Question

When \(20 \mathrm{~g} \mathrm{Fe}_{2} \mathrm{O}_{3}\) is reacted with \(50 \mathrm{~g}\) of \(\mathrm{HCl}, \mathrm{FeCl}_{3}\) and \(\mathrm{H}_{2} \mathrm{O}\) are formed. The amount of unreacted \(\mathrm{HCl}\) is \((\mathrm{Fe}=56)\) (a) \(27.375 \mathrm{~g}\) (b) \(22.625 \mathrm{~g}\) (c) \(30 \mathrm{~g}\) (d) \(4.75 \mathrm{~g}\)

Short answer

Answer: Approximately 22.625 g of unreacted HCl is left after the reaction.

Step-by-step solution

Write the balanced chemical equation

The chemical reaction between Fe₂O₃ and HCl is as follows: Fe₂O₃ (s) + 6HCl (aq) -> 2FeCl₃ (aq) + 3H₂O (l)

Calculate the moles of Fe₂O₃ and HCl

First, we need to calculate the molar mass of each compound involved: Fe₂O₃: (2 × 56) + (3 × 16) = 112 + 48 = 160 g/mol HCl: (1 × 1) + (1 × 35.5) = 1 + 35.5 = 36.5 g/mol Now, we can calculate the moles of each reactant: moles of Fe₂O₃ = mass of Fe₂O₃ / molar mass of Fe₂O₃ = 20 g / 160 g/mol = 0.125 mol moles of HCl = mass of HCl / molar mass of HCl = 50 g / 36.5 g/mol = 1.369 mol

Determine the limiting reactant and the excess reactant

To find out the limiting reactant, we need to compare the mole ratios of the reactants from the balanced chemical equation. Mole ratio of Fe₂O₃ to HCl: 1:6 Reaction ratio of Fe₂O₃ to HCl: 0.125mol : 1.369mol Now, we need to determine the number of moles of HCl that would be required for the given amount of Fe₂O₃: required moles of HCl = moles of Fe₂O₃ × 6 = 0.125 mol × 6 = 0.75 mol Since we have 1.369 mol of HCl, which is more than the required 0.75 mol for the reaction, the limiting reactant is Fe₂O₃, and the excess reactant is HCl.

Calculate the amount of unreacted HCl

Now that we know that Fe₂O₃ is the limiting reactant, we can determine the amount of unreacted HCl: unreacted moles of HCl = moles of HCl - moles of required HCl = 1.369 mol - 0.75 mol = 0.619 mol Now we convert moles of unreacted HCl to grams: mass of unreacted HCl = unreacted moles of HCl × molar mass of HCl = 0.619 mol × 36.5 g/mol = 22.594 g So the amount of unreacted HCl is approximately 22.625 g, which is the answer (b).

Key concepts

Limiting Reactant

In any given chemical reaction, reactants are substances transformed into products. But they don't always perfectly match up. Sometimes one reactant will run out before the others have fully reacted. This component, which is completely consumed first, is known as the **limiting reactant**. It limits the amount of product that can be formed because, once used up, the reaction cannot proceed further.
In the provided exercise, we see that the

• Fe₂O₃ - Our potential limiting reactant!
• HCl - Our potential excess reactant!

The limiting reactant is determined by calculating the mole ratio between the reactants provided in the balanced chemical equation. The limiting reactant is used to predict how much product can be formed from the available reactants, which is crucial in practical applications, such as the industrial production of chemicals.

Balanced Chemical Equation

A balanced chemical equation is akin to a recipe, detailing how substances react with one another. This type of equation ensures that the number of atoms for each element is the same on both sides, emphasizing the **law of conservation of mass**.
In our exercise, we have: Fe₂O₃ + 6HCl → 2FeCl₃ + 3H₂O.
This equation tells us that one mole of iron(III) oxide reacts with six moles of hydrochloric acid to produce two moles of iron(III) chloride and three moles of water. By being balanced, the equation helps us identify the proportions in which reactants combine and products form. This balance is crucial for figuring out the amounts of substances involved in reactions and plays a central role in identifying both the limiting and excess reactants.

Molar Mass Calculation

Understanding the concept of molar mass is essential for converting from grams to moles and vice versa, which is vital in stoichiometry — the mathematical relationship between reactants and products in a chemical reaction. The **molar mass** of a compound is the mass of one mole of its molecules.
For example, in the context of the exercise:

• The molar mass of Fe₂O₃ is calculated by summing the masses of
  • 2 iron atoms: 2 × 56 = 112 g/mol
  • 3 oxygen atoms: 3 × 16 = 48 g/mol
  giving a total of 160 g/mol.
• For HCl, the molar mass calculation involves
  • 1 hydrogen atom: 1 g/mol
  • 1 chlorine atom: 35.5 g/mol
  adding up to 36.5 g/mol.

These calculations aid in determining how many moles are present in a given mass of substance, thereby allowing us to identify the limiting and excess reactants. It’s these moles that participate in reactions, adhering to the ratios established in balanced equations.