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 $\mathrm{Fe}$ 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?

Key Concepts

Stoichiometry

Stoichiometry is the study of the quantitative relationships between reactants and products in a chemical reaction. It relies on the balanced chemical equation to provide the mole ratio between substances, which then allows for the calculation of the amount of one substance needed to react completely with a given amount of another or the amount of product formed from those reactants. This concept is crucial when determining theoretical yields in reaction processes.

Molar Mass and Mole Concept

The molar mass is the mass of one mole of a substance and is used to convert between the mass of a substance and the number of moles. The mole concept is central in chemistry because it allows chemists to count atoms, molecules, or ions by weighing them. These conversions are essential for applying mole ratios from balanced chemical equations in stoichiometric calculations.

Theoretical Yield

The theoretical yield of a reaction is the maximum amount of product that could be produced from given amounts of reactants, assuming the reaction goes to completion and there are no losses. It is calculated using stoichiometric relationships based on the balanced equation and is an ideal value against which actual yields are compared.

Percent Purity Calculation

Percent purity is a measure of the proportion of a specific compound in a mixture or sample. It is calculated by dividing the mass of the pure substance (obtained from stoichiometric calculations assuming complete reaction) by the total mass of the sample and then multiplying by 100 percent. This concept is essential in evaluating the quality and composition of raw materials used in chemical processes.

Transcript

00:01 One of the reactions that occurs in a blast furnace where iron ore is converted to cast iron is we have iron oxide reacting with co or carbon monoxide to form iron and carbon dioxide gas.

00:19 Suppose 1 .64 times 10 to the 3 kilograms of iron were obtained from 2 .62 times 10 to 3 kilograms of iron.

00:31 Iron oxide.

00:33 Assuming that the reaction goes all the way to completion, what is the percent purity of the iron oxide in the original sample? so we're going to start with this 1 .64 times 10 to the 3 kilograms of iron.

00:52 We're going to convert this to moles by saying one mole of pure iron weighs weighs 55 .845 grams.

01:05 Now notice we are in kilograms and grams.

01:08 So what i can do is i can make this kilograms and then one mole just becomes kilomoles.

01:16 So now we are in kilomoles of iron.

01:21 We can use the stoichiometric ratios from the chemical equation.

01:27 So we will say two moles, or rather kilomoles, of iron come from one kilomole of iron oxide.

01:40 This is really squished up near that equation.

01:47 So i'm just going to go ahead and move it down a little bit.

01:50 So now we're in kilomoles of iron.

01:53 We need to get to kilograms.

01:56 So we can say one kilomole of our iron oxide...