Problem 14 - Analytical Chemistry

Question

An EDTA solution is standardized against high-purity \(\mathrm{CaCO}_{3}\) by dissolving \(0.3982 \mathrm{~g} \mathrm{CaCO}_{3}\) in hydrochloric acid, adjusting the \(\mathrm{pH}\) to 10 with ammoniacal buffer, and titrating. If \(38.26 \mathrm{~mL}\) was required for the titration, what is the molarity of the EDTA?

Step-by-Step Solution

Answer

The molarity of the EDTA solution is approximately 0.104 M.

Step 1: Calculate Moles of CaCO₃

First, calculate the number of moles of calcium carbonate (\(\mathrm{CaCO}_{3}\)). The molar mass of \(\mathrm{CaCO}_{3}\) is approximately 100.09 g/mol. To find the moles, use the formula: \[\text{moles} = \frac{\text{mass}}{\text{molar mass}}\]Substitute the known values: \[\text{moles of } \mathrm{CaCO}_{3} = \frac{0.3982}{100.09} \approx 0.00398 \text{ mol}\]

Step 2: Determine EDTA Moles Needed

In a titration of \(\mathrm{Ca}^{2+}\) ions with EDTA, a 1:1 mole ratio is used between \(\mathrm{Ca}^{2+}\) and EDTA. Hence, the moles of EDTA required are equal to the moles of \(\mathrm{CaCO}_{3}\).Thus, the moles of EDTA required are also:\[0.00398 \text{ mol}\]

Step 3: Calculate Molarity of the EDTA Solution

Now, calculate the molarity of the EDTA solution using the formula:\[\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\]Given that the volume of the EDTA solution used is 38.26 mL, convert this to liters: \[38.26 \text{ mL} = 0.03826 \text{ L}\]Then, substitute the known values:\[\text{Molarity of EDTA} = \frac{0.00398 \text{ mol}}{0.03826 \text{ L}} \approx 0.104 \text{ M}\]

Key Concepts

Molarity Calculation

To determine the molarity of a solution, you need to know two essential things: the number of moles of the solute and the volume of the solution in liters. In our case, we want to find out the molarity of an EDTA solution. Molarity is symbolized by a capital M and is calculated by dividing the moles of solute by the liters of solution. The formula used is - \[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]For the EDTA titration, we converted 38.26 mL to liters because molarity calculations require volume to be in liters. Remember, 1000 mL is equivalent to 1 L, so:- \[ 38.26 \text{ mL} = 0.03826 \text{ L} \] After calculating the moles of the substance (in this exercise, calcium carbonate is used), the final step is dividing by this volume.

Calcium Carbonate

Calcium carbonate, with the chemical formula \(\mathrm{CaCO}_{3}\), is a compound often used in titration exercises. It has a molar mass of approximately 100.09 grams per mole, which is fundamental for converting grams to moles. You calculate the number of moles from a given mass using: - \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \]In the exercise, we worked with 0.3982 grams of \(\mathrm{CaCO}_{3}\). Given the mass and molar mass, this results in 0.00398 moles. We use \(\mathrm{CaCO}_{3}\) in standardization because it is stable and pure, making calculations more precise.

1:1 Mole Ratio

Titrations often deal with reactions that have stoichiometric ratios. In this specific example with EDTA and \(\mathrm{CaCO}_{3}\), a 1:1 mole ratio exists. This means that one mole of \(\mathrm{Ca}^{2+}\) from \(\mathrm{CaCO}_{3}\) reacts with one mole of EDTA. This ratio simplifies calculations because the moles of calcium carbonate directly equal the moles of EDTA needed for complete titration.This equivalence is what we utilized to calculate the moles of EDTA required, which were the same as the moles of \(\mathrm{CaCO}_{3}\). Always check the balanced equation of a reaction to determine these mole ratios.

Analytical Chemistry

Analytical chemistry involves using various techniques to measure and identify the composition of matter. An EDTA titration is a classic analytical technique for determining ion concentrations – particularly metal ions like calcium. It uses an agent like EDTA, which forms stable complexes with metal ions, to accurately measure the concentration of known elements. In this exercise, a known amount of \(\mathrm{CaCO}_{3}\) was used to standardize the solution of EDTA, allowing the accurate determination of its molarity. EDTA titrations are crucial in various industries, from ensuring water hardness levels to measuring nutrients in soil. This exercise demonstrates the fundamental principles of analytical chemistry by standardizing and calculating concentrations of chemical solutions.