Equation 2 · Lowering the Barrier: What a Catalyst Actually Does
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol k
k is part of the quantity the equation computes from the expression on the right.
Symbol A
A is one of the signed contributions combined to compute the quantity on the left.
Symbol E_mathrm a
athrm a occurs above the fraction bar. The numerator is divided by the entire denominator below it.
Symbol R
R occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
Symbol T
T occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
Denominator: RT
The complete quantity below the fraction bar; it must be nonzero for this division.
How to interpret it
With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.
What the article says around this equation
Arrhenius gave the empirical form. The rate constant depends on temperature as . where the exponential term is, to a good approximation, the fraction of molecular encounters carrying enough energy to clear the barrier, and the pre-exponential factor collects everything about how often encounters happen and how many of them are correctly oriented. The practical consequence of the exponential is severe. At around room temperature, lowering the activation energy by roughly six kilojoules per mole multiplies the rate by about a factor of ten. A catalyst that removes eighty kilojoules per mole from a barrier is not making the reaction somewhat faster; it is making it faster by…
Read the full surrounding passage
Arrhenius gave the empirical form. The rate constant depends on temperature as . where the exponential term is, to a good approximation, the fraction of molecular encounters carrying enough energy to clear the barrier, and the pre-exponential factor collects everything about how often encounters happen and how many of them are correctly oriented. The practical consequence of the exponential is severe. At around room temperature, lowering the activation energy by roughly six kilojoules per mole multiplies the rate by about a factor of ten. A catalyst that removes eighty kilojoules per mole from a barrier is not making the reaction somewhat faster; it is making it faster by a factor with thirteen or fourteen digits.
For background, read the article’s source list.
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