Question

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.)

Short answer

To prepare the standard solutions of copper concentrations, use the dilution formula C1V1 = C2V2 and the given 1000.0-ppm Cu solution. For the 10.0, 25.0, 50.0, 75.0, and 100.0 ppm concentrations, measure 1.0 mL, 2.5 mL, 5.0 mL, 7.5 mL, and 10.0 mL (respectively) of the 1000.0-ppm Cu solution. Pour the measured solution into a volumetric flask, add distilled water until the total volume reaches 100.0 mL, and mix thoroughly.

Step-by-step solution

Define the given information and goal

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.

Calculate the volume needed for each concentration

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 = \( \frac{(100.0 ppm)(100.0 mL)}{1000.0 ppm} \)

Evaluate the volume needed for each concentration

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

Prepare the standard solutions

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.

Key concepts

Standard Solutions

Standard solutions are essential components in chemistry, particularly in spectroscopic analysis, as they are used to determine the concentration of unknown solutions. These solutions have a known concentration of a solute, which in this case is copper. By preparing these solutions with concentrations of 10.0, 25.0, 50.0, 75.0, and 100.0 ppm from a stock solution of 1000.0 ppm, we ensure accuracy in our calibration process.

To create these standard solutions, precise measurements are crucial. Here, the dilution process is employed, where a concentrated solution is used to make a less concentrated one by adding a solvent, often distilled water. The concentrations are carefully calculated and prepared to ensure they remain reliable and provide consistent results in any analysis. These solutions enable the generation of a calibration curve by offering a range of known concentrations to compare against unknown sample measurements.

Calibration Curve

The calibration curve is a fundamental tool in spectroscopic analysis, serving as a graphical representation that allows the determination of unknown concentrations within a sample. By using standard solutions with known concentrations, one can plot a curve based on the measured absorbance or intensity.

The process involves measuring the absorbance of the standard solutions at a particular wavelength using a spectrophotometer. The concentration (usually on the x-axis) is plotted against the absorbance (y-axis) to create the curve. The linear portion of this graph is then used to interpret unknown concentrations.

• Accurate standard solutions are crucial for the reliability of this curve.
• The calibration curve should ideally pass through the origin, indicating a direct proportionality between concentration and absorbance.
• It allows easy interpolation to find out the unknown concentrations by comparing their measurements against the slope of the calibration curve.

Dilution Formula

The dilution formula, expressed as \( C_1V_1 = C_2V_2 \), is a simple yet powerful equation used to determine the volume of a concentrated solution needed to prepare a diluted solution of desired concentration. Here, \( C_1 \) and \( V_1 \) are the concentration and volume of the initial solution, while \( C_2 \) and \( V_2 \) refer to the target concentration and volume of the new solution.

In this exercise, the dilution formula enables the production of standard solutions with specific concentrations from a 1000.0 ppm copper stock solution. For example, to make 100.0 mL of a 10.0 ppm copper solution, the necessary volume from the 1000.0 ppm solution is determined by solving \( V_1 = \frac{10.0 \, \text{ppm} \times 100.0 \, \text{mL}}{1000.0 \, \text{ppm}} \).

• This formula ensures precision as it directly relates volume and concentration.
• It allows scientists to prepare various concentrations efficiently and consistently.

Volumetric Flask

A volumetric flask is a piece of laboratory glassware crucial for making precise solutions, particularly useful in preparing standard solutions in spectroscopic analysis. This type of flask is designed to measure a specific volume with high accuracy, contributing to the consistency and reliability of experimental results.

When preparing a standard copper solution, the calculated volume from the stock solution is transferred into a volumetric flask. The flask is then filled with distilled water up to the calibration mark, ensuring an exact final volume, such as 100.0 mL. This step is vital as:

• Volumetric flasks provide precision in solution preparation, reducing potential errors in the concentration.
• They allow thorough mixing of solutes and solvents, ensuring a homogenous solution.
• The narrow neck of the flask helps in minimizing evaporation and deviations from the intended concentration.

Using volumetric flasks appropriately guarantees that the prepared solutions maintain their intended concentration for accurate analysis.