May 17, 2024, 08:27:42 PM
Forum Rules: Read This Before Posting

### Topic: Converting iron(Ⅲ ) oxide into iron in a blast furnace  (Read 2031 times)

0 Members and 1 Guest are viewing this topic.

#### Win,odd Dhamnekar

• Full Member
• Posts: 165
• Mole Snacks: +0/-5
• Gender:
• Stock Exchange Trader, Investor,Chemistry Hobbyist
##### Converting iron(Ⅲ ) oxide into iron in a blast furnace
« on: April 05, 2023, 11:07:35 AM »
How many cubic feet of air at a pressure of 760 torr and 0 °C is required per ton of Fe2O3 to convert that Fe2O3 into iron in a blast furnace? For this exercise, assume air is 19% oxygen by volume.

In a blast furnace, iron(III) oxide (Fe2O3) is reduced to iron by carbon monoxide (CO) according to the following balanced chemical equation:

$$Fe_2O_3 + 3CO \to 2Fe + 3CO_2$$

This means that for every mole of Fe2O3 converted to iron, 3 moles of CO are required.

The molar mass of Fe2O3 is 159.69 g/mol. One ton of Fe2O3 is equivalent to 907185 g, so the number of moles of Fe2O3 in one ton is 907185 g / 159.69 g/mol = 5680.9 mol.

Since 3 moles of CO are required for every mole of Fe2O3, the number of moles of CO required to convert one ton of Fe2O3 into iron is 5680.9 mol * 3 = 20000 mol.

At a pressure of 760 torr and a temperature of 0 °C (273.15 K), the volume occupied by one mole of an ideal gas is given by the ideal gas law: V = nRT/P, where n is the number of moles, R is the ideal gas constant (62.3637 L·torr/K·mol), T is the temperature in kelvins, and P is the pressure in torr.

Substituting the values for n, R, T, and P into the ideal gas law gives the volume occupied by 20000 mol of CO at a pressure of 760 torr and a temperature of 0 °C: V = (20000 mol)(62.3637 L·torr/K·mol)(273.15 K) / (760 torr) = 400000 L.

Since air is assumed to be 19% oxygen by volume and oxygen is converted to CO in the blast furnace, the volume of air required to provide this amount of CO is 400000 L / 0.19 = 2000000 L.

There are approximately 28.317 liters in one cubic foot, so this volume in cubic feet is approximately 70000 cubic feet.

In my opinion, this answer seems to look correct. Do you agree with me?
Any science consists of the following process.
1) See 2) Hear 3) Smell if needed 4) Taste if needed
5) Think 6) Understand 7) Inference take decision [Believe or disbelieve, useful or useless, healthy or unhealthy, cause or effect, favorable or unfavorable, practical or theoretical, practically possible or practically impossible, true or false or  any other required criteria]

#### Hunter2

• Sr. Member
• Posts: 2199
• Mole Snacks: +174/-48
• Gender:
• Vena Lausa moris pax drux bis totis
##### Re: Converting iron(Ⅲ ) oxide into iron in a blast furnace
« Reply #1 on: April 05, 2023, 11:37:34 AM »
Its missing the reaction 2 C + O2 => 2 CO. Its not asked how much CO is used, Its asked the air used where the oxygen was obtained.

#### Borek

• Mr. pH
• Deity Member
• Posts: 27682
• Mole Snacks: +1801/-410
• Gender:
• I am known to be occasionally wrong.
##### Re: Converting iron(Ⅲ ) oxide into iron in a blast furnace
« Reply #2 on: April 05, 2023, 02:39:23 PM »
Short ton, long ton, or metric ton?

For this exercise, assume air is 19% oxygen by volume.

Rather surprising.

Quote
5680.9 mol * 3 = 20000 mol.

Really?

And as Hunter stated, CO/O2 is not taken into account.
ChemBuddy chemical calculators - stoichiometry, pH, concentration, buffer preparation, titrations.info

#### Win,odd Dhamnekar

• Full Member
• Posts: 165
• Mole Snacks: +0/-5
• Gender:
• Stock Exchange Trader, Investor,Chemistry Hobbyist
##### Re: Converting iron(Ⅲ ) oxide into iron in a blast furnace
« Reply #3 on: April 06, 2023, 02:30:44 AM »
5680.9 mol × 3 = 20000 mol using significant figures.

How can I include the reaction 2 C + O2 2CO into my answer  and how would the inclusion of that reaction  change the final answer?
« Last Edit: April 06, 2023, 03:11:54 AM by Win,odd Dhamnekar »
Any science consists of the following process.
1) See 2) Hear 3) Smell if needed 4) Taste if needed
5) Think 6) Understand 7) Inference take decision [Believe or disbelieve, useful or useless, healthy or unhealthy, cause or effect, favorable or unfavorable, practical or theoretical, practically possible or practically impossible, true or false or  any other required criteria]

#### Borek

• Mr. pH
• Deity Member
• Posts: 27682
• Mole Snacks: +1801/-410
• Gender:
• I am known to be occasionally wrong.
##### Re: Converting iron(Ⅲ ) oxide into iron in a blast furnace
« Reply #4 on: April 06, 2023, 03:00:17 AM »
5680.9 mol × 3 = 20000 mol using significant figures

No, you apply significant figures only to the final result, not to intermediate values.
ChemBuddy chemical calculators - stoichiometry, pH, concentration, buffer preparation, titrations.info

#### Win,odd Dhamnekar

• Full Member
• Posts: 165
• Mole Snacks: +0/-5
• Gender:
• Stock Exchange Trader, Investor,Chemistry Hobbyist
##### Re: Converting iron(Ⅲ ) oxide into iron in a blast furnace
« Reply #5 on: April 06, 2023, 05:03:46 AM »

To solve this problem, we need to first determine the amount of air required to convert one ton of $Fe_2O_3$ into iron. From the first reaction, we see that for every 1 mole of $Fe_2O_3$ reacted, we need 3 moles of CO. From the second reaction, we see that for every 1 mole of CO, we need 1/2 mole of O2. Therefore, for every mole of $Fe_2O_3$ reacted, we need 3/2 moles of O2.

One ton of $Fe_2O_3$ is equal to 2000 pounds. The molar mass of $Fe_2O_3$ is 159.69 g/mol, so one ton of $Fe_2O_3$ is equal to 5680.9 moles. Therefore, we need 3/2 * 5680.9 = 8521.35 moles of O2.

Since air is 19% oxygen by volume, we know that 1 volume of air contains 0.19 volumes of oxygen. Therefore, we need 8521.35 / 0.19 = 44849.21 volumes of air.

At standard temperature and pressure (STP), 1 mole of gas occupies 22.4 L. Therefore, 44849.21 volumes of air will occupy 44849.21 * 22.4 = 1004622.31 L of air.

Therefore, we need 1004622.31/28.317=35478 cubic feet of air at a pressure of 760 torr and 0°C per ton of $Fe_2O_3$ to convert that $Fe_2O_3$ into iron in a blast furnace.

Any science consists of the following process.
1) See 2) Hear 3) Smell if needed 4) Taste if needed
5) Think 6) Understand 7) Inference take decision [Believe or disbelieve, useful or useless, healthy or unhealthy, cause or effect, favorable or unfavorable, practical or theoretical, practically possible or practically impossible, true or false or  any other required criteria]

#### Enthalpy

• Chemist
• Sr. Member
• Posts: 4041
• Mole Snacks: +304/-59
##### Re: Converting iron(Ⅲ ) oxide into iron in a blast furnace
« Reply #6 on: April 09, 2023, 06:15:16 PM »
Much unburnt CO exits the blast furnace. Whoever asked that question ignores it.

You use more digits in the intermediate steps, good, but in reasonable amounts please. 9 digits don't fit a blast furnace. 1kg=2lbs and 5.7*3=20 aren't correct neither. You can compute with 1 or 2 places more than the final result.

#### Borek

• Mr. pH
• Deity Member
• Posts: 27682
• Mole Snacks: +1801/-410
• Gender:
• I am known to be occasionally wrong.
##### Re: Converting iron(Ⅲ ) oxide into iron in a blast furnace
« Reply #7 on: April 09, 2023, 06:21:25 PM »
You can compute with 1 or 2 places more than the final result.

Typically when using calculator you just use whatever it displays, if it is nine digits - so be it.

Copying them all here is a waste of time though, on that we can agree.
ChemBuddy chemical calculators - stoichiometry, pH, concentration, buffer preparation, titrations.info