Question

why does diffusion happen faster in hot water, and slower in cold water?

Answer 1

Because temperature controls how fast molecules move and how much the liquid resists that motion.

Short version
- Higher temperature → molecules have more kinetic energy and move faster, so they spread out more quickly.
- In liquids hotter water is also less viscous (flows more easily), so solute molecules are less impeded and diffuse faster.
- Note: in real experiments you often also get convection (bulk currents from density/temperature differences), which can make mixing in hot water appear much faster than diffusion alone.

A bit more detail
- Molecular picture: temperature sets the average kinetic energy ≈ (3/2)kBT of molecules, so higher T means faster random (Brownian) motion and more frequent, more energetic collisions that drive spreading.
- For small particles in a liquid the Stokes–Einstein relation gives the diffusion coefficient
D = kB T / (6π η r)
where kB is Boltzmann’s constant, T temperature, η the fluid viscosity, and r the particle radius. D increases with T and decreases as viscosity η increases. Heating usually raises T and lowers η, so both effects raise D.
- For gases diffusion scales roughly with the average molecular speed (∝ √T) and the mean free path, so it also increases with T.

Practical note
If you put a drop of dye into hot versus cold water, the dye spreads faster partly because of faster molecular diffusion and often largely because of convection currents set up by temperature differences. To observe pure diffusion, avoid any stirring or temperature gradients.