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 \(100.0 \mathrm{~mL}\). (See Exercise 113 for definitions.)

Short answer

To prepare the standard solutions from a 1000.0 ppm stock solution, use the dilution formula: 1. For a 10.0 ppm solution, take 1.0 mL of the stock solution and dilute to a final volume of 100.0 mL with the solvent. 2. For a 25.0 ppm solution, take 2.5 mL of the stock solution and dilute to a final volume of 100.0 mL with the solvent. 3. For a 50.0 ppm solution, take 5.0 mL of the stock solution and dilute to a final volume of 100.0 mL with the solvent. 4. For a 75.0 ppm solution, take 7.5 mL of the stock solution and dilute to a final volume of 100.0 mL with the solvent. 5. For a 100.0 ppm solution, take 10.0 mL of the stock solution and dilute to a final volume of 100.0 mL with the solvent.

Step-by-step solution

Solution 1: Preparing 10.0 ppm Solution

To prepare a 10.0 ppm solution, we have: C1 = 1000.0 ppm (stock concentration) C2 = 10.0 ppm (desired concentration) V2= 100.0 mL (final volume) Calculate V1: \(V1 = \frac{C2 \times V2}{C1}\) \(V1 = \frac{10 \times 100}{1000}\) \(V1 = 1 \text{ mL}\) To prepare a 10.0 ppm solution, take 1 mL of the 1000.0 ppm stock solution and dilute it to a final volume of 100.0 mL with the solvent (usually water).

Solution 2: Preparing 25.0 ppm Solution

Next, we will calculate the volume needed to prepare the 25.0 ppm solution: C2 = 25.0 ppm (desired concentration) Calculate V1: \(V1 = \frac{C2 \times V2}{C1}\) \(V1 = \frac{25 \times 100}{1000}\) \(V1 = 2.5 \text{ mL}\) To prepare a 25.0 ppm solution, take 2.5 mL of the 1000.0 ppm stock solution and dilute it to a final volume of 100.0 mL with the solvent.

Solution 3: Preparing 50.0 ppm Solution

Next, we will calculate the volume needed to prepare the 50.0 ppm solution: C2 = 50.0 ppm (desired concentration) Calculate V1: \(V1 = \frac{C2 \times V2}{C1}\) \(V1 = \frac{50 \times 100}{1000}\) \(V1 = 5.0 \text{ mL}\) To prepare a 50.0 ppm solution, take 5.0 mL of the 1000.0 ppm stock solution and dilute it to a final volume of 100.0 mL with the solvent.

Solution 4: Preparing 75.0 ppm Solution

Next, we will calculate the volume needed to prepare the 75.0 ppm solution: C2 = 75.0 ppm (desired concentration) Calculate V1: \(V1 = \frac{C2 \times V2}{C1}\) \(V1 = \frac{75 \times 100}{1000}\) \(V1 = 7.5 \text{ mL}\) To prepare a 75.0 ppm solution, take 7.5 mL of the 1000.0 ppm stock solution and dilute it to a final volume of 100.0 mL with the solvent.

Solution 5: Preparing 100.0 ppm Solution

Finally, we will calculate the volume needed to prepare the 100.0 ppm solution: C2 = 100.0 ppm (desired concentration) Calculate V1: \(V1 = \frac{C2 \times V2}{C1}\) \(V1 = \frac{100 \times 100}{1000}\) \(V1 = 10.0 \text{ mL}\) To prepare a 100.0 ppm solution, take 10.0 mL of the 1000.0 ppm stock solution and dilute it to a final volume of 100.0 mL with the solvent. Now we have obtained the volumes of the stock solution needed to prepare the standard solutions containing 10.0 ppm, 25.0 ppm, 50.0 ppm, 75.0 ppm, and 100.0 ppm of copper from the 1000.0 ppm stock solution.

Key concepts

Spectroscopic Analysis

Spectroscopic analysis is a method used to determine the composition of a substance by measuring the amount of light that it absorbs or emits. This technique is grounded in the principle that each element can absorb or emit light at specific wavelengths, which are considered its unique spectral fingerprint.

When conducting a spectroscopic analysis, a sample is illuminated with light and the unique pattern of absorption or emission is recorded. By comparing this pattern to known standards, the concentration of different elements within the sample can be determined. Spectroscopic methods are widely used across various industries, including environmental monitoring, pharmaceuticals, and food safety, due to their sensitivity and specificity.

Preparing accurate standard solutions, as per the exercise described, is critical for ensuring the reliability of the spectroscopic measurements. The reason is that variations in concentration can significantly affect the absorption and emission readings, leading to erroneous conclusions about the presence and concentration of substances within a sample.

Calibration Curve

A calibration curve is an instrumental tool in the analysis of substances, serving as a reference for determining unknown concentrations within a sample. It plots known concentrations of a substance (often from standard solutions) on the x-axis against the measured instrument response (such as absorbance or intensity) on the y-axis.

The creation of a calibration curve involves measuring the spectroscopic response of multiple standard solutions with known concentrations like those prepared in the exercise above. By plotting these known values, a line or curve of best fit can be drawn. Ideally, this curve should be linear, meaning the instrument response is directly proportional to the concentration, although non-linear relationships can also be calibrated mathematically.

To analyze an unknown sample, its instrument response is measured and then compared to the calibration curve to ascertain its concentration. The accuracy of a spectroscopic analysis thus heavily relies on the precision of the standard solutions and the calibration curve derived from them.

Solution Concentration

Solution concentration is the measure of the amount of solute present in a given quantity of solvent. It is expressed in various units such as parts per million (ppm), molarity, or weight/volume percentage. Understanding and accurately preparing solutions with specific concentrations, like in the textbook exercise, is fundamental to many scientific procedures including laboratory experiments and industrial processes.

In the context of the exercise, the concentration of the copper standard solutions was expressed in ppm, which is a common unit in spectroscopy for very dilute solutions. The ppm unit is akin to saying 'out of a million parts, this many parts are solute.' For example, a 10.0 ppm solution means that for every million parts of the solution, 10 parts are copper.

Preparing solutions of precise concentrations requires thorough methodology, mindful of potential dilution and contamination errors. By using a stock solution with a known higher concentration, as in the exercise steps, you can create more dilute solutions through accurate measurement and appropriate scaling. This process, called serial dilution, is used to create a range of standard solutions with different but known concentrations, essential for plotting a calibration curve in spectroscopic analysis.