5. The instantaneous velocity of a molecule tells you little about the time it t

Question

5. The instantaneous velocity of a molecule tells you little about the time it takes a molecule to move cellular distances because the molecule?s trajectory is constantly altered by collisions with other molecules in solution. The average time that it takes for a molecule to travel x cm by diffusion in three dimensions is given by t = x^2/6D, where t is time in seconds, and D is the diffusion coefficient, which is a constant that depends on the size and shape of a molecule. Glucose and myoglobin have diffusion coefficients of 5 X 10^-6 cm^2/sec and 5 X 10^-7 cm^2/sec, respectively. Calculate the average time that it would take for a molecule of glucose and a molecule of myoglobin to diffuse a distance of 20 mu, an approximate width for a mammalian cell.

Explanation / Answer

The average time that it takes for a molecule to travel x cm by diffusion in three dimensions is given by t = x2/6D, where t is time in seconds, and D is the diffusion coefficient, which is a constant that depends on the size and shape of a molecule

Diffusion coefficients of glucose = 5 X 10-6  cm2/sec

Diffusion coefficients of myoglobin = 5 X 10-7  cm2/sec   

Average time for glucose molecule to diffuse = 400/0.000005 = 8 X 107 ns

Average time for myoglobin to diffuse = 400/ 0.0000005 = 80 X 107 ns

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