Titrate it.
Drag a burette and watch a real titration curve redraw, shift the Haber equilibrium and reshape a Maxwell-Boltzmann distribution — every number computed properly, not sketched.
The burette, on a slider
FIG. 01 · ACIDS & BASES · 3.1.12.5Ethanoic acid is 4.76. Only bites when the flask holds a weak acid.
Why it is marked: the pH is solved from the full charge-balance equation, so every part of the curve is real — the buffer plateau, the half-equivalence point where pH = pKa, and the near-vertical jump. An indicator only works if its whole colour-change range sits inside that vertical section, which is exactly why phenolphthalein passes a weak-acid / strong-base titration and methyl orange does not.
Push the equilibrium
FIG. 02 · EQUILIBRIA · 3.1.6.1N₂(g) + 3H₂(g) ⇌ 2NH₃(g) ΔH = −92 kJ mol⁻¹ · 1:3 feed, ideal-gas model
Forward reaction is exothermic, so heating shifts it back — and cuts the yield.
4 mol of gas become 2, so squeezing pushes the equilibrium to the right.
Watch the yield when you add it. Then read the note.
Live mole fractions of the mixture at equilibrium.
Why it is marked: Kp changes with temperature only — raise the pressure and the number in the readout does not move, but the position of equilibrium does, because the mole fractions rearrange to keep Kp constant. The catalyst changes neither. That is the whole three-mark answer, and it is why industry settles on a compromise near 450 °C and 200 atm: a colder reactor would yield more but take far too long.
The tail that does the work
FIG. 03 · KINETICS · 3.1.5.2The dashed curve stays at 500 K so you can see the shift. Same area under both — the molecules do not go anywhere, they just redistribute.
A catalyst does not move the curve. It moves the line — an alternative route with a lower activation energy.
Why it is marked: a 10 °C rise barely moves the peak, yet it can roughly double the rate — because the rate depends on the fraction of molecules in the tail beyond Ea, and that fraction is exponential in −Ea/RT. Examiners want the shaded-area language: more molecules with energy greater than or equal to the activation energy, so more collisions are successful per second.