor at 1000K, given the frequencies of the three normal modes of vibration, 1595,3652, and 3756cm -1 . Translation comtributes R 2 5 To Cp , and assuming ideal gas behavior Cp = Cv + R . Since three angles are required to describe the orientation of a water molecule, there are three degrees of rotational freedom that contribute R 2 3 (Section 1.12). The contribution of the first normal mode is given by the following expression from Table 13.3. 1 1 2.294 2 1 1 2 2.294 2 2 5.460J K mol ( 1) (8.314J K mol )(2.294) ( 1) - - - - = × × - × × = - e e e x e R x x where (1.381 10 J K )(1000 ) (6.626 10 J s)(2.998 10 m s )(1595cm )(100cm m ) 23 1 34 8 -1 1 1 kT K hc x - - - - - ´ × ´ × ´ × × = = v =2.295 The other two normal modes contribute 1.213 and 1.100 J·K -1·mol-1 . The sum of these contributions is 41.03 J·K -1·mol-1 , compared with 41.218J·K -1·mol-1 from Table A.2. In the statistical mechanical calculation we have assumed that water vapor is a perfect gas, and this is not quite true