Question

If the diffusion coefficient doubles, and the average diffusion distance across a membrane remains the same, what can be said about the time it takes to cross the membrane g

Answer 1

Answer:

time taken will be halved

Explanation:

we have

$t=\frac{x^{2}}{2D}$   ..................(1)

where

t = time elapsed since diffusion began

$x^{2}$ = mean distance traveled by the diffusion solute

D = Diffusion coefficient

now, according to the conditions given in the question

when, diffusion coefficient (D) doubles i.e D' = 2D

Average diffusion distance remains same i.e $x' = x$

substituting the values in the equation we get

$t=\frac{x'^{2}}{2D'}$

or

$t=\frac{x^{2}}{2(2D)}$

or

$t=\frac{x^{2}}{4D}$ ...............(2)

hence, on comparing equation (1) and (2) we can say that the time taken will be halved when the diffusion coefficient doubles and the mean distance traveled remains the same