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University of Maine

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Problem 106

The multistep smelting of ferric oxide to form elemental iron occurs at high temperatures in a blast furnace. In the first step, ferric oxide reacts with carbon monoxide to form $\mathrm{Fe}_{3} \mathrm{O}_{4}$ . This substance reacts with more carbon monoxide to form iron(II) oxide, which reacts with still more carbon monoxide to form molten iron. Carbon dioxide is also produced in each step. (a) Write an overall balanced equation for the iron-smelting process. (b) How many grams of carbon monoxide are required to form 45.0 metric tons of iron from ferric oxide?

Answer

a)

$\mathrm{Fe}_{2} \mathrm{O}_{3}+3 \mathrm{CO} \longrightarrow 2 \mathrm{Fe}+3 \mathrm{CO}_{2}$

b)

$\mathrm{m}(\mathrm{CO})=\mathrm{Mr}^{*} \mathrm{n}=33,86$ metric tons

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## Discussion

## Video Transcript

given descriptions of steps of a complex chemical reaction, we can find the overall chemical reaction by adding together the individual equation. The first step is to take our words and write them in equations, So the first reaction has a compound called ferric oxide. Feyerick is the eye on with a plus three charge, and oxide is a to minus. So ferric oxide, the neutral compound is Effie to 03 This reacts with carbon monoxide, which is CEO to make a new compound F E 304 plus carbon dioxide, which is CEO, too. In the second step, take a product that I formed in the first and reacted with more carbon monoxide to make iron two oxide iron to means it has a charge of two plus, and again, oxide is o to minus. So the formula is FV oh, plus carbon dioxide. Finally, the F B o reacts with carbon monoxide to form molten iron, which is just solid metal iron plus sio two. Once we have the skeleton equations, we can balance them for the first equation. I have two irons here and three irons here, so I need a three here and two here for my coefficient. This gives me six irons and six irons. I have a total of 10 oxygen's on the side and 10 oxygen's on this side and one carbon. So the equations balanced for the second equation. Normally, I would balance it looking for the lowest whole number ratio, but in this case, I have to of these produced. So I have to balance the equation, taking that into account so it won't necessarily be the lowest whole number ratio. And in fact, the ratio is two of these with six irons here, for a total of 10 oxygen's on this side in 10 oxygen's on this side and two carbons and to carpet. And so similarly for the last equation, even though the way it's written, it's already balanced. Because I produced six of these. I need six of these to produce 66 so the first step is to find the individual equations. We can then add them and combine like terms to come up with a simplified overall equation for the process. So I have three F E 20 threes, combining with a total of one plus two plus six or nine carbon monoxide plus two f e 304 plus six f e O. Making on my product side to F E 304 was a total of nine carbon dioxides plus six f e o plus six f e, and we can cancel out any terms that appear on both sides. So, for example, there are two F e 30 fours. There are six F EOS that gives us our overall equation of three F e 203 which is a solid plus nine CEO, which is a gas makes nine carbon dioxides, the gas plus six F E solids. It is now appropriate to simplify this. So dividing by the lowest common multiple, which is three. This is a one with three, the three and a two for the overall balanced equation. Using the balanced equation, we can then make conversions if we want to produce, for example, 45 metric tons. So iron. The question is how much how many grams of carbon monoxide are needed. So we need to change our metric tons, two grams our grams of iron, two moles of iron. And we do that using the molar mass once we have moles of iron. We confined moles of carbon monoxide using the balanced equation, the mole ratio. And finally, we can change it to grams of carbon monoxide using the molar mass of carbon monoxide. One metric ton is equal to 1000 kilograms. The Moeller massive iron we find on the periodic table and that's 55 went 845 grams and the molar mass of carbon monoxide we find by adding the massive carbon, which is 12.11 plus the mass of oxygen, 15.999 or 28 0.1 grams. So now we can do our conversion. 45 metrics Chun's times 1000 kilograms for one metric ton and we know there are 1000 grams and every kilogram. Then we changed two moles by dividing by the molar math. And then we can change two moles of CEO using the balanced equation. There are three moles of carbon monoxide for every two moles of iron. And then finally we multiply by the molar mass of carbon monoxide, and this indicates that we should have three 0.39 times 10 to the seven grams CEO is needed

## Recommended Questions

If ferric oxide is heated strongly in a stream of carbon monoxide gas, it produces elemental iron and carbon dioxide gas. Write the unbalanced chemical equation for this process.

In a blast furnace, iron(lll) oxide is used to produce iron by the following (unbalanced) reaction:

Fe $_{2} \mathrm{O}_{3}(s)+\mathrm{CO}(g) \longrightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g)$

a. If 4.00 $\mathrm{kg} \mathrm{Fe}_{2} \mathrm{O}_{3}$ are available to react, how many moles of CO are needed?

b. How many moles of each product are formed?

Given the mass in grams of a substance in a reaction, calculate the mass in grams of another substance in the reaction.

Iron(III) oxide reacts with carbon to give iron and carbon monoxide.

$$

\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+3 \mathrm{C}(s) \longrightarrow 2 \mathrm{Fe}(s)+3 \mathrm{CO}(g)

$$

a. How many grams of C are required to react with $16.5 \mathrm{g}$ of $\mathrm{Fe}_{2} \mathrm{O}_{3} ?$

b. How many grams of CO are produced when $36.0 \mathrm{g}$ of C reacts?

c. How many grams of Fe can be produced when $6.00 \mathrm{g}$ of $\mathrm{Fe}_{2} \mathrm{O}_{3}$ reacts?

When steel wool (iron) is heated in pure oxygen gas, the steel wool bursts into flame and a fine powder consisting of a mixture of iron oxides $\left(\mathrm{FeO} \text { and } \mathrm{Fe}_{2} \mathrm{O}_{3}\right)$ forms. Write separate unbalanced equations for the reaction of iron with oxygen to give each of these products.

The balanced equation for a reaction in the process of reducing iron ore to the metal is

$$

\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}) \longrightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{g})

$$

(a) What is the maximum mass of iron, in grams, that can be obtained from $454 \mathrm{g}(1.00 \mathrm{lb})$ of iron(III) oxide?

(b) What mass of $\mathrm{CO}$ is required to react with $454 \mathrm{g}$ of $\mathrm{Fe}_{2} \mathrm{O}_{3} ?$

The balanced equation for the reduction of iron ore to the metal using CO is $$\mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+3 \mathrm{CO}(\mathrm{g}) \rightarrow 2 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{g})$$

(a) What is the maximum mass of iron, in grams, that can be obtained from $454 \mathrm{g}(1.00 \mathrm{lb})$ of iron(III) Oxide?

(b) What mass of $\mathrm{CO}$ is required to react with $454 \mathrm{g}$ of $\mathrm{Fe}_{2} \mathrm{O}_{3} ?$

An alternative method for preparing pure iron from $\mathrm{Fe}_{2} \mathrm{O}_{3}$ (Problem 3.61$)$ is by reaction with carbon monoxide:

$\mathrm{Fe}_{2} \mathrm{O}_{3}+\mathrm{CO} \longrightarrow \mathrm{Fe}+\mathrm{CO}_{2} \quad$ Unbalanced

(a) Balance the equation.

(b) How many grams of CO are needed to react with 3.02 $\mathrm{g}$ of $\mathrm{Fe}_{2} \mathrm{O}_{3}$ ?

(c) How many grams of $\mathrm{CO}$ are needed to react with 1.68 $\mathrm{mol}$ of $\mathrm{Fe}_{2} \mathrm{O}_{3} ?$

Iron oxide ores, commonly a mixture of FeO and $\mathrm{Fe}_{2} \mathrm{O}_{3},$ are given the general formula $\mathrm{Fe}_{3} \mathrm{O}_{4}$ . They yield elemental iron when heated to a very high temperature with either carbon monoxide or elemental hy- drogen. Balance the following equations for these processes.

$$\begin{array}{l}{\mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{H}_{2}(g) \rightarrow \mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{O}(g)} \\ {\mathrm{Fe}_{3} \mathrm{O}_{4}(s)+\mathrm{CO}(g) \rightarrow \mathrm{Fe}(s)+\mathrm{CO}_{2}(g)}\end{array}$$

Iron ore is converted to iron by heating it with coal (carbon), and oxygen according to the following equation: $2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+6 \mathrm{C}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow 4 \mathrm{Fe}(\mathrm{s})+6 \mathrm{CO}_{2}(\mathrm{g})$ If the process is run until $3940 .$ g of Fe is produced, how many grams of $\mathrm{CO}_{2}$ will also be produced?

When iron ore is reduced in a blast furnace, some of the $\mathrm{SiO}_{2}$ impurity is also reduced by reaction with carbon to give elemental silicon and carbon monoxide. The silicon is subsequently reoxidized in the basic oxygen process, and the resulting $\mathrm{SiO}_{2}$ reacts with CaO, yielding slag, which is then separated from the molten steel. Write balanced equations for the three reactions involving $\mathrm{SiO}_{2}$