Problem 17 - Analytical Chemistry

Question

Calcium in powdered milk is determined by dry ashing (see Chapter 1 ) a \(1.50-\mathrm{g}\) sample and then titrating the calcium with EDTA solution, 12.1 mL being required. The EDTA was standardized by titrating \(10.0 \mathrm{~mL}\) of a zinc solution prepared by dissolving \(0.632 \mathrm{~g}\) zinc metal in acid and diluting to \(1 \mathrm{~L}(10.8 \mathrm{~mL}\) EDTA required for titration). What is the concentration of calcium in the powdered milk in parts per million?

Step-by-Step Solution

Answer

The concentration of calcium in the powdered milk is approximately 288,667 ppm.

Step 1: Calculate Moles of Zinc

First, we need to find the moles of zinc in the standard solution. Zinc has a molar mass of approximately 65.38 g/mol. So, the moles of zinc in the solution can be calculated using the formula: \[ \text{moles of Zn} = \frac{0.632 \text{ g}}{65.38 \text{ g/mol}} \] This calculation gives: \[ \text{moles of Zn} = 0.00967 \text{ mol} \]

Step 2: Determine Concentration of EDTA

Using the amount of EDTA required to titrate the zinc solution, we determine the molarity of the EDTA solution. Since 10.8 mL is needed for 0.00967 mol of Zn, the concentration of EDTA is: \[ \text{molarity of EDTA} = \frac{0.00967 \text{ mol}}{0.0108 \text{ L}} \] This results in: \[ \text{molarity of EDTA} = 0.895 \text{ M} \]

Step 3: Calculate Moles of Calcium

Now, calculate the moles of calcium using the EDTA titration data from the milk sample. With 12.1 mL of EDTA required: \[ \text{moles of Ca}^{2+} = 0.895 \text{ M} \times 0.0121 \text{ L} \] The moles of calcium is then \[ \text{moles of Ca}^{2+} = 0.0108 \text{ mol} \]

Step 4: Find Mass of Calcium

Convert the moles of calcium to grams. The molar mass of calcium (Ca) is approximately 40.08 g/mol: \[ \text{mass of Ca} = 0.0108 \text{ mol} \times 40.08 \text{ g/mol} \] This gives: \[ \text{mass of Ca} = 0.433 \text{ g} \]

Step 5: Calculate Concentration in Parts Per Million (ppm)

To find the concentration of calcium in the powdered milk, use the formula for parts per million: \[ \text{ppm} = \left(\frac{\text{mass of Ca (g)}}{\text{mass of sample (g)}}\right) \times 10^6 \] Substitute the values: \[ \text{ppm} = \left(\frac{0.433 \text{ g}}{1.50 \text{ g}}\right) \times 10^6 \approx 288,666 \text{ ppm} \]

Step 6: Final Answer

Therefore, the concentration of calcium in the powdered milk in parts per million is approximately 288,667 ppm.

Key Concepts

Dry Ashing

Dry ashing is a process used in analytical chemistry to extract minerals from samples by subjecting them to high temperatures. This technique involves heating a sample in a furnace at temperatures often ranging between 500°C and 600°C. The organic components are decomposed, leaving behind inorganic minerals, including calcium, in an ash form.

• Advantages: Dry ashing is robust and can handle large samples, which helps in getting enough material for analysis.
• Disadvantages: It can lead to the loss of some volatile elements and may take several hours to complete.
• Applications: It's used extensively in food, agriculture, and environmental testing to determine metal content.

Understanding dry ashing is crucial because it prepares samples in such a way that allows for accurate quantification by further analytical methods, such as titration.

EDTA Standardization

EDTA (Ethylenediaminetetraacetic acid) standardization is a pivotal step in complexometric titration, used to determine concentrations of metal ions in solutions. EDTA acts as a chelating agent, binding with metal ions to form stable complexes. To ensure accurate titration results, establishing the exact concentration of the EDTA solution is essential. In the context of this exercise, the EDTA was standardized using a known amount of zinc solution. By titrating a 10.0 mL zinc solution where 0.632 g of zinc was dissolved, the precise molarity of the EDTA solution was determined. This standardized solution then serves as a reliable tool to calculate unknown concentrations of metal ions, such as calcium in this exercise. Standardization involves:

• Dissolving a known mass of a metal, such as zinc, to prepare a solution of known molarity.
• Titrating this solution with EDTA, using an appropriate indicator to mark the endpoint.
• Calculating the molarity of EDTA from the known amounts to assure it is accurate for further usage.

This standardization ensures confidence in the data obtained from subsequent titrations.

Parts Per Million Calculation

Calculating concentration in parts per million (ppm) is a common practice in chemistry, especially useful for expressing small quantities in a large volume or mass matrix. It provides a measure of the solute concentration by weight.The formula to calculate ppm is: \[\text{ppm} = \left(\frac{\text{mass of solute (g)}}{\text{mass of solution (g)}}\right) \times 10^6\]In the calcium titration problem, the mass of the calcium ion was determined through titration using the standardized EDTA. Then, using the formula above, the mass of calcium found is divided by the mass of the milk sample. The result is multiplied by a million to convert it into ppm. This quick and simple calculation gives an understandable concentration value, making it easier to compare with standards and regulations.Key points in ppm calculation:

• Ensures the result is appropriately scaled for easy comprehension and reporting.
• Used in many fields including environmental science, food quality testing, and water analysis.

Parts per million is a versatile and essential concept in analytical measurements, providing a reliable indicator of purity or contamination levels.