Catalysts do not shift the Boltzmann distribution at constant temperature

Steps:

• The Boltzmann distribution plots the fraction of molecules with a given energy at a fixed temperature.
• Room temperature is maintained, so the distribution shape and peak remain unchanged.
• A catalyst like MnO₂ lowers the activation energy for H₂O₂ decomposition but does not affect molecular energies or temperature.
• Thus, the energy distribution diagram stays identical to the uncatalyzed case.

Why B is correct:

• B shows the standard Boltzmann curve for room temperature, unchanged by the catalyst, per the Maxwell-Boltzmann distribution formula $f(E) = \frac{2\pi}{kT}^{3/2} E^{1/2} e^{-E/kT}$, which depends only on T.

Why the others are wrong:

• A: Depicts a shifted curve, implying lower temperature, which contradicts constant room temperature.
• C: Shows a broader or higher-energy distribution, suggesting increased temperature.
• D: Illustrates a altered shape, like bimodal peaks, unrelated to catalysis effects.

Final answer: B