I have two identical glass beakers, X and Y, full of water. I introduce a

concentrated drop of ink into each beaker. I stir beaker Y until the ink

concentration is uniform. What can you say about the diffusive motion of the

ink molecule?

The molecule diffuses with the same diffusion coefficient in both X

and Y.

The molecule diffuses in X but not in Y.

The molecule diffuses in Y but not in X.The molecule diffuses at the site of the original droplet but not close to

the boundary.

The correct answer is: The molecule diffuses with the same diffusion coefficient in both X and Y. Diffusion coefficient, a material property depending on temperature, solvent, and molecule size, remains unchanged regardless of stirring, as it quantifies random molecular motion driven by concentration gradients.

Diffusion Basics

Ink molecules in beaker X spread slowly via natural diffusion from high to low concentration areas without stirring. In beaker Y, stirring achieves uniform concentration instantly through convection, masking ongoing diffusion. However, the intrinsic diffusion coefficient stays identical in both, as stirring does not alter molecular-scale properties like viscosity or temperature.

Option Explanations

• The molecule diffuses with the same diffusion coefficient in both X and Y: Correct. Diffusion coefficient $D$ follows Fick’s laws, independent of macroscopic mixing; it’s the same in identical conditions.

• The molecule diffuses in X but not in Y: Incorrect. Stirring eliminates gradients in Y, stopping net diffusion observation, but random molecular motion persists.

• The molecule diffuses in Y but not in X: Incorrect. Unstirred X shows clear diffusion; Y’s uniformity hides it, but diffusion continues.

• The molecule diffuses at the site of the original droplet but not close to the boundary: Incorrect. Diffusion occurs everywhere based on local gradients, not fixed to the drop site.