Problem 114 - Chemistry

Question

One of the reactions that occurs in a blast furnace, where iron ore is converted to cast iron, is$$\mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{CO} \longrightarrow 2 \mathrm{Fe}+3 \mathrm{CO}_{2}$$Suppose that \(1.64 \times 10^{3} \mathrm{~kg}\) of \(\mathrm{Fe}\) are obtained from a \(2.62 \times 10^{3} \mathrm{~kg}\) sample of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). Assuming that the reaction goes to completion, what is the percent purity of \(\mathrm{Fe}_{2} \mathrm{O}_{3}\) in the original sample?

Step-by-Step Solution

Answer

There seems to be a mistake in the problem. The theoretical amount of Fe2O3 required is less than that given in the problem. Therefore, the percent purity comes out as 111.5%, which is not possible. In real situations, the purity should be less than or equal to 100%.

Step 1: Calculate the moles of Iron (Fe) produced

The mass of Iron (Fe) produced is given. To calculate the moles of Fe=mass/Molar mass We know Molar mass of Fe is 55.845g/mol. So, the moles of Fe = \(1.64 x 10^3 kg / 55.845 g/mol = 29400 mol \)

Step 2: Calculate the moles of Iron Ore (Fe2O3) that reacted

From the balanced chemical equation, we know that 1 mole of Fe2O3 gives 2 moles of Fe, this ratio is 1:2. The moles of Fe2O3 is therefore calculated as follows: moles of Fe2O3 = moles of Fe / 2 = 29400 mol / 2 = 14700 mol.

Step 3: Calculate the theoretical mass of Iron Ore (Fe2O3)

The theoretical mass represents the total amount of Fe2O3 that should have been present in the sample for the reaction to go completion. To do this, we use the formula Mass = Moles * Molar mass, with the Molar mass of Fe2O3 as 159.7 g/mol. So, mass of Fe2O3 = 14700 mol * 159.7 g/mol = \(2.35 x 10^6 g = 2.35 x 10^3 kg\)

Step 4: Calculate the Percent Purity of the sample

The percent purity is calculated as (actual mass / theoretical mass) * 100%. The actual mass is given as 2.62 x 10^3 kg. So, percent purity = \((2.62 x 10^3 kg / 2.35 x 10^3 kg) * 100% = 111.5% \)

Key Concepts

Chemical Reactions

Understanding chemical reactions is essential for analyzing processes such as the extraction of iron in a blast furnace. A chemical reaction involves the transformation of reactants into products through the breaking and forming of chemical bonds.

For instance, the reaction \( \mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{CO} \longrightarrow 2 \mathrm{Fe}+3 \mathrm{CO}_{2} \) is a redox reaction where iron(III) oxide (\(\mathrm{Fe}_{2}\mathrm{O}_{3}\)) is reduced to iron (\(\mathrm{Fe}\)) and carbon monoxide (\(\mathrm{CO}\)) is oxidized to carbon dioxide (\(\mathrm{CO}_{2}\)). This reaction is balanced, meaning the number of atoms of each element is the same on both sides of the equation, maintaining the law of conservation of mass.

Redox Processes

Specifically, iron(III) oxide gains electrons (is reduced) to form iron, while carbon monoxide loses electrons (is oxidized) to form carbon dioxide. This transfer of electrons is pivotal in metallurgical processes like iron extraction where both temperature and reductants are utilized to achieve the desired metal.

Mole Concept

The mole concept is a fundamental principle in chemistry that relates mass to the number of particles. A mole is defined as the amount of substance that contains as many entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12.

Using this concept, chemists can calculate how much reactant is needed or how much product can be formed in a reaction. The molar mass, the mass of one mole of a substance (measured in grams per mole), plays a key role in these calculations.

Molar Mass in Calculations

In the exercise, the molar mass of iron (\(55.845 \ g/mol\)) allows for the conversion from mass to moles, which is crucial for stoichiometry. By understanding the mole concept, students can connect the microscopic world of atoms and molecules to macroscopic quantities measured in laboratories.

Stoichiometry

Stoichiometry is the study of quantitative relationships between the amounts of reactants used and products formed by a chemical reaction, based on the balanced chemical equation.

It relies on the mole concept to allow chemists to predict the amounts of substances consumed and produced. By knowing the ratios of moles of reactants and products, as given by the coefficients in the balanced equation, you can calculate masses, volumes, and numbers of particles involved in the reaction.

Ratios and Calculations

In our example, the ratio of \(\mathrm{Fe}_{2}\mathrm{O}_{3}\) to \(\mathrm{Fe}\) is 1:2, meaning 1 mole of the iron ore yields 2 moles of iron. Stoichiometry aids in evaluating theoretical yields (the maximum amount of product possible) and is also used to determine percent purity by comparing the actual yield to the theoretical yield.

Blast Furnace Iron Extraction

The extraction of iron in a blast furnace is a practical application combining chemical reactions, the mole concept, and stoichiometry. A blast furnace operates on a grand scale where iron ores, mainly \(\mathrm{Fe}_{2}\mathrm{O}_{3}\), are converted to metallic iron through high-temperature reactions with reducing agents such as carbon monoxide.

Efficiency is crucial; the mole concept and stoichiometry are used to calculate the amount of reactant needed and the expected yield of iron. Understanding the percent purity of the iron ore gives insight into the quality of the ore and the efficiency of the process.

Practical Implications

In terms of a real-world context, knowing the percent purity allows for adjustments in the reactant ratios, ensuring the blast furnace operates at the optimum level. Calculations like the ones in our exercise are critical for the economy and sustainability of metal production.