In the spectroscopic analysis of many substances, a series of standard solutions of known concentration are measured to generate a calibration curve. How would you prepare standard solutions containing \(10.0,25.0,50.0,75.0,\) and \(100 .\) ppm of copper from a commercially produced 1000.0 -ppm solution? Assume each solution has a final volume of \(100.0 \mathrm{mL}\). (See Exercise 123 for definitions.)

To prepare a 10 ppm copper solution, we can use the dilution formula: \(C_1V_1 = C_2V_2\) \(1000 \text{ ppm} \times V_1 = 10 \text{ ppm} \times 100 \text{ mL}\) Now, to solve for the volume, \(V_1\), required from the 1000 ppm solution: \(V_1 = \frac{10 \text{ ppm} \times 100 \text{ mL}}{1000 \text{ ppm}} = 1 \text{ mL}\) Hence, to prepare a 10 ppm copper solution with a volume of 100 mL, 1 mL of the 1000 ppm copper solution is needed.

Using the same formula used above, we can easily calculate the necessary volumes for the other desired concentrations: For 25 ppm (\(C_2\)): \(V_1 = \frac{25 \text{ ppm} \times 100 \text{ mL}}{1000 \text{ ppm}} = 2.5 \text{ mL}\) For 50 ppm (\(C_2\)): \(V_1 = \frac{50 \text{ ppm} \times 100 \text{ mL}}{1000 \text{ ppm}} = 5 \text{ mL}\) For 75 ppm (\(C_2\)): \(V_1 = \frac{75 \text{ ppm} \times 100 \text{ mL}}{1000 \text{ ppm}} = 7.5 \text{ mL}\) For 100 ppm (\(C_2\)): \(V_1 = \frac{100 \text{ ppm} \times 100 \text{ mL}}{1000 \text{ ppm}} = 10 \text{ mL}\) To prepare the standard solutions, we will need to add the calculated volume of the 1000 ppm solution to the proper amount of solvent (usually water) to achieve a final volume of 100 mL.

To prepare each of the standard solutions listed above, follow the steps below: 1. Measure the calculated volume of the 1000 ppm copper solution. 2. Add this volume to an appropriately sized volumetric flask. 3. Add solvent (usually water) to the flask until the final volume of the solution reaches the 100 mL mark. 4. Mix the solution thoroughly. By following these steps for each of the desired concentrations (10 ppm, 25 ppm, 50 ppm, 75 ppm, and 100 ppm), you will have made the necessary calibration standards for spectroscopic analysis.