Question

(8) The C = Ö group in acetone (CH;CO CH3) has a strong absorption line at 189 nm, and a weak absorption line at 280 nm. The line at 280 nm corresponds to a B transition; and the line at 189 nm corresponds to a B. transition." (a) x ) a (c) * ( n t * (2) Cyclohexane (CH) has two conformations, i.e. the chair conformation (c) and boat conformation (b). At 298 ®K, the chair conformation (e) is at the ground state with energy = 0; and the boat conformation (b) is at the energy level of 22,000 J/ mol. (i) Calculate the molecular partition function (q) of cyclohexane at 298 °K. (ii) Calculate the Boltzmann distribution (the most probable distribution) of the two conformations, and respectively. (iii) Compare these two conformations, which conformation is more populated? (Avogadro's constant NA - 6.022 x 10”/mol; Boltzmann constant k = 1.38 x 10-2 J/°K) (25 points)

Dang. That's all I was given. Thank you for your help!

Answer 1

8.

Acetone have two peaks : strong peak at 189 nm corresponds to $\pi$-->$\pi$* (higher energy required and it is allowed transition so strong) and weak peak at 280 nm corresponds to n-->$\pi$* (lesser energy required and it is non-allowed transition so less intense )

(what is wrong with answer !)

2. Cyclohexane : boat and chair

At 298 K ; E(c) = 0 and E(b) = 22000 J/mol

(a) Molecular partition function : ( 2 energy states ) (e0 = 1)

q = 1 + exp(-E(b)/RT

q = 1 + exp(-22 x 10³ J/mol /(8.314 J/k-mol x 298 K))

q = 1.0001

It suggests that only one energy level will be occupied at this temperature.

(b) Nc / N and Nb/N (boltzmann most probable distribution )

Nc / N = exp(-E(b)/RT) = exp(0) = 1

Nb / N = exp(-E(b)/RT) = exp(-22 x 10³ J/mol /(8.314 J/k-mol x 298 K)) = 1.4 * 10^-4

(c) comparing two conformations :

The relative population of the two conformations at a given temperature (298K) can be found from t

Nb /Nc = exp(-22 x 10³ J/mol /(8.314 J/k-mol x 298 K)) = 1.4 * 10^-4

or Nc/Nb = exp(22 x 10³ J/mol /(8.314 J/k-mol x 298 K)) = 7143

This shows the very low population of the boat conformation at 298 K .

So, chair conformation is more populated.