Q1. A molecule is switching among three conformations (A, B, and C) at 25^oC as shown below. From the given switching rate constants, estimate the relative stability (energy) of A to B and B to C in terms of kJ/mol. Hint: Modify "numerical_simulation_equilibrium.xlsx" in CANVAS to numerically simulate the time trajectories of [A], [B], and [C] and find out their equilibrium values [A]_e, [B]_e, and [C]_e. Use the Boltzmann distribution function to compute ΔE_A·B(= E_A - E_B) from [A]_e/[B]_e and ΔE_B-C (= E_B - E_C) between states B and C from [B]_e/[C]_e.

A ⇔ B ⇔ C

k₁ = 7.5/s; rate constant switching from A to B

k_-1 = 2.5/s; rate constant switching from B to A

k₂ = 3.5/s; rate constant switching from B to C

k_-2 = 4.5/s; rate constant switching from C to B

Q2. Using the 3D velocity distribution function in a spherical polar coordinate system. F(v)v²sinθdθdΦdv = (m/2πk_BT)^3/2exp(-mv²/2k_BT)v2sinθdθdΦdv, derive the general flux equation. Based on the general flux equation, derive the diffusion coefficient of an ideal gas as a function of its mass, diameter, partial pressure, and temperature.

Q3. When an electronically (i.e. fluorescently) excited molecule is put on a metal surface, its fluorescence is quenched. The unquenched fluorescence decay time of the molecule is 0.50 ns. If the quenched fluorescence decay time is 2.0 ps, what is the rate constant of electron transfer from the molecule to the metal surface?

Assignment Files -

https://www.dropbox.com/s/2jvuk3ie7bm5y5a/HW.zip?dl=0