Question

The halogen elements are so reactive that the halides of many metals can be prepared by the direct combination of the elements. For example, iron(III) chloride can be prepared by the following reaction: $$2 \mathrm{Fe}(s)+3 \mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{FeCl}_{3}(s)$$ Calculate the mass of \(\mathrm{FeCl}_{3}\) that is formed if \(12.4 \mathrm{g}\) of iron reacts completely.

Short answer

When 12.4 g of iron completely reacts, \(36.009 \: g\) of FeCl\(_3\) will be formed.

Step-by-step solution

Calculate the moles of Fe

First, we need to find the moles of Fe which are reacting. The molar mass of Fe can be found in the periodic table as 55.845 g/mol. Given that we have 12.4 g of Fe, we can find the moles using the formula: moles = mass / molar_mass moles of Fe = 12.4 g / 55.845 g/mol = 0.222 moles

Determine the moles of FeCl3 produced

Now that we have the moles of Fe reacting, we can use the stoichiometry of the balanced chemical equation to find the moles of FeCl3 produced. The balanced equation is: 2 Fe(s) + 3 Cl2(g) → 2 FeCl3(s) As we can see from the equation, the ratio of moles of FeCl3 produced to moles of Fe reacting is 2:2 (or 1:1). Therefore, the number of moles of FeCl3 produced will be equal to the moles of Fe reacting: moles of FeCl3 = moles of Fe = 0.222 moles

Calculate the mass of FeCl3 produced

Now that we have the moles of FeCl3 produced, we can determine the mass by multiplying with its molar mass. The molar masses of Fe and Cl are 55.845 g/mol and 35.453 g/mol, respectively. The molar mass of FeCl3 is: Molar mass of FeCl3 = 1 * (Molar mass of Fe) + 3 * (Molar mass of Cl) = 1 * 55.845 + 3 * 35.453 = 162.204 g/mol Using the moles of FeCl3 and its molar mass, we can determine the mass of FeCl3 produced: mass of FeCl3 = moles of FeCl3 * molar mass of FeCl3 mass of FeCl3 = 0.222 moles * 162.204 g/mol = 36.009 g So, when 12.4 g of Fe reacts completely, 36.009 g of FeCl3 will be formed.

Key concepts

Chemical Reaction

Understanding a chemical reaction is like unraveling a story where substances, the reactants, transform into new substances, the products. In this narrative, reactants undergo various processes, which could involve breaking bonds and forming new ones, to become products with different properties. For instance, when the highly reactive halogen chlorine (\textrm{Cl}_2) reacts with iron (\textrm{Fe}), iron(III) chloride (\textrm{FeCl}_3) is formed.

This transformation can be understood through a balanced chemical equation, which displays the substances involved and the ratios in which they react. Here, the equation \(2 \textrm{Fe}(s) + 3 \textrm{Cl}_2(g) \rightarrow 2 \textrm{FeCl}_3(s)\) illustrates that two moles of solid iron react with three moles of chlorine gas to produce two moles of solid iron(III) chloride. It is paramount to balance the chemical equation so that the number of atoms for each element is the same on both sides, adhering to the law of conservation of mass.

Molar Mass

In stoichiometry, molar mass serves as a bridge between the microscopic world of atoms and molecules and the macroscopic world we handle in labs. This value tells us the mass of one mole of a substance, essentially how heavy are 6.022 \(\times\) 10^{23} (Avogadro's number) of its units, measured in grams per mole (g/mol).

For each element, the molar mass is conveniently found on the periodic table. Iron (\textrm{Fe}), for example, has a molar mass of 55.845 g/mol. Compounds, like iron(III) chloride (\textrm{FeCl}_3), have a molar mass that is the sum of the molar masses of their constituent elements—here, it's the sum of the mass of one mole of iron and three moles of chlorine, resulting in a molar mass of 162.204 g/mol. This knowledge is essential when calculating how much of a substance is involved in a reaction.

Mole Calculation

The mole is a unit representing an enormous number—Avogadro's number—of particles, whether they're atoms, molecules, or ions. Mole calculations are fundamental in converting between the mass of a substance and the number of entities it contains. Using the formula moles \( = \frac{mass}{molar\_mass} \) , we can decipher how many moles are present in a given mass of a substance.

To illustrate, with our reaction, we started with 12.4 g of iron. By using iron's molar mass of 55.845 g/mol, the calculation puts us at 0.222 moles of iron. This is how we quantify our reactant in terms of entities rather than just mass, enabling us to predict what will happen in the chemical reaction. Performing mole calculations is a cornerstone of stoichiometry, ensuring precision in predicting the outcomes of chemical reactions.

Chemical Equation Balancing

The precision of a well-balanced chemical equation cannot be emphasized enough. In essence, balancing an equation ensures that it abides by the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction. Each atom of the reactants must be accounted for in the products.

Referring to our scenario, the equation \(2 \textrm{Fe}(s) + 3 \textrm{Cl}_2(g) \rightarrow 2 \textrm{FeCl}_3(s)\) communicates that for every two atoms of iron that react, three molecules of chlorine are required. For every mole of iron that reacts, a mole of iron(III) chloride is produced. This stoichiometric balance is key when calculating the amount of products formed. It's through this understanding, and the use of coefficients in the equation that the respective quantities of reactants and products are correlated in our calculations.