The average time it takes for a molecule to diffuse a distance of x cm is given by t=x^2/2D where t is the time in seconds and D is the diffusion coefficient. Given that the diffusion coefficient of glucose is 5.7 x 10^-7 cm2/s, calculate the time it would take for a glucose molecule to diffuse 10 pm, which is roughly the size of a cell.

Question

Chemistry

Bambino

23 May, 04:18

The average time it takes for a molecule to diffuse a distance of x cm is given by t=x^2/2D where t is the time in seconds and D is the diffusion coefficient. Given that the diffusion coefficient of glucose is 5.7 x 10^-7 cm2/s, calculate the time it would take for a glucose molecule to diffuse 10 pm, which is roughly the size of a cell.

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Annabel · Answer 1

time to diffuse x cm is given by the relation

t = X² / 2D

D = 5.7 x 10⁻⁷

t = X² / 2 x 5.7 x 10⁻⁷ = X² x 10⁷ / 11.4 s

X = 10 pm = 10 x 10⁻¹² m = 10 x 10⁻¹⁰ cm = 10⁻⁹ cm

t = (10 ⁻⁹) ² x 10⁷ / 11.4 = 10⁻¹¹ / 11.4 = 8.77 x 10⁻¹³ s