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

time taken will be halved

Step-by-step explanation:

we have

`t=(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=(x'^(2))/(2D')`

or

`t=(x^(2))/(2(2D))`

or

`t=(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