Recently Baldwin and Chapman (JOC 2005.70, 377) studied 1,5- sigmatropic shift o
ID: 696069 • Letter: R
Question
Recently Baldwin and Chapman (JOC 2005.70, 377) studied 1,5- sigmatropic shift of H atoms for 1,3-cyclohexadienes by synthesizing the monodeuterated molecule and studying its interconversion between the three forms: In their study they measured the time for the system to equilibrate between the three forms, and they found the following temperature dependence for this reaction T (K) k (s) 527 557 0.394 × 104 3.00 × 10-4 a) From their data, determine the activation enthalpy for this reaction. Comment on the size of the activation enthalpy you find; i.e., is it what you would expect and why (or why not)? b) From their data, determine the activation entropy for the reaction. Comment on the sign of the activation entropy; i.e., is it what you expect and why (or why not)? In their analysis they assume that the H atoms move but that the D atom stays in place. Is this a good assumption? Justify your answer with an estimate of the relative rates in the two cases. c)Explanation / Answer
From the given reaction data,
a) Using the relation
ln(k2/k1) = -dH/R[1/T2 - 1/T1]
with,
k1 = 0.394 x 10^-4 s-1
k2 = 3 x 10^-4 s-1
T1 = 527 K
T2 = 557 K
R = gas constant
dH = enthalpy
So,
ln(3 x 10^-4/0.394 x 10^-4) = -dH/8.314[1/557 - 1/527]
dH = -165.141 kJ
So enthalpy change for the reaction is -ve, that is the reaction is exothermic in nature
b) dS = entropy change,
dS = dH/T
= -165.141 x 1000/527
= -313.360 J/K
The dS for the reaction is -ve, that is the entropy of the system decreases as the reaction proceeds
c) C-H bond has lower bond energy than the C-D bond, therefore at lower temperature only the H moves. As the temperature is increased the rate of C-H bond cleavage and the H moving increases and thus, the rate value as seen from the data also increases. The assumption of D being stable is thus correct as C-D would need much greater energy that C-H bond.
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