Problem 50 - Chemistry Matter and Change

Question

The most important commercial ore of chromium is chromite \(\left(\mathrm{FeCr}_{2} \mathrm{O}_{4}\right)\) One of the steps in the process used to extract chromium from the ore is the reaction of chromite with coke (carbon) to produce ferrochrome \(\left(\mathrm{FeCr}_{2}\right)\) $$2 \mathrm{C}(\mathrm{s})+\mathrm{Fe} \mathrm{Cr}_{2} \mathrm{O}_{4}(\mathrm{s}) \rightarrow \mathrm{FeCr}_{2}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g})$$ What mole ratio would you use to convert from moles of chromite to moles of ferrochrome?

Step-by-Step Solution

Answer

The mole ratio between chromite (FeCr₂O₄) and ferrochrome (FeCr₂) in the given balanced chemical equation is 1:1. This means that for every one mole of chromite reacted, one mole of ferrochrome is produced. \[ \frac{\text{moles of FeCr}_2}{\text{moles of FeCr}_2\text{O}_4} = \frac{1}{1} \]

Step 1: Write down the balanced chemical equation

The balanced chemical equation for the reaction between chromite and coke is given as: \[2\, C(s) + FeCr_2O_4(s) \rightarrow FeCr_2(s) + 2\, CO_2(g)\]

Step 2: Identify the mole ratio between chromite and ferrochrome

The stoichiometric coefficients in a balanced chemical equation represent the mole ratios of the reactants and products in the reaction. We can find the mole ratio between chromite (FeCr₂O₄) and ferrochrome (FeCr₂) by looking at their coefficients in the balanced equation. For each mole of chromite, there is one mole of ferrochrome produced. Therefore, the mole ratio between chromite and ferrochrome is: $$ \frac{\text{moles of FeCr}_2}{\text{moles of FeCr}_2\text{O}_4} = \frac{1}{1} $$

Step 3: Interpret the mole ratio

The mole ratio between chromite and ferrochrome is 1:1. This means that for every one mole of chromite reacted, one mole of ferrochrome is produced in this reaction.

Key Concepts

Balanced Chemical Equation

A balanced chemical equation is a representation of a chemical reaction where the number of atoms for each element is equal on both the reactant and product sides. This is important because it reflects the conservation of mass, a fundamental principle of chemistry. For the reaction involving chromite and coke, the balanced equation is: \[2\, C(s) + FeCr_2O_4(s) \rightarrow FeCr_2(s) + 2\, CO_2(g)\]

• The left side features reactants: carbon (\(C\)) and chromite (\(FeCr_2O_4\)).
• The right side includes the products: ferrochrome (\(FeCr_2\)) and carbon dioxide (\(CO_2\)).

Balancing ensures that:

• All carbon atoms are accounted for.
• The chromium and oxygen atoms in chromite are balanced by those in ferrochrome and carbon dioxide, respectively.

Balancing is essential for determining the correct stoichiometry, the quantitative relationships in a chemical reaction.

Mole Ratio

The mole ratio is derived from the coefficients of the reactants and products in a balanced chemical equation. This ratio enables you to convert between moles of different substances involved in the reaction. In our example:

• For chromite (\(FeCr_2O_4\)) and ferrochrome (\(FeCr_2\)), the coefficient is 1 for both in the balanced equation.

Hence, the mole ratio is 1:1, meaning:

• One mole of chromite produces one mole of ferrochrome.

This ratio assists in determining how much of one substance is needed or produced when a certain amount of another is used or formed. Grasping this can be vital for practical applications like determining reactant quantities in industrial synthesis.

Chromite

Chromite is a significant industrial mineral used as the primary ore for extracting chromium. It is chemically represented as \(FeCr_2O_4\), forming black to brownish-black crystals. Important points about chromite include:

• It is an oxide mineral composed primarily of chromium, iron, and oxygen.
• Chromite is valued for its chromium content, a metal essential in manufacturing various alloys and for metallurgy.

Chromium obtained from chromite is used in creating stainless steel and other corrosion-resistant alloys. Its extraction process includes the chemical reaction with coke to produce ferrochrome in a highly temperature-controlled environment. Understanding the composition and role of chromite is crucial for fields like materials science and industrial chemistry.

Ferrochrome

Ferrochrome is an iron-chromium alloy directly extracted from chromite through chemical reactions with carbon. It appears as a silvery-grey metal used primarily in steel production, providing:

• Hardness and challenge to steel and cast iron against rust and corrosion.
• Enhancement of aesthetic appearances in metal products.

In the reaction equation, one mole of chromite yields one mole of ferrochrome, highlighting:

• Efficiency in the reaction process.
• Economically favorable production from a metallurgy standpoint.

Understanding ferrochrome's properties and applications shows its importance in advancing technology and infrastructure. This alloy is widely used in making stainless steel, due to its resistance to heat and wear, making it indispensable in modern engineering and architecture.