One of the reactions that occurs in a blast furnace, where...

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 $\mathrm{Fe}$ is 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?

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 $\mathrm{Fe}$ is 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?

Key Concepts

Balanced Chemical Equation

A balanced chemical equation provides the mole ratios of the reactants and products in a chemical reaction. It ensures that the number of atoms for each element is conserved and allows the quantification of how much product can be formed from a given amount of reactant.

Stoichiometry

Stoichiometry involves using the mole ratios from the balanced chemical equation to convert between masses and moles of reactants and products. This process is essential for predicting the outcomes of reactions, determining how much of one substance is needed to react with another, or how much product will be formed.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance and is used as a conversion factor between moles and grams (or kilograms). It is crucial in stoichiometric calculations because it bridges the gap between the microscopic world (mole quantities) and macroscopic masses measured in the lab.

Percent Purity

Percent purity is a measure of the concentration of a specific substance within a mixture. It is defined as the mass of the pure target substance divided by the total mass of the sample, multiplied by 100. This concept is important in analytical chemistry to determine how much of the sample is composed of the desired chemical compound.

Theoretical Yield Calculation

Theoretical yield represents the maximum amount of product that can be formed from given amounts of reactants based on the stoichiometric relationships in a balanced chemical equation. It is calculated by converting the mass of a reactant to moles using its molar mass, applying the mole ratio from the balanced equation to find the moles of product, and then converting those moles back to mass. This calculation is critical when assessing the efficiency or purity of a reaction.

Transcript

00:01 So for this problem, we want to find the percent purity of fe03 in some sample, given some reaction that occurs in a blast furnace.

00:10 And so we know that 1 .64 times 10 to 3 kilograms of iron are obtained from a 2 .62 times 10 to 3 kilogram sample of fe203.

00:26 So this quantity will have some other things other than fe203.

00:30 We want to find how much of that is actually within the sample.

00:34 So the first thing that we want to do is we want to actually find the molar mass of fe2 -03, so we can do some basic dimensional calculations with this.

00:44 So you have two iron atoms, each of which are 55 .85.

00:52 And then we have three oxygen atoms, each of which are 16 .0.

00:58 And so when we multiply that through, we will get that the molar mass that we are dealing with, is 159 .70 grams per mole.

01:13 So the next thing that we want to do is you want to convert kilograms of fe into kilograms of fe 203 to find how much of that sample is actually pure and how much fe203 it actually contains.

01:27 So we're going to start with 1 .64 times 10 to 3 kilograms of fe.

01:34 So you want to convert this into grams.

01:40 And now we want to divide by the molar mass, the atomic mass of iron, so that we can get moles of iron and then do some dimensional analysis.

01:50 So we know that that is 55 .85 grams per one mole of iron...

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