Then calculate the inital ClO^- concencentrations for 1st, 2nd, and 3rd reactions.

Calculate [ClO^-] in a 6% bleach solution. A 6% bleach solution contains 6 grams of NaClO per 100 grams bleach. The density of 6% bleach is 1.07g/mL.

Chemical reaction: Blue dye + ClO^- -->oxidized dye +Cl^-

Reaction #1: 5.0 mL or diluted bleach solution, 15.0mL of distilled water, 10.0 mL of diluted blue dye
Reaction #2: 10.0mL of diluted bleach solution, 10.0mL distilled water, 10.0mL diluted blue dye
Reaction #3:20.0 mL diluted bleach, 10.0 mL of diluted blue dye, 0mL of distilled water

To calculate the initial concentration of ClO^- for each reaction, we need to determine the moles of NaClO in the given amount of bleach solution. Here's how we can calculate it:

1. Calculate the mass of NaClO in the bleach solution:
Mass of NaClO = (6% bleach solution) x (total mass of bleach solution)
Mass of NaClO = (6 grams NaClO / 100 grams bleach) x (100 grams bleach)
Mass of NaClO = 6 grams NaClO

2. Calculate the volume of the bleach solution:
Volume of bleach solution = (mass of bleach solution) / (density of bleach solution)
Volume of bleach solution = (100 grams bleach) / (1.07 grams/mL)
Volume of bleach solution = 93.458 mL

3. Calculate the concentration of NaClO in the bleach solution:
Concentration = (moles of NaClO) / (volume of bleach solution in liters)
Concentration = (mass of NaClO) / (molar mass of NaClO) / (volume of bleach solution in mL) / (1000 mL/L)
Concentration = (6 grams NaClO) / (74.44 g/mol NaClO) / (93.458 mL) / (1000 mL/L)
Concentration = 0.0010 M

Now we have the initial concentration of ClO^- in the bleach solution, which is 0.0010 M. We can use this concentration for all three reactions as the initial concentration of ClO^- remains the same regardless of the reaction being carried out.