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Transcript
statistical physics → reaction kinetics FFF Dissociation of a Diatomic Gas Let us consider the following simple model for a diatomic gas: a diatomic molecule consists of a pair of point-like atoms, each of mass m, separated by a rigid rod of length a. The rigid rod corresponds to the chemical bond, which requires an energy to break. Now, at any finite temperature T , we know that some fraction of these diatomic molecules will actually break apart. Consider the reaction where one diatomic molecule breaks up into 2 monoatomic molecules. As usual, we can determine the equilibrium state of this system by comparing chemical potentials of the reactants. Let n0 be the number density of diatomic atoms, at T = 0. (a) Treating the diatomic molecule as a classical object, compute the chemical potential of both the diatomic molecules, and the monoatomic molecules. (b) Determine the fraction α of diatomic molecules which will be disassociated in chemical equilibrium. (c) For diatomic hydrogen, we have m ≈ 10−27 kg and a ≈ 10−10 m. At room temperature of T ≈ 300 K, what is the fraction of hydrogen molecules which we expect to disassociate? Verify that this effect is negligible.
