A 25.00 mL solution of potassium nitrate (KNO3) was diluted to 125.0 mL, and 25.00 mL of this solution were then diluted to 1.000 103 mL. The concentration of the final solution is 0.00421 M. Calculate the concentration of the original solution.

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To calculate the concentration of the original solution, we can use the concept of dilution. The concentration of a solution is given by the equation:

C1V1 = C2V2

where C1 and V1 are the concentration and volume of the initial solution, and C2 and V2 are the concentration and volume of the final solution.

Let's solve the equation step-by-step to find the concentration of the original solution.

Step 1: Use the given information to calculate the concentration and volume of the final solution.

C2 = 0.00421 M (given)
V2 = 1.000 x 10^3 mL (given)

Step 2: Use the dilution equation to calculate the concentration and volume of the intermediate solution.

C1V1 = C2V2

V1 = 25.00 mL (given)

C1 = (C2V2) / V1
= (0.00421 M)(1.000 x 10^3 mL) / 25.00 mL
= 0.1684 M

Thus, the concentration of the intermediate solution is 0.1684 M.

Step 3: Repeat Step 2 to calculate the concentration and volume of the original solution.

C1 = (C3V3) / V2

C3 = 0.1684 M (from Step 2)
V3 = 25.00 mL (given)

C1 = (0.1684 M)(25.00 mL) / 1.000 x 10^3 mL
= 0.00421 M

Therefore, the concentration of the original solution is 0.00421 M.