16_562ln08

16_562ln08 - MIT OpenCourseWare http:/ocw.mit.edu 5.62...

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MIT OpenCourseWare http://ocw.mit.edu 5.62 Physical Chemistry II Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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5.62 Lecture #16: Chemical Equilibrium. I . Readings: Hill, pp. 177-182 Maczek, pp. 77-83 Metiu, pp. 179-191 Following the treatment of equilibrium in 5.60. aA + bB = cC + dD A,B,C,D are all ideal gases µ i ( T,p i ) = µ o i (T) + RTlnp i o means standard state, usually p° = 1 bar. at equilibrium, C + dµ D – aµ A – bµ B = 0 plug in equations for each µ i (T,p i ) 0 = C o (T) + o D (T) o A (T) o B (T) + RTln p p C c a A p p D d B b term in [ ] is G°(T). In 5.60 we can look up values for G f o (T) for each substance. In 5.62 we will use Statistical Mechanics to compute each µ i o (T) . 0 = G ° (T) + RTlnK p (T) K p (T) = e G ° (T) RT µ i o (T) is chemical potential in units of J/mole of i. N = N a . What is µ i ? G A n i T,p,n j i = n i T,V,n j i  more convenient in Statistical Mechanics Both definitions of µ will give the same result. You should verify this.
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5.62 Spring 2008 Lecture #16, Page 2 Need µ i o (T) for i = A, B, C, D A = kTlnQ ⎛ ∂ A = kT ⎛ ∂ lnQ µ i = n i T,V,n j i n i T,V N i N Q i = ( q trans,i N i ! ) q int,i i = N i lnq trans,i N i lnN i + N i + N i int,i i = N i = N a [ trans,i i 1 + 1 + int,i ] n i N i n i   N a 2T = N a ln ( q trans,i N i ) + ln ( q * int e θ vib,i ) N a ) + * int,i θ vib,i µ i o = kTN a ln ( q trans,i Look at the last term in the previous equation: θ vib,i hc ω i hc ω i ( kTN a ) = + kN a 2k = + N a 2 = E 0,i kTN a = RT * µ i o (T) = RTln ( q i N a ) + E We will soon need to worry about putting all chemical species into a common energy scale. This will be to set the zero of energy at all separated gas phase atoms.
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16_562ln08 - MIT OpenCourseWare http:/ocw.mit.edu 5.62...

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