Chemistry:
The persulfate - iodide reaction was run in the presence of a delayed indicator solution of sodium thiosulfate (Na2S2O3). The reaction of S2O82- with I- produces I2. As we see in the second reaction, the I2 is rapidly reduced to I- by S2O32-. When all the thiosulfate solution was consumed, there was an excess of I2 and the blue starch-I2 complex formed ,and you observed the formation of a blue solution.
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The time it take for the solution in the mixing beaker to turn blue is a measure of the rate of reaction.