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# Math Info - âˆ-= C a x a e xdx e ax ax 1 âˆ-= C ax ax a e...

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1 Mathematical Formulas for Physical Chemistry Trigometric Formulas: e ix = cos x + i sin x where i = -1 sin x = (1/2 i )[e ix - e -ix ] e -ix = cos x - i sin x cos x = (1/2)[e ix + e -ix ] sinh x = (1/2)[e x - e -x ] cosh x = (1/2)[e x + e -x ] Power Series Expansions: (a + b) n = a n + na n-1 b + (1/2!)n(n-1)a n-2 b 2 + .... (binomial expansion; good for all n; very useful when b<<a because then series converges rapidly; finite series for pos integer n) sin x = x - (1/3!)x 3 + (1/5!)x 5 - .... (x in radians; good for small x; an odd function) cos x = 1 - (1/2!)x 2 + (1/4!)x 4 - .... (an even function) e x = 1 + x + (1/2!)x 2 + .... (x real or imaginary; converges rapidly when x is small) ln x = (x-1) - (1/2)(x-1) 2 + (1/3)(x-1) 3 - ... (good for x>0) ln(1+x) = x - (1/2)x 2 + (1/3)x 3 - .... (useful when x is small; pos or neg) a/(1-x) = a(1 + x + x 2 + ….) | x | < 1 a/(1 - x) 2 = a(1 + 2x + 3x 2 + .... ) | x | < 1
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Unformatted text preview: âˆ« +-= C a x a e xdx e ax ax ) 1 ( âˆ« + +-= C ax ax a e dx x e ax ax 1 2 ) ( 2 2 3 2 ) ( ! 1 = âˆ« âˆž +-a a n dx x e n n ax âˆ« âˆž-= 2 1 2 a dx e ax Ï€ âˆ« âˆž-= 3 2 4 1 2 a dx x e ax âˆ« âˆž-= 5 4 8 3 2 a dx x e ax Important Constants h = 6.626x10-34 J s e = 1.60x10-19 C c = 3.00x10 8 m/s k = R/N o = 1.38x10-23 J/K m e = 9.10x10-31 kg m p = 1.673x10-27 kg m n = 1.675x10-27 kg N o = 6.02x10 23 /mole a o = 4 Ï€Îµ o Ä§ 2 /m e e 2 Îµ o = 1.113x10-12 J-1 C 2 m-1 R = 8.314 J/mâ€¢K 1 bar = 10 5 Pa 1 atm. = 101.325 kPa = 0.082 Lâ€¢atm/mâ€¢K 1 atm. = 760 Torr f (s) = 4 Ï€ [m/2 Ï€ RT] 3/2 s 2 exp[-ms 2 /2RT] s rms = [3RT/m] 1/2 ax ax a x xa a x axdx cos sin 2 1 2 1 ) 2 sin 2 1 ( 2 1 sin 2-=-= âˆ«...
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