Question

Droplets of two different dyes, ? and ?, are placed far apart in a container of some liquid. The dyes diffuse through the liquid (we can assume the diffusion is three-dimensional). The diffusion coefficient of dye ? is 4 times larger than the diffusion coefficient of dye ?. After both dyes are allowed to diffuse for an equal amount of time, how do the volumes of the liquid medium filled by each of the dyes, ?? and ?? respectively, compare?

a. ?? = 2??

b. ?? = 4??

c. ?? = 8??

d. ?? = 64??

e. None of the above

I know the answer is C but can you show the work please, thank you!

Answer 1

For a given diffusion coefficient D, the time taken to travel a distance r is given by

(The equation is emperical, and I am not sure about the actual value of constant k. But it doesnot matter . It is a unit less dimensionless number)

Gere, we have two liquids.

For liquid A,

For liquid B,

Taking the time for diffusion to be the same,

the ratio distance of diffusion is got by equating both the equations

The ratio of volumes is then given by

The diffusion constant of X is 4 times of Y

So,

Option C