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The concentrations and orders of the reactants represent the reaction mechanism (how many molecules must collide for the reaction to proceed, which is more clear when we go into elementary reactions), whereas the rate constant k depends on the temperature and activation energy. The higher the value of k, the faster the rate of the reaction, so we can make the conclusion that higher temperatures and lower activation energies correspond with larger rate constants k. Hope this helps.
Something else to remember is that you can calculate k if the reaction rate, concentration of reactants, and the order of the reaction are known. Also, k is always positive and is the slope of the first order graph of ln[A] vs time.
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