Question

How does the time it takes to diffuse a certain distance change as the radius of the particle increases?

Answer 1

Diffusion time of the particle will definetely depends upon the particle radius

Diffusiion over a distance can be expressed as

x2 = qiDt

where X is the mean displacement of the particle

qi is the numerical constant

D is the diffusion coefficient

t is the time taken by the particle to diffuse the x displacement

if the mean displacement is contant then,

Diffusion coefficient(D) is inversly proportional to the time(t)

Diffusion coefficent depends upon the frictional force of the particle

D = (1/f)kT

f is the frictioanal force and k, T, - Boltzman constant, absolute temperature

frictional force f = f = 6pi *n*r

where n is the viscosity and r is the radius of the particle,

as the radius of the particle increases, the frictional force increases.When the frictional force increases the Diffusion coefficient (D) decreases.

Diffusion coefficient(D) is inversly proportional to the time(t)

So, the diffuison time will increases

Conclusion

diffusion time will increases with increase in the size of the particle