Step 1: Core idea using an energy profile.
Draw the potential-energy versus reaction-progress curve. The reactants must climb an energy barrier (activation energy) to reach the transition state. A catalyst offers a different, lower hill to climb.
Step 2: Effect on rate.
Because the barrier is smaller, at the same temperature a larger fraction of molecules possesses the required threshold energy (seen from the Maxwell distribution). More successful collisions per second means a faster rate.
Step 3: Symmetry of the effect.
The same lowered peak is shared by the reverse process, so the reverse rate is boosted too. Consequently the ratio of forward to backward rate constants, and therefore \( K_{eq} \), stays the same.
Step 4: What stays unchanged.
A catalyst does not supply energy, does not shift equilibrium, and does not alter the overall energy released or absorbed. It merely shortens the time needed to reach equilibrium.
Conclusion: The catalyst raises the reaction rate by cutting the activation energy while leaving the thermodynamics untouched.