# soln1 - × 1 CKD 1.2 The units in the preceding problem...

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Unformatted text preview: × 1. CKD 1.2 The units in the preceding problem were in kJ/mole, which is an example of SI units. Give values for the following quantities both in kJ/mole and in the indicated alternative units in parentheses: (a) heat capacity of liquid water at 15 °C and 1 atm (cal mole-1 K-1 ): -1-1-2 K kJ Cp =-3 kJ -1-1 K Cp = mol 7.5x10 1 cal = 4.186 x 10 mol cal 18 (b)vibrational fundamental frequency of H 35 Cl (cm-1 ): -1 o ν = cm 2990 10 x 986 . 1 − 16 kJ cm 1000 1- N a =-1 o ν = mole kJ 8 . 35 cm 2990 1- × (c) ionization potential of H atom (eV): IP = eV 13.6 10 602 . 1 − 22 kJ x eV 1 = -1 3 kJ mole 10 x 1.31 eV 6 . 13 × N × a (d)RM.S. average translational kinetic energy of Br 2 at 300 K (ergs molecule-1 ): 3 1- KE RMS = RT = 3 × kJ 00831451 . mol-1 K × K 300 = 2 2 1- mole kJ 3.74 2 g 1000 × cm 100 m 1 × 1 N a =-1-14 molecule ergs 10 x 6.21 J 3740 mole 1- × kg 1 (e) energy of CO 2 laser photons having a wavelength of 10.59 µ m (Hz): c h kJ × N × = a 10 x 10.59 6 - m J 1000 -1 mole kJ 11.3 c = 10 x 10.59 6- m 2. CKD Problem 1.3 Hz 13 10 x 2.83 a) Derive the integrated rate equation for a reaction of 3/2 order in a single reactant. Derive the expression for the half-life of such a reaction. Assume a reaction of the form: A → B, with a rate expression, 2 - d[A] = k[A] 3 dt 2 A] [ − 3 d[A] =- kt A(t) 1 k t = [A] 1 2 2 A o kt [A(t)] − 1 2 = ] [A 1- 2 + o 2 ( ) 2 2 1 o kt − − + = ] [A [A(t)] half-life derivation: ] [A o At t 1/2 ,[A ] = , t 1 2 2 ] [A − 1 2 kt 1 2 o 1- 2 − ] [A + = 2 o 2 2 − 1 kt 1 2 2 ] [A 1 2 = , o 2 1 o 2 1 1) 2 2( t − = ] k[A For reaction order n: A → B, with a rate expression, - d[A] n = k[A] dt n - A] [ d[A] = kt - A(t) [A] 1 − n n − 1 = kt A o 1 − n [A(t)] n - 1 = ( ] [A + (n − 1)kt ) o ( ) n 1 1 n 1 o 1)kt (n − −...
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soln1 - × 1 CKD 1.2 The units in the preceding problem...

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