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practicefinal - YOUR NAME HERE May 11, 2010 Chem 120B Final...

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Unformatted text preview: YOUR NAME HERE May 11, 2010 Chem 120B Final Examination Definitions and Useful Formulas: E = TS pV + i i dN i A = E TS G = E TS + pV H = E + pV 1 /T = ( S/E ) V,N = ( A/N ) T,V S = k B ln W dE = TdS pdV + i i dN i SdT V dp + i N i d i = 0 dG = SdT + V dp + dN p ( ) = exp( E ) /Q = 1 /k B T dE = dw + dq Q = exp( E ) ( E ) = ( ln Q/ ) V,N dS dq/T Q = exp( A ) ( G ) T,p,N ( A ) T,V,N G = i i N i Q = q N /N ! q trans = V/ 3 = h/ 2 mk B T # ways to distribute N indistinguishable objects among M places = M ! / [ N !( M N )!] ln( M ! / [ N !( M N )!]) ln( M N /N !) for N M i = (0) i + k B T ln ( i / ) e x 1 + x + x 2 / 2 (0) = ( q 2 / 2 R )(1 1 / ) k TST = (1 / 2) (| d/dt |) p ( ) / integraltext A d p ( ) a A + b B = c C + d D for a A + b B c C + d D u ( r ) = qq / ( r ) ( E 2 ) = k B T 2 C V = radicalbig / (4 i i q 2 i ) ln N ! N ln N N, d ln N ! /dN ln N Q = ( m/h ) integraltext dx integraltext dv exp[ E ( x,v )] ( x 2 ) = 2 Dt dp/dT = S/ V integraltext dxe x 2 / 2 2 = 2 2 integraltext dxe x 2 / 2 2 e x = 2 2 e 2 2 / 2 You may neglect quantum mechanical effects in all parts of this exam. 1 1. Consider a dilute molecule A (represented in figures as ) in solution. Two A molecules can bind to form a dimer A 2 (represented as ), as sketched below. single-cell partition function q 1 single-cell partition function q 2 As usual, we have divided space into cells of a three-dimensional lattice. Each of the M cells comprising the volume V = M 3 has side length . The partition function of an A molecule, when confined to a single lattice cell, is q 1 . Whenever two A molecules occupy the same cell, they dimerize; confined to that cell, the dimer has partition function q 2 . You will first analyze solutions that contain N 1 unbound A monomers, and N 2 bound A 2 dimers. The total number of A units N = N 1 + 2 N 2 is fixed. Because the solution is dilute, N M . 5 pts (i) Calculate the partition function Q for this collection of monomers and dimers. (Dont forget that A and A 2 species can explore the entire volume V ; the single-cell partition functions q 1 and q 2 do not include contributions from these translational fluctuations.) Your answer should involve some, but not necessarily all, of the quantities: N 1 , N 2 , M , T , q 1 , q 2 , , and fundamental constants. 2 5 pts (ii) Sketch ln Q as a function of the extent of dimerization N 2 , at fixed T , p , and N . Only the gross shape of ln Q , which you should know from basic principles, is important here. Note that the equilibrium value ( N 2 ) is marked on the N 2-axis....
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This note was uploaded on 09/12/2011 for the course CHEM 107B taught by Professor Jamesames during the Spring '09 term at UC Davis.

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practicefinal - YOUR NAME HERE May 11, 2010 Chem 120B Final...

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