Chemistry
Chemistry
Problem
For an elementary gas-phase reaction, the fraction of collisions with sufficient energy is 2.0 % at 298 K and 3.6 % at 308 K. All other factors (collision frequency and orientation probability) remain unchanged. By what factor does the initial reaction rate at 308 K exceed that at 298 K? a) b) c) d)Intuitive explanation
The key insight is that the fraction of collisions with sufficient energy depends on the activation energy barrier through the Boltzmann distribution. Since collision frequency and orientation stay constant, the rate ratio depends only on how the fraction of energetic collisions changes with temperature. Use the ratio of these fractions directly—they already encode the temperature dependence of the exponential factor that controls reaction rates.
Intuitive explanation
The key insight is that the fraction of collisions with sufficient energy depends on the activation energy barrier through the Boltzmann distribution. Since collision frequency and orientation stay constant, the rate ratio depends only on how the fraction of energetic collisions changes with temperature. Use the ratio of these fractions directly—they already encode the temperature dependence of the exponential factor that controls reaction rates.