Chem288_2005_Prelim_I_Formulas

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 π = 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 τ = 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 θ ≈ 1 + θ + 1 2 θ 2 + 1 3! θ 3 + ··· log (1- θ ) ≈ θ- 1 2 θ 2 + 1 3 θ 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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