Chemical kinetics question?
in the arrhenius rate equation, why is 1/t a measure of the rate constant k?
Answer:
The average rate of a chemical reaction over a certain interval of time is equal to the change in concentration of a reactant or product that occurs during that time divided by the time.
Rate of reaction = delta Molarity / delta Time
Now, when comparing the rate of reactions, say at different concentrations, in a practical settings, one of the methods is to detect a fixed end-point (e.g. change in colour of a constant amount of indicator). Since the end-point is the same for all reaction mixtures, the change in concentration of reactants required to achieve that change in end point for all reactions is the same. Thus delta Molarity becomes constant.
Thus Rate of reaction = delta Molarity / delta Time
becomes Rate = constant.(1/delta t)
or: Rate is proportional to (1/t)
[assuming that delta t is t - t(initial) and t(initial) is 0]
Now, for the Arrhenius equation, the general form of a rate equation is:
Rate = rate constant*[concentration]^order
In Arrhenius rate equation experimentals, we only vary the temperature, and thus between one experiment and the next, the concentration is kept the same and, hopefully, so is the order (otherwise you don't get a straight line Arrhenius plot). However, the constant changes with temperature.
Thus [concentration]^order is now constant and
Rate is proportional to rate constant.
Since rate is proportional to (1/t), then (1/t) is also proportional to rate constant.
Hope this helps.
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