Polyethylene in solution can exist in two conformations: either as a random coil

Question

Polyethylene in solution can exist in two conformations: either as a random coil (conformation A) or being fully stretched (conformation B). At 298 degree K, random coil conformation (A) is at the ground state, with energy = 0; and the fully stretched conformation (B) is at the energy level of 24,000 J/mol. Calculate the molecular partition function (q) of polyethylene at 298 degree K. Calculate the Boltzmann distribution (the most probable distribution) of the two conformations, N_A/N and N_B/N, respectively. Compare these two conformations, which conformation is more populated? (Avogadro's constant N_A = 6.022 times 10^23 / mol; Boltzmann constant k = 1.38 times 10^-23 J / degree K)

Explanation / Answer

1a) 2.273

1b) NA/N Boltmann distribution = 2.545

NB/N Boltmann distribution = 1.256

1c) Random coil conformation is more populated

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