Chem288_2005_Prelim_I_Formulas - Chemistry 288 Preliminary...

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Unformatted text preview: Chemistry 288 Preliminary Exam I Spring 2005, Marohn PHYSICAL CONSTANTS g = 9 . 8 m / s 2 k B = 1 . 38066 10 23 J/K h = 6 . 62618 10 34 J s 1 h = h/ 2 = 1 . 05459 10 34 J s 1 N A = 6 . 02205 10 23 mol 1 q e = 1 . 60219 10 19 C R = 8 . 31441 J mol 1 K 1 1 amu = 1 . 66057 10 27 kg 1 atm = 1 . 013 10 5 N m 2 1 eV = 1 . 60219 10 19 J 1 J = C V = kg m 2 s 2 At room temperature, T = 300 K, and = k B T = 4 . 14 10 21 J K 1 RT = N A k B T = 2 . 50 10 3 J mol 1 = 2 . 5 kJ mol 1 MATHEMATICAL FORMULAS For large numbers: N ! = N ( N- 1) ( N- 2) 1 log ( N !) N log N- N Series expansions: f ( x ) f ( x ) + f ( x ) ( x- x ) + 1 2! f ( x ) ( x- x ) 2 + e 1 + + 1 2 2 + 1 3! 3 + log (1- ) - 1 2 2 + 1 3 3 + Infinite series: 1 + x + x 2 + + x N 1 = 1- x N 1- x Integrals: integraldisplay e ax 2 dx = parenleftBig...
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