Problem 109 - Chemistry An Atoms First Approach

Question

Douglasite is a mineral with the formula \(2 \mathrm{KCl} \cdot \mathrm{FeCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O}\) Calculate the mass percent of douglasite in a 455.0 -mg sample if it took \(37.20 \mathrm{mL}\) of a \(0.1000-M \mathrm{AgNO}_{3}\) solution to precipitate all the \(\mathrm{Cl}^{-}\) as \(\mathrm{AgCl}\). Assume the douglasite is the only source of chloride ion.

Step-by-Step Solution

Answer

The mass percent of Douglasite in the 455.0-mg sample is calculated by first determining the moles of \(\mathrm{Cl}^-\) using the volume and concentration of the \(\mathrm{AgNO}_3\) solution, then finding the moles of Douglasite based on its formula and molar mass. Lastly, we divide the mass of Douglasite by the total mass of the sample and multiply by 100. The mass percent of Douglasite = \(\frac{\text{Mass of Douglasite}}{\text{Mass of Sample}} \times 100\%\).

Step 1: Determine the moles of AgNO3

First, we find the moles of \(\mathrm{AgNO}_3\) which were used to precipitate the \(\mathrm{Cl}^-\) by using the volume and the concentration of the \(\mathrm{AgNO}_{3}\) solution. Moles of \(\mathrm{AgNO}_{3}\) = Volume × Molarity Moles of \(\mathrm{AgNO}_{3}\) = \(37.20 \times 10^{-3}\; \mathrm{L} \times 0.1000\; \frac{\mathrm{mol}}{\mathrm{L}}\)

Step 2: Find moles of Cl-

Since \(\mathrm{Cl}^-\) ions come only from Douglasite, the number of moles of \(\mathrm{Cl}^-\) is equal to the moles of \(\mathrm{AgNO}_3\). Moles of \(\mathrm{Cl}^-\) = Moles of \(\mathrm{AgNO}_{3}\)

Step 3: Calculate moles of Douglasite

From the formula of Douglasite, we can see that there are 3 moles of \(\mathrm{Cl}^-\) ions in one mole of Douglasite. Therefore, we can calculate the moles of Douglasite by dividing the moles of \(\mathrm{Cl}^-\) by 3. Moles of Douglasite = \(\frac{\text{Moles of Cl}^-}{3}\)

Step 4: Calculate the molar mass of Douglasite

To find the molar mass of Douglasite, we'll add the molar masses of each component in the formula. Molar mass of Douglasite = \(2 \times \text{Molar mass of KCl} + \text{Molar mass of FeCl}_2 + 2 \times \text{Molar mass of H}_2\text{O}\)

Step 5: Calculate the mass of Douglasite

Now, we multiply the moles of Douglasite by its molar mass to find the mass of Douglasite in the sample. Mass of Douglasite = Moles of Douglasite × Molar mass of Douglasite

Step 6: Calculate the mass percent of Douglasite

Finally, we can calculate the mass percent of Douglasite in the sample by dividing the mass of Douglasite by the mass of the sample and multiplying by 100. Mass Percent of Douglasite = \(\frac{\text{Mass of Douglasite}}{\text{Mass of Sample}} \times 100\%\)

Key Concepts

Stoichiometry

Stoichiometry is the cornerstone of chemical reactions. It essentially involves calculations that relate the quantities of reactants and products in a chemical reaction. At its core, stoichiometry is based on the law of conservation of mass and the concept that matter cannot be created or destroyed in a closed system. Hence, the amount of each element must remain constant through the reaction, allowing us to predict the quantities required and produced.

For instance, in the reaction between silver nitrate and chloride ions to form silver chloride, stoichiometry enables us to calculate the exact amount of silver nitrate needed to react with a known quantity of chloride ions. This is crucial in laboratory settings and in industrial applications where precise measurements are essential for expected outputs and cost-efficiency.

Molar Mass Calculation

The molar mass of a substance is the weight of one mole (6.022 × 10²³ units) of that substance. It is expressed in grams per mole (g/mol) and is obtained by summing the atomic masses of each element, as found on the periodic table, in its chemical formula.

In the exercise provided, the molar mass calculation of Douglasite involves the addition of the molar masses of potassium chloride (KCl), iron(II) chloride (FeCl₂), and water (H₂O), all of which are multiplied by their respective coefficients as indicated in the compound's formula. The resulting molar mass allows us to convert moles of Douglasite into grams, a step essential for determining the mass percent in the given sample.

Precipitation Reactions

Precipitation reactions are a type of chemical reaction where two soluble salts react in solution to form one or more insoluble products, known as precipitates. These reactions are commonly used to isolate a particular compound, removing it from the solution.

In the context of our exercise, when aqueous silver nitrate (AgNO₃) is added to a solution containing chloride ions (Cl^-), an insoluble white precipitate of silver chloride (AgCl) forms. Precipitation reactions are not only important for laboratory chemical synthesis but also have applications in water treatment, where they are used to remove unwanted ions from water.

Molarity and Solution Concentration

Molarity is a measure of the concentration of a solute in a solution. Expressed in moles per liter (mol/L), it quantifies how much of a substance is dissolved in a given volume of solution. The molarity formula is: Molarity = Moles of Solute / Volume of Solution in Liters.

In the precipitation reaction from the exercise, molarity is used to determine the moles of silver nitrate, and from there, the moles of chloride ions present. Understanding molarity is crucial in chemistry because it helps in predicting how substances in solutions will react with each other, which is necessary for creating desired products, carrying out titrations, and numerous other chemical analyses and reactions.