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 \(1.067 \mathrm{~g} / \mathrm{mL}\).

Short answer

99.17 g of iron is required.

Step-by-step solution

Determine the Balanced Chemical Equation

Iron(III) chloride is formed by reacting iron metal with chlorine gas. The unbalanced reaction is: \( \text{Fe} + \text{Cl}_2 \rightarrow \text{FeCl}_3 \). To balance it, we need to have equal numbers of each type of atom on both sides. The balanced equation is:\[ 2\text{Fe} + 3\text{Cl}_2 \rightarrow 2\text{FeCl}_3 \]

Find Total Mass of the Solution

To find the total mass of the solution, use the volume and density. The volume is \(3.00\, \text{L}\) which is \(3000\, \text{mL}\) (since \(1 \text{L} = 1000 \text{mL}\)). The density is \(1.067\, \text{g/mL}\), so:\[ \text{Total Mass} = 3000\, \text{mL} \times 1.067\, \text{g/mL} = 3201\, \text{g} \]

Find Mass of Iron(III) Chloride in Solution

Given that iron(III) chloride is \(9\%\) of the solution by mass, calculate the mass of \(\text{FeCl}_3\):\[ \text{Mass of FeCl}_3 = 9\% \times 3201\, \text{g} = 288.09\, \text{g} \]

Convert Mass of Iron(III) Chloride to Moles

To find how much iron is needed, convert the mass of \(\text{FeCl}_3\) to moles. The molar mass of \(\text{FeCl}_3\) (from periodic table values) is approximately \(55.85\, \text{g/mol Fe} + 3 \times 35.45\, \text{g/mol Cl} = 162.2\, \text{g/mol}\):\[ \text{Moles of FeCl}_3 = \frac{288.09\, \text{g}}{162.2\, \text{g/mol}} = 1.776\, \text{mol} \]

Relate Moles of Iron(III) Chloride to Moles of Iron

From the balanced equation \(2\text{Fe} + 3\text{Cl}_2 \rightarrow 2\text{FeCl}_3\), we see that 2 moles of iron produce 2 moles of \(\text{FeCl}_3\), so: \[ \text{Moles of Fe} = \text{Moles of FeCl}_3 = 1.776\, \text{mol} \]

Convert Moles of Iron to Mass

Finally, convert moles of iron to grams. The molar mass of iron (\(\text{Fe}\)) is approximately \(55.85\, \text{g/mol}\):\[ \text{Mass of Fe} = 1.776\, \text{mol} \times 55.85\, \text{g/mol} = 99.17\, \text{g} \]

Key concepts

Chemical Reactions

Chemical reactions involve the rearrangement of atoms to transform reactants into products. These reactions must be balanced, meaning that the number of each type of atom on the reactant side is equal to the number on the product side. This reflects the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction.

In the problem, iron metal reacts with chlorine gas to form iron(III) chloride. The initially proposed equation is:

• \( \text{Fe} + \text{Cl}_2 \rightarrow \text{FeCl}_3 \)

However, this equation is not balanced because there are unequal numbers of chlorine atoms on each side. By balancing the equation, 2 iron atoms and 3 chlorine molecules react to form 2 molecules of iron(III) chloride, making the stoichiometry straightforward for further calculations:

• \( 2\text{Fe} + 3\text{Cl}_2 \rightarrow 2\text{FeCl}_3 \)

Molar Mass

Molar mass is a crucial concept in chemistry that allows us to convert between moles and grams, giving us a way to directly relate amounts of different substances in a reaction. It is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). You can find it by adding the atomic masses of all atoms in a molecule from the periodic table.

For example, calculating the molar mass of iron(III) chloride (\( \text{FeCl}_3 \)) involves summing the mass of one iron atom and three chlorine atoms:

• Mass of \( \text{Fe} = 55.85 \, \text{g/mol} \)
• Mass of \( \text{Cl} = 35.45 \, \text{g/mol} \) (and there are 3 chloride ions, so multiply by 3)

This gives a total of \( 162.2 \, \text{g/mol} \) for \( \text{FeCl}_3 \). Knowing the molar mass allows us to convert the 288.09 grams of iron(III) chloride to moles, aiding in determining how much reactant iron is necessary for this compound.

Density Calculations

Density calculations enable us to relate the mass of a substance to its volume, which is useful in determining the amount of solute in a solution. Density is defined as mass per unit volume (typically in g/mL or g/L). This concept plays a critical role when converting between volume and mass in problems involving solutions.

For the problem at hand, we calculate the total mass of the iron(III) chloride solution knowing its volume and density:

• Volume \( = 3.00 \, \text{L} \) which converts to \( 3000 \, \text{mL} \)
• Density \( = 1.067 \, \text{g/mL} \)

By using the formula \( \text{mass} = \text{volume} \times \text{density} \), we find the total mass of the solution is 3201 grams. Given the solution is 9% iron(III) chloride by mass, we find that \( 9\% \) of this mass is the solute, yielding 288.09 grams of \( \text{FeCl}_3 \). This allows us to determine how much elemental iron is necessary to produce this mass of the compound.