If k only depends on temperature, what about the other factors that affect the rate of the reaction? (concentration, type of rxn, phase, catalysyts, etc)

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Wikipedia states:      In this equation k(T) is the reaction rate coefficient or rate constant, although it is not really a constant, because it includes all the parameters that affect reaction rate, except for concentration, which is explicitly taken into account. Of all the parameters described before, temperature is normally the most important one.