Question

B P . The Sunne two large molecular groups A and B can react to form a macromolecule P. in the reaction A quilibrium constant for the reaction is ke/co, where he 3 and UM Initially, the concentration of molecular group A is A-0.1 M, the concentration of molecular croup B is B 02 M and the concentration of the macromolecule Pis (PJ-0. What will be the concentration Pof macromolecule P in mole/L when this reaction comes to equilibrium? (b) Suppose macromolecule P has two energy states and separated by AE = 2.0 x 10-* J. What percentage of the macromolecules are in the lower energy state Pat T = 300K? at T = 300 K? Note: Recall the (c) What is the osmotic pressure associated with the macromolecules in state conversion factors 1 mole 6.02 x 10" molecules and 1 m = 1000 L. (d) Two rectangular prisms with surface contact area 1.00 pm are nearby each other in solution. Suppose macro molecule P has a radius of 20.0 nm. What is the free energy difference associated with the depletion interaction caused by the macromolecules in state P, and what is the approximate depletion force between the rectangular prisms?

Answer 1

3.

A + B ==> P

a.

we have, Keq = 3

              A + B ==> P

initial      0.1M       0.2 M         0

at eq.     0.1 -x      0.2 -x        x

Keq = 3 =   [P] / [A] [B] =   x / (0.1- x) (0.2- x)

3 =   x / (0.1- x) (0.2- x)

 3*(x^2-0.3x+0.02) = x

3*(x^2-0.3x+0.02) - x = 0

(3x^2-1.9x+0.06) = 0

x = 0.033 ==> [P] = 0.0334 mol/L

b.

P1/P2 = exp. (-(-2.0*10-21 J*6.022*1023 Mol-1 /8.314 J/K-mol * 300 K )) = 1.62

thus, P1 fraction = P1/(P1+P2) *100 = 1.62/2.62*100 = 62 %

c.

osmotic pressure , P1 associated:

P : 1 M

P1 = 0.62*P

$\pi$ = 0.62* C*RT

= 0.62 1 mol/L *0.0821 L-atm/mol-K * 300 K = 15.27 atm