Using the data in Table 4.3, calculate the ratio (to 2 SF) of themore stable cha
ID: 686216 • Letter: U
Question
Using the data in Table 4.3, calculate the ratio (to 2 SF) of themore stable chair conformation to the less stable conformation atequilibrium at 298 K for the following compounds: chlorocyclohexaneand iodocyclohexane.First compound:
1
Second compound:
2
Explanation / Answer
Please Remember to Rate Me! More stable ---> Less stable = equatorial substitutedcyclohexane -> axial substituted cyclohexane. Draw the ring flip conformers of both compounds, with the"reactants" as the more stable, and the "products" as the lessstable. You can tell from the picture that there is zero 1,3-diaxialinteraction strain when the chlorine or iodine is in the equatorial( more stable ) position, however when you perform the ring flip,one can tell that there is a 1, 3 - diaxial interaction between the2 hydrogens and the 1 chlorine, or iodine. Include the data from your table next time. I just so happen to remember that a 1,3-diaxial interaction betweenchlorine and hydrogen is equal to 1kJ/mol. You must double thisvalue to attain your delta(E), or difference in energy. As the ring flip is performed from a more stable conformer to aless stable conformer, the difference in energy must bepositive. To figure out the ratios, you must use the equation: delta(E)= -RT lnk where R is the gas constant, and K is the equilconst. So, you have as follows : +2000J (2kJ) = -(8.314J)(298K)lnK , solvefor K. lnK= 2000J / -(8.314J)(298K) , K = e^(2000J / -(8.314J)(298K)) K= 0.446. Think of this as 0.446 / 1, to see it in terms ofratios. Because K = products OVER (/) reactants, for every 0.446 lessstable (axial chlorine conformer) there is 1 more stable(equatorial chlorine conformer). The ratio would be from left toright 1(more stable) : 0.446 (less stable). To take it a step further, you can find the percentages of eachconformer that exist at this state at one time (a chlorocyclohexaneis changing from equatorial to axial a million times a second). 1 / 1.446 = 69% reactants, 31% products. So at any given moment,69% of the time, you will find the chlorocyclohexane in theequatorial ( more stable ) position. -Iodocyclohexane is done in the exact same manner, you need yourtable to find out what the 1,3-diaxial interactions are "worth" fora iodine - hydrogen interaction, and double it to get yourdelta(E).
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