Henry's Law Soda Bottle Lab - 3D Kitchen Bench

Setting up the lab bench...

Presets

Live readouts

Graphs

Dissolved CO2 and its equilibrium value kH p

Headspace CO2 pressure (gauge)

Sealed bottle: equilibrium pressure against temperature (red = now)

Foam height and liquid lost to overflow

What is happening now

Starting.

Numerical checks

running...

How to use

Start with the chilled sealed bottle and watch the orange dots (dissolved CO2) and blue dots (gas above): they are in equilibrium, C = kH p. Then try: (1) drag Temperature up while the cap is on: kH falls, gas leaves the liquid and the gauge climbs (graph 3 shows how far); (2) press Shake while sealed: nothing changes in the end state, only the speed of exchange; (3) press Open cap: pressure collapses and the liquid is suddenly supersaturated; (4) shake first and then open to see a foam overflow, or drop in a mint for a geyser; (5) Seal cap again to trap what is left. Keys: O cap, S shake, Space pause, R reset.

The 3D page uses a Blender-built kitchen bench: a clear bottle with ribbed base, label and knurled cap, a steel tray, a pressure gauge, a thermometer and a dish of mints. Liquid height, foam, bubbles, molecules, the flying cap, the gauge needle and the thermometer column all come from the same model as the 2D lab. Drag to orbit, wheel to zoom.

The science

Gas solubility follows Henry's law: at equilibrium the concentration of dissolved gas is proportional to its partial pressure above the liquid.

C = k_H(T) · p k_H(T) = k_H° exp[ d (1/T − 1/298.15 K) ], k_H° = 0.034 mol/(L atm), d = 2400 K

The van 't Hoff factor makes CO2 less soluble when warm: k_H falls by about a third between 25 C and 35 C, which is why a warm bottle is more dangerous to open.

Sealed bottle. With n mol of CO2 split between liquid (volume V_l) and headspace (V_g), mass balance and the ideal gas law give the equilibrium in closed form:

x = k_H R T n / [V_g(1+β)], β = k_H R T V_l / V_g, p = (n − x V_l) R T / V_g

and after a disturbance the dissolved concentration relaxes exponentially, dC/dt = −k_La (C − k_H p), at rate k_La (1 + β). The page checks this against a numerical integration. Carbonation is given in "volumes": 1 volume = 1 L of CO2 (at 0 C, 1 atm) per litre of drink, so n = vol V_l / 22.414 L/mol.

Open bottle. The headspace vents through the neck, dn_g/dt = −κ (n_g − n_amb), so p drops to the 0.0004 atm of ambient air. The liquid is then supersaturated, S = C/(k_Hp) in the hundreds; gas leaves through the surface and, above all, as bubbles. Shaking and nucleation sites (a mint's rough surface) raise k_La by up to a factor 40 to 100. Bubble gas feeds a foam of volume n_bRT/P that decays with the lifetime τ; if it fills the bottle the excess leaves as overflow, carrying liquid with it (30% liquid fraction in the model).

pH. Dissolved CO2 forms carbonic acid, [H⁺] ≈ √(K_a1 k_H p) with K_a1 = 4.45×10⁻⁷: pH 3.9 at 1 atm.

Honest simplifications. One lumped liquid concentration (no gradients, no diffusion), a single mass-transfer coefficient, a linear neck-venting law instead of choked flow, no cooling from expansion, no sugar or salt effect on solubility, constant temperature within a run, a 30% liquid fraction in the foam and a cylindrical bottle. The headspace air is assumed at 1 atm, so the gauge reading equals the CO2 pressure. The 0 C solubility of the fitted law is 3.13 g/L against a tabulated 3.35 g/L (7% low). Real bottle pressures also depend on the fill and on the cap seal.