Question

Water is added to \(25.0 \mathrm{~mL}\) of a \(0.866 \mathrm{M} \mathrm{KNO}_{3}\) solution until the volume of the solution is exactly \(500 \mathrm{~mL}\). What is the concentration of the final solution?

Short answer

The concentration of the final solution is \(0.0433 \mathrm{M}\).

Step-by-step solution

Determine Given Values

Identify the known values given in the exercise. The initial volume (V1) is \(25.0 \mathrm{~mL}\), the initial molarity (M1) is \(0.866 \mathrm{M}\), and the final volume (V2) is \(500 \mathrm{~mL}\). The final molarity (M2) is what we are trying to find.

Convert volumes to same units

Here the volumes are already in the same units (\(mL\)), so no conversion is necessary.

Apply the Dilution Formula

Use the dilution formula \(M1V1 = M2V2\) to solve for the final molarity (M2). Substituting the numbers from step 1 gives us \(0.866 \mathrm{M} * 25.0 \mathrm{~mL} = M2 * 500 \mathrm{~mL}\).

Calculate the Final Molarity

Solving the equation from Step 3 for M2 gives us \(M2 = (0.866 \mathrm{M} * 25.0 \mathrm{~mL}) / 500 \mathrm{~mL}\). This simplifies to \(M2 = 0.0433 \mathrm{M}\). Therefore, the final concentration of the solution is \(0.0433 \mathrm{M}\).