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 mL. (See Exercise 135 for definitions.)

The given information includes: - A commercially produced 1000.0-ppm Cu solution - Desired concentrations: 10.0, 25.0, 50.0, 75.0, and 100.0 ppm - Final volume for each solution: 100.0 mL Our goal is to determine the amount of the 1000.0-ppm Cu solution needed to create standard solutions with the given desired concentrations.

To achieve the desired concentrations, we can use the dilution formula: C1V1 = C2V2, where C1 and V1 are the initial concentration and volume of the commercially produced 1000.0-ppm Cu solution and C2 and V2 are the final concentration and volume of each standard solution. We will need to solve for V1 in each case. For 10.0 ppm concentration: (1000.0 ppm)(V1) = (10.0 ppm)(100.0 mL) V1 = \( \frac{(10.0 ppm)(100.0 mL)}{1000.0 ppm} \) For 25.0 ppm concentration: (1000.0 ppm)(V1) = (25.0 ppm)(100.0 mL) V1 = \( \frac{(25.0 ppm)(100.0 mL)}{1000.0 ppm} \) For 50.0 ppm concentration: (1000.0 ppm)(V1) = (50.0 ppm)(100.0 mL) V1 = \( \frac{(50.0 ppm)(100.0 mL)}{1000.0 ppm} \) For 75.0 ppm concentration: (1000.0 ppm)(V1) = (75.0 ppm)(100.0 mL) V1 = \( \frac{(75.0 ppm)(100.0 mL)}{1000.0 ppm} \) For 100.0 ppm concentration: (1000.0 ppm)(V1) = (100.0 ppm)(100.0 mL) V1 = \( \frac{(100.0 ppm)(100.0 mL)}{1000.0 ppm} \)

Now let's calculate the value of V1 for each concentration: For 10.0 ppm concentration: V1 = \( \frac{(10.0 ppm)(100.0 mL)}{1000.0 ppm} \) = 1.0 mL For 25.0 ppm concentration: V1 = \( \frac{(25.0 ppm)(100.0 mL)}{1000.0 ppm} \) = 2.5 mL For 50.0 ppm concentration: V1 = \( \frac{(50.0 ppm)(100.0 mL)}{1000.0 ppm} \) = 5.0 mL For 75.0 ppm concentration: V1 = \( \frac{(75.0 ppm)(100.0 mL)}{1000.0 ppm} \) = 7.5 mL For 100.0 ppm concentration: V1 = \( \frac{(100.0 ppm)(100.0 mL)}{1000.0 ppm} \) = 10.0 mL

To prepare the standard solutions, follow these steps for each desired concentration: 1. Measure the calculated volume (V1) of the 1000.0-ppm Cu solution using a pipette. 2. Pour the measured solution into a volumetric flask. 3. Add distilled water to the volumetric flask until the total volume reaches 100.0 mL. 4. Mix the solution thoroughly to ensure a homogenous distribution of copper ions.