The energy difference in these two conformations has been measured to be about 23 kj per mole. how much of this energy difference is due to the torsional energy of gauche relationships?

The answer is 7.8 kJ / mol.

Explanation:

Energy = (number of methyl group) (Gauche interactions)(3.8kJ/mol per interaction)

           = (2)(2)(3.8 kJ / mol)

            = 15.2 kJ / mol.

The energy  = (number of methyl group) - ( energy of gauche interactions)

                    = (23 kJ/mol) - 15.2 kJ/mol

                    = 7.8 kJ / mol.

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explanation:

we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .