Calculate the yield if 437.463 g of 2-methylcyclohexanone gives 13.805571 g of 2

Question

Calculate the yield if 437.463 g of 2-methylcyclohexanone gives 13.805571 g of 2-methylcyclohexanol. Calculate the cis/trans equilibrium constant for a 1.3-disubstituted cyclohexane compound at 3.2 Kelvin, as shown below. The A value for substituent X is 6.5 kJ/mol, while the A value for substituent Y is 2.3 kJ/mol. Assume that the lowest-energy chairs of each stereoisomer are in equilibrium. Consider a solution containing a conformationally-locked ring system with a single substituent. Upon analysis at 250.8 K. the axial conformer is found to have a concentration of 2.03 mM, and the equatorial conformer is found to have a concentration of 7.2 mM. Given this, calculate the A value for this substituent in kJ/mol.

Explanation / Answer

1) No. of moles of 2-methylcyclohexanone = 437.463 g / 112.16958 g/mole = 3.9 moles

one mole of 2-methylcyclohexanone will gives you one mole of 2-methylcyclohexanol

weight of 2-methylcyclohexanol corresponding to 3.9 moles = 3.9 moles x 114.18546 g/mol = 445.3249 g

This will be the theoretical yield

The % yield = (13.805571 / 445.3249) * 100 = 3.1 %

2)

Let us keep the lowest energy substitute Y at axial position to get trans isomer, as we know the cis isomer will contain both subsistent at equatorial positions.

Hence th energy difference Delta G = 2.3 KJ/mole = 2300 j/mole = 547.62 Cal/mole

The equilibrium constant K = e(–G/ RT) where R is the universal gas constant (1.987 cal/mol·K) and T is the temperature at which the measurement is being made (3.2 K in this case).

K = e -(0547.62 / 1.987 x 3.2 ) = 0.00427

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