A dilute solution behaves like an ideal gas of the solute molecules. The diffusi

Question

A dilute solution behaves like an ideal gas of the solute molecules. The diffusion coefficient of glucose in a dilute aqueous solution at 20°C is 6.7 x 10-10 m2/s. a. What will the diffusion coefficient of glucose be at body temperature (37 °C)? You can assume the pressure is the same at both 20ºC and 37ºC. b. How far will a glucose molecule diffuse in 1 second at 20 °C? Consider the diffusion to occur in three dimensions. c. How long will it take a glucose molecule to diffuse a distance of 50 m at 20 °C? Consider the diffusion to occur in three dimensions.

b. How far will a glucose molecule diffuse in 1 second at 20 °C? Consider the diffusion to occur in three dimensions.

c. How long will it take a glucose molecule to diffuse a distance of 50 m at 20 °C? Consider the diffusion to occur in three dimensions.

Explanation / Answer

Temperature dependence of diffusion coefficient can be representated by

D=D0e^-Ea/kT where D is the diffusion coefficient at temperature T and D0 is the maximal diffusion coefficient at infinite temperature, Ea is the activation energy and k=Boltzmann constant

So lnD1=lnD0-Ea/kT1 equation (1) and lnD2=lnD0-Ea/kT2 equation ( 2)

Substracting equation (2) from equation (1) we get lnD2/D1=Ea/k(1/T1-1/T2) equation( 3)

D1=6.7*10^-10 m^2/s as per given in the problem, T1=(20+273) K=293 K and T2=(37+273) K=310 K

We have to find out D2 using equation (3)

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