Problem 150 - General Chemistry

Question

Iron(III) chloride can be prepared by reacting iron metal with chlorine. What is the balanced equation for this reaction? How many grams of iron are required to make \(3.00 \mathrm{~L}\) of aqueous solution containing \(9.00 \%\) iron(III) chloride by mass? The density of the solution is \(1.067 \mathrm{~g} / \mathrm{mL}\).

Step-by-Step Solution

Answer

The balanced equation is \(2\mathrm{Fe} + 3\mathrm{Cl}_2 \rightarrow 2\mathrm{FeCl}_3 \). You need 99.11 grams of iron.

Step 1: Write the Unbalanced Chemical Equation

The chemical reaction involves iron (Fe) reacting with chlorine gas (Cl_2) to form iron(III) chloride (FeCl_3). The unbalanced equation is: \[ \mathrm{Fe} + \mathrm{Cl}_2 \rightarrow \mathrm{FeCl}_3 \]

Step 2: Balance the Chemical Equation

To balance the equation, we need equal numbers of each type of atom on both sides of the reaction. Start by balancing the chlorine atoms since there are 3 chlorine atoms in FeCl_3. Thus, use 3 Cl_2 molecules:\[ \mathrm{Fe} + \frac{3}{2} \mathrm{Cl}_2 \rightarrow \mathrm{FeCl}_3 \]Convert half coefficients to whole numbers:\[ 2\mathrm{Fe} + 3\mathrm{Cl}_2 \rightarrow 2\mathrm{FeCl}_3 \]

Step 3: Calculate Mass of Iron(III) Chloride in the Solution

The mass of the solution can be found from its volume and density: \[ \text{Mass of solution} = 3000\, \text{mL} \times 1.067\, \text{g/mL} \]\[ \text{Mass of solution} = 3201\, \text{g} \]The mass of iron(III) chloride is 9% of the total mass of the solution:\[ \text{Mass of } \mathrm{FeCl}_3 = 0.09 \times 3201\, \text{g} = 288.09\, \text{g} \]

Step 4: Calculate Moles of Iron(III) Chloride

Determine the moles of FeCl_3 using its molar mass (162.2 g/mol): \[ \text{Moles of } \mathrm{FeCl}_3 = \frac{288.09\, \text{g}}{162.2\, \text{g/mol}} = 1.776 \text{ mol} \]

Step 5: Calculate Moles of Iron Needed

From the balanced equation, 2 moles of FeCl_3 require 2 moles of Fe. Therefore, 1.776 moles of FeCl_3 need 1.776 moles of Fe.

Step 6: Calculate Mass of Iron Needed

The molar mass of Fe is 55.85 g/mol. Therefore, the mass of iron required is:\[ \text{Mass of Fe} = 1.776\, \text{mol} \times 55.85\, \text{g/mol} = 99.11\, \text{g} \]

Key Concepts

Chemical Equation Balancing

Balancing a chemical equation is essential because it ensures that matter is conserved during a chemical reaction. This means that the same number of atoms for each element must be present on both the reactant and the product sides. For the synthesis of iron(III) chloride from iron and chlorine, the unbalanced reaction looks like this: \[ \text{Fe} + \text{Cl}_2 \rightarrow \text{FeCl}_3 \]To balance the equation, note that there are three chlorine atoms in the product \( \text{FeCl}_3 \). Therefore, we need one and a half \( \text{Cl}_2 \) molecules, but using half molecules isn't practical. Instead, multiply through by two to get whole numbers:\[ 2 \text{Fe} + 3 \text{Cl}_2 \rightarrow 2 \text{FeCl}_3 \]Now, the equation is balanced with 2 iron atoms and 6 chlorine atoms on both sides. This balanced equation helps us understand the stoichiometry, or the relationship between the quantities of reactants and products.

Mole Calculation

Mole calculations enable us to quantify the amount of substances involved in a chemical reaction. It's a fundamental concept in chemistry that relates to the number of particles in a given mass. Using the balanced equation, we find that 2 moles of \( \text{Fe} \) produce 2 moles of \( \text{FeCl}_3 \). To calculate the moles of \( \text{FeCl}_3 \), the problem gives us its mass as 288.09 g. By dividing by the molar mass (162.2 g/mol), we find:\[ \text{Moles of } \text{FeCl}_3 = \frac{288.09 \text{ g}}{162.2 \text{ g/mol}} = 1.776 \text{ mol} \]The stoichiometry from the balanced equation tells us that the moles of iron required will match the moles of iron(III) chloride, 1.776 mol in this case. Moles provide a bridge between the macroscopic amounts we can measure and the microscopic world of atoms and molecules.

Solution Density

Density is a physical property defined as mass per unit volume. It is significant when trying to determine the mass of a solution from its volume, as in this exercise involving iron(III) chloride solution. Given the solution's volume of 3000 mL and its density of 1.067 g/mL, you can calculate the total mass of the solution using the formula:\[ \text{Mass of solution} = \text{Volume} \times \text{Density} \]This becomes:\[ 3000 \text{ mL} \times 1.067 \text{ g/mL} = 3201 \text{ g} \]Understanding solution density is crucial in analytical chemistry for converting between volume and mass, especially when preparing solutions for reactions or analyses.

Mass Percentage

Mass percentage is a way of expressing the concentration of a component in a mixture, and it's often used when dealing with solutions. It refers to the mass of a component divided by the total mass of the solution, multiplied by 100%. For the iron(III) chloride solution, we know it contains 9% \( \text{FeCl}_3 \) by mass. Therefore, to find the mass of \( \text{FeCl}_3 \) in the 3201 g solution:\[ \text{Mass of } \text{FeCl}_3 = 0.09 \times 3201 \text{ g} = 288.09 \text{ g} \]Mass percentage is a key concept in chemistry for describing solution concentration and is essential when mixing chemicals with precise ratios, ensuring consistent and reliable results in chemical processes.