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.

There are two ways to solve this dilution problem; i.e., forward or backwards. Backwards first.

0.00421 x (1000/25) x (125/25) = ?

The forward way is this.
x*(25/125)*(25/1000) = 0.00421 and solve for x, the beginning concn.

To calculate the concentration of the original solution, we can use the concept of dilution.

Here's how you can find the concentration of the original solution:

1. Determine the moles of potassium nitrate (KNO3) in the final solution.
- Concentration (M) = moles (mol) / volume (L)
- Concentration (M) = 0.00421 M
- Volume (L) = 1.000 x 10^3 mL = 1.000 L

Therefore, the moles of KNO3 in the final solution can be calculated as:
Moles = Concentration x Volume = 0.00421 M x 1.000 L = 0.00421 mol

2. Since 25.00 mL of the final solution were diluted to 1.000 x 10^3 mL (or 1.000 L), the ratio of volumes can be used to find the moles in the 25.00 mL aliquot of the final solution.
- Volume of final solution = 1.000 x 10^3 mL = 1.000 L
- Volume of aliquot = 25.00 mL = 0.025 L

Therefore, the moles of KNO3 in the 25.00 mL aliquot can be calculated as:
Moles = Moles in final solution x (Alquot volume / Final solution volume) = 0.00421 mol x (0.025 L / 1.000 L) = 0.00010525 mol

3. Now we need to find the moles of KNO3 in the original solution.
Since 25.00 mL of the original solution were diluted to the final solution, the ratio of volumes can be used again.
- Volume of original solution = 25.00 mL = 0.025 L

Therefore, the moles of KNO3 in the original solution can be calculated as:
Moles = Moles in aliquot x (Original solution volume / Aliquot volume) = 0.00010525 mol x (0.025 L / 0.025 L) = 0.00010525 mol

4. Finally, we can find the concentration of the original solution by dividing the moles by the volume of the original solution.
Concentration (M) = moles (mol) / volume (L)
Concentration (M) = 0.00010525 mol / 0.025 L = 0.00421 M

Therefore, the concentration of the original solution is 0.00421 M, which is the same as the concentration of the final solution.