QUANTITATIVE CHEMISTRY / INTERACTIVE MODELS

Diffusion and pH: interactive models

Explore two quantitative relationships: the dependence of diffusion time on distance and the relation between pH and hydrogen-ion activity.

DISTANCE × DIFFUSION

Diffusion time and length scale.

For a fixed diffusion coefficient, a characteristic diffusion time grows with the square of the distance. Halve the distance and the time becomes one quarter.

Distance 100 μmExample diffusion coefficient

CHARACTERISTIC TIME5.00 s

At 100 μm and D = 1 × 10⁻⁹ m²/s.

The model: t ≈ L² / (2D), using one-dimensional mean-square diffusion. This characteristic timescale is not a guaranteed complete-mixing time. The example D values are illustrative; real diffusivity depends on the molecule and medium. Flow, geometry, surfaces and temperature can change the practical result.

Read the microfluidics explainer ↗

PH × POWERS OF TEN

Hydrogen-ion activity ratios.

Compare hydrogen-ion activity at two pH values. A lower pH means greater hydrogen-ion activity.

First pH

Second pH

ACTIVITY RATIO / FIRST ÷ SECOND1,000×

Hydrogen-ion activity at pH 4 is 1,000 times that at pH 7.

The model: activity ratio = 10^{(second pH − first pH)}. This comparison does not measure total acidity, buffering capacity or safety. The 0–14 input range is a teaching choice, not an absolute limit of pH.

Get to know the pH scale ↗