Question

Question #a9c4a

Answer 1

The minimum energy required for isomerization is 267 000 J/mol or `4.43 × 10^"-19"color(white)(l)"J/molecule"`. The minimum frequency of light required is `6.69 × 10^14color(white)(l)"Hz"`.

Explanation:

The isomerization of cis-but-2-ene to trans-but-2-ene requires breaking of the π bond.

The bond energy of a C-C σ bond is 347 kJ/mol.

The bond energy of a C=C double bond (σ + π) is 614 kJ/mol.

So the bond energy of a π bond is (614 – 347) kJ/mol = 267 kJ/mol =
267 000 J/mol.

On a molecular level, the bond energy of a π bond is

`"267 000 J"/"1 mol" × "1 mol"/(6.022 × 10^23"molecules") = 4.43 × 10^"-19"color(white)(l)"J/molecule"`

A quantum of light can excite a π electron to a π* orbital and allow free rotation about the central C-C bond.

We can calculate the minimum frequency required.

`E = hf`

`f = E/h = (4.43 × 10^"-19"cancel("J"))/(6.626 × 10^"-34"cancel("J")"·s") = 6.69 × 10^14color(white)(l)"Hz"`