Chemistry
Chemistry
Problem
For a sealed container of at 500 K, a Maxwell–Boltzmann plot shows that about 6 % of the molecules have kinetic energies greater than 100 kJ mol. The container is then heated, and the chemist finds that roughly 12 % of the molecules now exceed the same energy. Which new temperature is most likely to produce this result? (Assume ideal-gas behavior and no change in the number of molecules.) a) 550 K b) 525 K c) 650 K d) 485 KIntuitive explanation
The Maxwell–Boltzmann distribution describes how molecular kinetic energies spread out, and it shifts dramatically with temperature—higher pushes more molecules into the high-energy tail. You're using the fact that doubling the fraction of molecules above a fixed energy threshold tells you how much the distribution broadened, which is directly tied to the new temperature. The key is recognizing that the high-energy tail is exponentially sensitive to , so a modest temperature increase can roughly double the population in that region.
Intuitive explanation
The Maxwell–Boltzmann distribution describes how molecular kinetic energies spread out, and it shifts dramatically with temperature—higher pushes more molecules into the high-energy tail. You're using the fact that doubling the fraction of molecules above a fixed energy threshold tells you how much the distribution broadened, which is directly tied to the new temperature. The key is recognizing that the high-energy tail is exponentially sensitive to , so a modest temperature increase can roughly double the population in that region.