Q.Explain, in terms of activation energy, how a catalyst increases the rate of a reaction without itself being permanently consumed.

[!TLDR] A catalyst opens an alternate pathway with a lower activation energy, so more molecules can react at the same temperature. [!ANSWER] A catalyst provides a different reaction pathway (via a different activated complex) with a lower activation energy than the uncatalyzed route, so a larger fraction of molecules can cross the (now lower) energy barrier at the same temperature, increasing the rate without the catalyst itself being consumed.

A catalyst does not supply energy to the reacting molecules or change the reactants'/products' own energy levels; instead, it offers the reaction an entirely different mechanistic route -- typically by temporarily bonding to, or otherwise interacting with, the reactants -- whose activated complex sits at a LOWER potential energy than the activated complex of the original, uncatalyzed pathway. Since the fraction of molecules with energy sufficient to cross a barrier grows exponentially as that barrier is lowered (the Boltzmann factor, $e^{-E_a/RT}$), even a modest reduction in $E_a$ produces a large increase in the number of successful, product-forming collisions per second at the same temperature. The catalyst itself is regenerated at the end of the catalytic cycle, unchanged in identity and amount, so it does not appear in the overall balanced equation and is not consumed by the reaction, even though it is essential to how fast the reaction proceeds. [!ANSWER] By opening an alternative pathway with a lower activation energy, a catalyst lets a larger fraction of reactant molecules react at a given temperature, speeding the reaction while being regenerated, unchanged, at the end.

Explain that a catalyst lowers $E_a$ via an alternate mechanism/pathway, and connect a lower $E_a$ to a larger reacting fraction of molecules via the exponential Boltzmann factor.

A common vague answer says only 'it speeds up the reaction' without explaining the activation-energy mechanism, or incorrectly suggests the catalyst is consumed or permanently altered.