In 1885 J. J. Hood published a paper

*On the Influence of Heat on the Rate of Chemical Change*in Philosophical Magazine in which he gave the empirical fit by an exponential function for some data on the reaction rate for the oxidation of ferrous sulfate (FeSO

_{4}) by potassic chlorate (KClO

_{3}) at various temperatures. The justification for the use of an exponential function is that the data appears to be almost linear in a semi-log plot.

Later in 1889 Svante Arrhenius published

*Über die Reaktionsgeschwindigkeit bei der Inversion of Rohrzucker durch Säuren*(

*On the Reaction Rate in the Inversion of Cane Sugar by Acids*) in Zeitschrift für Physicalische Chemie which gave a better fit for Hood's data based on some thermodynamics considerations. In the table on the page of the link "beob." is the observed rate of the reaction, "ber.

_{1}" is the calculated rate using formula (1) in the paper and "ber.

_{2}" gives the calculated rates for Hood's empirical formula for comparison.

Formula (1) in this paper is equivalent to the statement that the reaction rate ρ divided by e

^{-A/T}is equal to a constant which is essentially the Arrhenius equation. This is the exponential that is found in Schrödinger's equation for the 'time of expectation'. The Arrhenius constant A is now written as activation energy divided by the gas constant R, the constant from the ideal gas law, PV = nRT. The k in Schrödinger's equation is the corresponding constant for a molecule. His 'time of expectation' is inversely proportional to the reaction rate.

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