A liquid cellular protein secretion has proteins that can exist in one of three

Question

A liquid cellular protein secretion has proteins that can exist in one of three states at a particular temperature T:

(i) State 1 with energy equal to 1.93 k subscript B T and rho = 2.51 g divided by c m cubed

(ii) State 2 with energy equal to 1.67 k subscript B T and rho = 2.18 g divided by c m cubed

(iii) State 3 with energy equal to 1.51 k subscript B T and rho = 2.57 g divided by c m cubed.

If a container has a volume of 251 c m cubed and contained only a large number of these proteins, how heavy would you expect it to be. Report your answer in grams. (Tip: Figure out what the probability of finding a protein in each state is first, they find the average density of the whole secretion)

Explanation / Answer

usign equation

P(Ei) = exp ( -Ei / kT )

E1 = 1.93 k T ,

E2 = 1.67 k T ,

E3 = 1.51 k T ,

Z = exp ( -E1 / kT ) + exp ( -E2 / kT ) + exp ( -E3 / kT )

Z = exp ( -1.93 ) + exp ( -1.67 ) + exp ( -1.51 )

Z = 0.5543

P ( E1 ) = exp ( -E1 / kT ) / Z

= 0.261

P ( E2 ) = exp ( -E2 / kT ) / Z

= 0.339

P ( E3 ) = exp ( -E3 / kT ) / Z

= 0.396

M = 251 X ( 2.51 X P ( E1 ) + 2.18 X P ( E2 ) + 2.57 X P ( E3 ) )

M = 251 X ( 2.51 X 0.261 + 2.18 X 0.339 + 2.57 X 0.396 )

M = 605.374 g

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