Fraction of Molecules Exceeding a Given Energy

The students in Chemistry 101A can determine graphically the fraction of molecules that exceed a given energy value, and they can use a simple theoretical computer program to determine exact values for comparison. The Basic computer program developed incorporates the function F₀(x) from quantum chemistry to determine 7-significant-figure results for student comparison. The usual integral formulation for the Maxwell-Boltzmann distribution is transformed into an expression that uses F₀(x) after several changes of variable. The ultimate integration is effected by two different methods that are used for different ranges of the variable E/RT. Downward recursion and a limiting functional form are used. A table of indicative student values is included for comparison with results generated by other workers. A short computer program in the Basic language is included for implementation and further development.