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Unformatted text preview: Boltzmann distribution formula for calculating the relative populations (numbers of molecules in a state) of states of various energies N i /N j = e-(Ei-Ej)/kT k = 1.381 x 10-23 JK-1 R = N A k So for the Boltzmann distribution of molar gases: N i /N j = e-(Ei-Ej)/RT The higher the energy, the lower the population (only ground state has molecules at T = 0) The higher the temperature, the more likely it is that higher energy states are populated More levels significantly populated if close together in comparison with kT than if they are far apart Maxwell distribution fraction of molecules that have a particular speed V mean (T/M) 1/2 Average speed increases as the square root of temperature and decreases as the square root of molar mass Equipartition theorem alternative to Boltzmann to calculate the average energy associated with translational and rotational motion In a sample at temperature T, all quadratic contributions to the total energy have the same mean value, namely kT per molecule, or RT per mole...
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