An antifreeze protein, with a molecular weight of 17000 Da, was found to be present at...

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An antifreeze protein, with a molecular weight of 17000 Da, wasfound to be present at a concentration of 10g dm-3 in the serum ofan Antarctic fish. calculate the expected depression of thefreezing point and compare your result with 1) the observeddepression of 0.6K and 2) the depression of 0.0014K observed for10g dm-3 solution of lysozyme, molecular weight of 14500 Da. forpure water, Lf=6.02kj ml-1 and Tm=273.15 K

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Solution:

We know âˆ†T_f = -K_f x m

Where, âˆ†T_f = depression of freezing point, K_f = is the freezing point depression constant, and m = molality.

Concentration of the protein = 10g dm^-3

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =10/17000 mol dm^-3 = 5.88x10^-4 mol/L

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 5.88x10^-4 mol/kgÂ Â Â Â Â (assuming density of water = 1kg/L)

Therefore, âˆ†T_f = -K_f x m = -274.86x5.88x10^-4 = -0.16 K Â Â Â Â Â Â Â Â (since, k_f = 274.86 K/m)

Similarly, Concentration of lysozyme = 10g dm^-3

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =10/14500 mol dm^-3 = 6.89x10^-4 mol/L

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 6.89x10^-4 mol/kgÂ Â Â Â Â (assuming density of water = 1kg/L)

Therefore, âˆ†T_f = -K_f x m = -274.86x6.89x10^-4 = -0.19 KÂ Â Â Â Â Â Â Â Â (since, k_f = 274.86 K/m)

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