How many cubic feet of air (assume 21 % by volume of oxygen...

How many cubic feet of air (assume $21 \%$ by volume of oxygen in air) at $25^{\circ} \mathrm{C}$ and 1.00 atm are required to react with coke to form the CO needed to convert one metric ton of hematite ore $\left(92 \% \mathrm{Fe}_{2} \mathrm{O}_{3}\right)$ to iron?

Key Concepts

Stoichiometry of Reduction Reactions

This concept involves writing and balancing chemical equations to determine the relationships among reactants and products. In metallurgical processes, such as converting iron ore (hematite) to iron, stoichiometry is crucial to calculate how much reducing agent (e.g., CO produced from coke) is needed to convert a given mass of ore into the desired metal, based on the mole ratios from the balanced reduction reaction.

Mass-to-Mole Conversion

Converting the given mass of a substance into moles is a fundamental step in stoichiometric calculations. It involves using the molar mass of the substance and, in cases involving impure samples (like ore with a given percent purity), adjusting for the actual amount of the active component. This conversion is essential for determining the moles of reactants that participate in the reaction.

Ideal Gas Law

The ideal gas law (PV = nRT) provides a relationship among pressure, volume, temperature, and the number of moles of a gas. It is used to convert between the number of moles of a gas, calculated from stoichiometry, and the volume that gas occupies under specific conditions of temperature and pressure. This allows for the determination of the volume of gases, such as air, required for a reaction.

Gas Mixture Analysis

Understanding the composition of gas mixtures, such as air, is essential when using components available in a fixed proportion (e.g., 21% oxygen). This concept involves calculating the actual volume of the required reactive gas (oxygen) from the total volume of the gas mixture, by accounting for its percentage in the mixture. This ensures the calculated volume meets the stoichiometric requirement for the reaction.

Transcript

00:01 Element that can readily form positive ions and has metallic bonds.

00:03 So metals are sometimes described as a lattice of positive ions that are surrounded by a cloud of delocalised electrons.

00:09 So here we have the balanced equation for the reaction of fe 203 and co.

00:13 So we have f .e 203, add 3 co.

00:19 So this is balanced.

00:20 We get two f .e as the liquid, add 3 co2 as a gas.

00:26 So the molar ratio between f .e 203 and co.

00:29 We have a 1 to 3 ratio because we can imagine that we have a 1 here got 1 to 3 and so we can calculate the number of moles of fe 203 where the number of moles is 5 .76 times 10 to the 3 moles because the mass is 92 times 10 to the 4 grams and the molar mass is 159 .7 so then to calculate the number of moles of fe203 by dividing its mass by the molar mass.

01:13 So then we can calculate the number of moles of co.

01:17 So what we do is multiply that value by three.

01:19 It's got 17 .3 times 10 to the three moles, the moles of co.

01:29 So then we can write the balanced equation for the reaction between carbon and oxygen.

01:35 So we have 2c, that's a solid, add 02 as a gas, gives us 2co as a gas.

01:43 So the molar ratio between carbon monoxide and oxygen.

01:51 You can see it's 2 to 1, if we had an imaginary 1 here.

01:57 And so the moles of 02, that is 17 .3 times 10 to the 3 moles of co, multiplied by 1 mole of 02 divided by 2 moles of co...