In an experiment dealing with dissolving and alka seltzer tablet into water, is the rate in which the reaction is occurring the dependent variable?

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It should be, in an experiment the dependent variable is the one that is caused by the "independent variable." The independent variable is likely time (the passage of time caused the rate to change) or # of tablets (more tablets made for a faster rate of bubbles given off) or temperature (higher temperature sped up the rate of dissolving).  Without knowing a bit more about your experiment, I can't be absolutely sure, but unless it's a very unusual experiment, the rate should be the dependent variable