The amount of methylcycloheane with the substituent in the equatorial orientation at room temperature (25C) would be
The Gibbs free energy for axial methyl to equatorial methyl is -7.28Kj/mol (the universal gas constant is 8.314 j/deg-mol).
I cant remember how to solve this!!!!! thanks!
To determine the amount of methylcyclohexane with the substituent in the equatorial orientation at room temperature (25°C), you can use the concept of equilibrium and the Gibbs free energy.
The Gibbs free energy change (∆G) is related to the equilibrium constant (K) by the equation:
∆G = -RT ln(K)
Where:
∆G = Gibbs free energy change
R = Universal gas constant (8.314 J/deg-mol)
T = Temperature in Kelvin (25°C + 273.15 = 298.15 K)
ln = natural logarithm
K = equilibrium constant
Since we know the Gibbs free energy change (∆G) and the universal gas constant (R), we can rearrange the equation to solve for the equilibrium constant (K):
K = e^(-∆G/RT)
Now, substitute the values into the equation:
K = e^((-7.28 kJ/mol) / (8.314 J/deg-mol × 298.15 K))
To convert kJ to J, multiply by 1000:
K = e^((-7280 J/mol) / (8.314 J/deg-mol × 298.15 K))
Simplifying the equation gives us:
K = e^(-3.068)
Finally, calculate the value of K using a scientific calculator or any calculator with an "exponential" function (usually denoted by "e^x"). The value of K obtained will represent the extent of the equilibrium between the axial and equatorial conformations of methylcyclohexane at room temperature (25°C).