Grade 12 Chemistry · Arrhenius and the hill
Over the hill
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Over the hill

Molecules collide constantly and mostly bounce. A reaction happens only when a collision arrives with enough energy to climb the activation energy — the hill between reactants and products. Arrhenius counts how many make it: k=AeEa/RTk = A\,e^{-E_a/RT}, read aloud k equals A e to the minus E-a over R T. kk is the rate constant you are usually after (per second, for a first-order reaction). AA is the pre-exponential factor, sometimes called the frequency factor: how often the attempt is even made, and it wears the same units as kk. EaE_a is the activation energy in joules per mole — the height of the hill. RR is the gas constant, 8.314 J/(molK)8.314\ \mathrm{J/(mol \cdot K)}, given on every exam paper. And TT is the absolute temperature, in kelvin.

Two rules, and they are the two marks this lesson is worth. Kelvin only. The exponent divides by TT, and Celsius has a zero in the wrong place — on this paper T(K)=t(C)+273T(\mathrm{K}) = t(^\circ\mathrm{C}) + 273. Put 27 where 300 belongs and your answer misses by dozens of orders of magnitude, which is the most spectacular way to lose two marks in all of chemistry. Joules only. Tables publish EaE_a in kJ/mol while RR speaks joules, so multiply by 1000 before the exponent, every single time.

And feel the shape of it: EaE_a sits in a negative exponent, so a taller hill means a smaller kk, and a hotter TT means a bigger one. That is why a fridge works.