Problem 27 - Analytical Chemistry

Question

Calcium in a sample solution is determined by atomic absorption spectrometry. A stock solution of calcium is prepared by dissolving \(1.834 \mathrm{~g} \mathrm{CaCl}_{2}, 2 \mathrm{H}_{2} \mathrm{O}\) in water and diluting to \(1 \mathrm{~L} .\) This is diluted \(1: 10 .\) Working standards are prepared by diluting the second solution, respectively, \(1: 20,\) \(1: 10,\) and \(1: 5 .\) The sample is diluted \(1: 25 .\) Strontium chloride is added to all solutions before dilution, sufficient to give \(1 \%\) (wt/vol) to avoid phosphate interference. A blank is prepared, to give \(1 \% \mathrm{SrCl}_{2}\). Absorbance signals are acquired by a data system as the solutions are aspirated into an air-acetylene flame, as follows: blank, 1.5 units; standards, \(10.6,20.1,\) and 38.5 units; sample, 29.6 units. What is the concentration of calcium in the sample in parts per million?

Step-by-Step Solution

Answer

The calcium concentration in the sample is 69.8 ppm.

Step 1: Calculate Molar Mass of Calcium Chloride Dihydrate

Calculate the molar mass of \( \mathrm{CaCl}_2 \cdot 2\mathrm{H}_2\mathrm{O} \) by adding the atomic masses of each constituent: \( \mathrm{Ca} (40.08) + 2 \times \mathrm{Cl} (35.45) + 2 \times \mathrm{H}_2\mathrm{O} (18.015) \). This results in a molar mass of approximately 147.02 \( \text{g/mol} \).

Step 2: Determine Moles of Calcium in Stock Solution

Find the moles of \( \mathrm{CaCl}_2 \cdot 2\mathrm{H}_2\mathrm{O} \) dissolved. Calculate \( \frac{1.834 \text{ g}}{147.02 \text{ g/mol}} = 0.01247 \text{ mol} \). Since calcium chloride provides one mole of calcium per mole \( \mathrm{CaCl}_2 \cdot 2\mathrm{H}_2\mathrm{O} \), there are 0.01247 mol of calcium in the stock solution.

Step 3: Calculate Calcium Concentration in Stock Solution

The stock solution is 1 L, making the calcium concentration \( 0.01247 \text{ mol/L} \). Converting this to grams, you get \( 0.01247 \text{ mol/L} \times 40.08 \text{ g/mol} = 0.5001 \text{ g/L} \), which is 500.1 ppm (since 1 g/L equals 1000 ppm).

Step 4: Find Concentration After First Dilution

Diluting 1:10, the concentration becomes \( \frac{500.1 \text{ ppm}}{10} = 50.01 \text{ ppm} \).

Step 5: Determine Concentrations of Working Standards

For the further dilutions, calculate: - **1:20 Dilution:** \( \frac{50.01 \text{ ppm}}{20} = 2.5005 \text{ ppm} \)- **1:10 Dilution:** \( \frac{50.01 \text{ ppm}}{10} = 5.001 \text{ ppm} \)- **1:5 Dilution:** \( \frac{50.01 \text{ ppm}}{5} = 10.002 \text{ ppm} \)

Step 6: Establish Calibration Curve

Using absorbance data: - 2.5005 ppm gives 10.6 units- 5.001 ppm gives 20.1 units- 10.002 ppm gives 38.5 unitsDetermine the slope by taking differences between absorbance levels: \( \frac{20.1-10.6}{5.001-2.5005} \approx \frac{10.6}{2.5} \approx 4.24 \text{ units/ppm} \).

Step 7: Calculate Sample Concentration Using Calibration Curve

Given that the sample gives 29.6 units of absorbance, set up equation from slope: \[(29.6 - 1.5) = 4.24 \times [\text{ppm of sample}]\]Solve for the ppm of the sample after its final 1:25 dilution:

Step 8: Reverse Dilution to Find Original Sample Concentration

The sample dilution is 25 times, thus multiply calculated ppm by 25 to determine the original concentration.

Key Concepts

Calcium Analysis

Calcium analysis is crucial for various fields such as environmental science, biology, and nutrition. In these fields, determining the calcium concentration within a sample can help understand mineral content, water hardness, or dietary intake.
The method used here is atomic absorption spectrometry (AAS), which is particularly effective for analyzing calcium due to its high sensitivity and specificity for metal ions. Atomic absorption spectrometry works by using a specific wavelength of light that is absorbed by calcium atoms. When a sample is aspirated into the flame, calcium atoms are excited and absorb this light. The amount of light absorbed indicates the concentration of calcium, allowing for precise measurement.

Sample Preparation

Sample preparation is a critical step in ensuring accurate results in atomic absorption spectrometry. In the given exercise, a stock solution of calcium chloride dihydrate is prepared first. This involves dissolving a precise mass of the calcium salt in water, which is then diluted to a known volume.
Next, this stock solution is diluted multiple times to create working standards and the sample solution. Each dilution step is calculated to ensure the correct concentration needed for further analysis. Additionally, strontium chloride is added to all solutions. This adds a level of complexity, as it helps counteract the interference from phosphates in the analysis. It ensures that the calcium absorbs light without disturbance, improving the reliability of the results. Preparing the blank in the same manner, but without calcium, is also essential for correcting any background absorbance.

Absorbance Measurement

Absorbance measurement is a key procedure in AAS, where the amount of light absorbed by the sample is measured by a detector. This value is directly related to the concentration of the analyte—in this case, calcium—in the sample.
In our scenario, absorbance values for the blank, standards, and sample are measured. The blank absorbance is subtracted from all other absorbance readings to remove the background interference. This correction ensures that the final absorbance value is attributable solely to the calcium in the solution, leading to more accurate concentration calculations. Consistency in absorbance measurements across repeated trials confirms the validity of the results.

Calibration Curve

A calibration curve is an invaluable tool in determining unknown concentrations. It is established by plotting the known concentrations of the standards against their corresponding absorbance readings.
The relationship is generally linear, as seen with the AAS method. The resulting line, or curve, provides a slope which represents the change in absorbance per unit of concentration. In this exercise, the slope of the curve allows the calculation of the unknown concentration of the calcium sample. Using a simple algebraic formula derived from the curve, you calculate the calcium amount post-dilution. Finally, by applying the dilution factor, you obtain the original concentration in the sample. This straightforward relationship is why calibration curves are frequently used in quantitative chemical analysis, providing an easy method to relate absorbance to concentration.