The diffusion constant for glucose in water is 5 x 10 ^-10 m^2/s. An aquatic cel

Question

The diffusion constant for glucose in water is 5 x 10 ^-10 m^2/s. An aquatic cell is roughly spherical wth a radius of 20 microns and a permeable membrane of just 2 microns thick. The cell contains 3.2 million glucose molecules and is surrounded outside by a extracellular fluid woth a 1 micromolar (i.e. 10^-6 moles per liter) consentration of glucose. Which direction will the glucose flow: into the cell or out from the cell why? [distance squared =Square root (2 x Diffusion constant x Time)]

(p.s. This is all the information given. I am beyond confused. I assume that I need to compare consentrations on either side of the membrane but I am not sure how else to proceed)

Explanation / Answer

Inside of the cell has 3.2 million glucose molecule .

This means 3.2 x 106 molecules are present .

Now , to calculate the concentration in molecules per litre ( because we have to compare to the outside of the cell ) , we will have to calculate the volume of the cell .

Volume of a sphere is -

V= 4/3 x 3.14 x (20 x 10-6)3

= 4.1 x 8 x 10 -15

= 32.8 x 10-15 m 3

Now , 1000 litres are equal to 1 m 3 ,

Therefore , V= 32.8 x 10 -12 L .

Therefore concentration of glucose molecule inside the cell is

3.2 x 106 / 32.8 x 10 -12

= 105 ( approx ) / L

outside the concentration is 10-6 moles pper litre

one mole is 6.02 x 10 23 , which means there are 6.02 x 1018 molecules per litre .

it is very clear that the concentration outside the cell is much more than the inside.

Therefore , the milecules will move from outsooutsode to inside .

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