Problem 154 - Chemistry

Question

A major industrial use of hydrochloric acid is in metal pickling. This process involves the removal of metal oxide layers from metal surfaces to prepare them for coating. (a) Write an equation between iron(III) oxide, which represents the rust layer over iron, and \(\mathrm{HCl}\) to form iron(III) chloride and water. (b) If 1.22 moles of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) and \(289.2 \mathrm{~g}\) of HCl react, how many grams of \(\mathrm{FeCl}_{3}\) will be produced?

Step-by-Step Solution

Answer

The balanced chemical equation is \(Fe_{2}O_{3} + 6HCl \rightarrow 2FeCl_{3} + 3H_{2}O\), and 396.2 g of \(FeCl_{3}\) will be produced from 1.22 moles of \(Fe_{2}O_{3}\) and 289.2 g of HCl.

Step 1: Write the Unbalanced Chemical Equation

First write the chemical equation for the reaction between iron(III) oxide (\(Fe_{2}O_{3}\)) and hydrochloric acid (\(HCl\)), producing iron(III) chloride (\(FeCl_{3}\)) and water (\(H_{2}O\)). This comes out as \(Fe_{2}O_{3} + HCl \rightarrow FeCl_{3} + H_{2}O\).

Step 2: Balance the Chemical Equation

Next balance the equation. A balanced equation keeps the same number of atoms for each element on both sides of the equation. The balanced equation becomes \(Fe_{2}O_{3} + 6HCl \rightarrow 2FeCl_{3} + 3H_{2}O\).

Step 3: Convert grams of HCl to moles

Before we start calculating the amount of \(FeCl_{3}\) that will be produced, we need to convert the grams of HCl into moles. The molar mass of \(HCl\) is approximately \(36.46 \, g/mol\). So we divide the given mass of \(HCl\) (289.2 g) by its molar mass to get the number of moles: \(289.2 \, g / 36.46 \, g/mol = 7.93 \, mol\).

Step 4: Use the Balanced Chemical Equation to Determine the Amount of \(FeCl_{3}\) Produced.

Now we can use the balanced chemical equation to find out how many moles of \(FeCl_{3}\) would be produced by 1.22 moles of \(Fe_{2}O_{3}\) and 7.93 moles of \(HCl\). According to the balanced equation, 1 mole of \(Fe_{2}O_{3}\) reacts with 6 moles of \(HCl\) to produce 2 moles of \(FeCl_{3}\). Since the \(Fe_{2}O_{3}\) is the limiting reactant, it will determine the amount of \(FeCl_{3}\) produced: \(1.22\,moles \times 2 = 2.44\,moles \, of \, FeCl_{3}\).

Step 5: Convert Moles of \(FeCl_{3}\) to Grams

Finally, convert the moles of \(FeCl_{3}\) into grams. The molar mass of \(FeCl_{3}\) is approximately \(162.2\,g/mol\). So we multiply the number of moles of \(FeCl_{3}\) by its molar mass to get the weight in grams: \(2.44\,moles \times 162.2\,g/mol = 396.2\,g\).

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that deals with the quantitative relationships between the amounts of reactants and products in a chemical reaction. At its core, stoichiometry is like the math of chemistry. It helps chemists figure out exactly how much of a substance is needed or produced in a reaction. This is critical when working in labs or industries.
When tackling stoichiometric problems, chemists first write a balanced chemical equation, which is an essential step. This equation allows them to understand the proportion of reactants to products. Knowing these proportions can then be used to calculate the desired quantities. For example, in the reaction between iron(III) oxide and hydrochloric acid to produce iron(III) chloride, stoichiometry helps determine how much iron(III) chloride is formed when a certain amount of iron(III) oxide reacts.

Balancing Chemical Equations

Balancing chemical equations is all about ensuring that the number of each type of atom is equal on both sides of a chemical equation. For a chemical equation to accurately represent a chemical reaction, it must follow the law of conservation of mass, which states that mass cannot be created or destroyed.

• First, write down the unbalanced equation using the proper chemical formulas.
• Next, adjust the coefficients (numbers placed before the chemical formulas) to balance the atoms for each element on both sides of the equation.
• Check each element one by one, systematically adjusting until the equation is balanced.

Consider our example, when balancing the equation for iron(III) oxide and hydrochloric acid, the balanced form becomes: \[\text{Fe}_2\text{O}_3 + 6\text{HCl} \rightarrow 2\text{FeCl}_3 + 3\text{H}_2\text{O}\] Here, each atom type has the same count on both sides of the equation.

Limiting Reactant

The limiting reactant in a chemical reaction is the substance that is completely consumed first, limiting the amount of product that can be made. To find the limiting reactant, compare the mole ratio of the reactants used with those in the balanced equation.
In the problem given, we used iron(III) oxide and hydrochloric acid to produce iron(III) chloride. We determined how much reactant we had in moles and used stoichiometry based on the balanced equation to see which reactant runs out first. Since 1.22 moles of \(\text{Fe}_2\text{O}_3\) reacts proportionally with 7.93 moles of \(\text{HCl}\), the \(\text{Fe}_2\text{O}_3\) becomes the limiting reactant, dictating the amount of \(\text{FeCl}_3\) produced regardless of the excess \(\text{HCl}\).

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is used to convert between the mass of a substance and the number of moles, aiding in stoichiometric calculations.
In any chemical problem, determining the molar mass of the involved compounds is crucial. For example, in our exercise:

• The molar mass of \(\text{HCl}\) is approximately 36.46 g/mol.
• The molar mass of \(\text{FeCl}_3\) is about 162.2 g/mol.

We used these molar masses to first convert grams of \(\text{HCl}\) into moles (for further stoichiometric calculations) and finally convert the moles of produced \(\text{FeCl}_3\) back into grams to find out how much product was obtained after the reaction.