Question

Suppose you want to convert iron ore to a specific amount of pure iron using the following reaction: $$ \mathrm{Fe}_{3} \mathrm{O}_{4}(s)+4 \mathrm{CO}(g) \longrightarrow 3 \mathrm{Fe}(s)+4 \mathrm{CO}_{2}(g) $$ (a) What mole ratio would you use in the following equation to determine the number of moles of \(\mathrm{CO}\) needed to react with a known amount of \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) ? \(\mathrm{mol} \mathrm{Fe}_{3} \mathrm{O}_{4} \times=\mathrm{mol} \mathrm{CO}\) (b) If you add more than enough \(\mathrm{CO}\) so that all the \(\mathrm{Fe}_{3} \mathrm{O}_{4}\) reacts, what mole ratio would you use in the following equation to determine the moles of \(\mathrm{CO}_{2}\) produced? \(\mathrm{mol} \mathrm{Fe}_{3} \mathrm{O}_{4} \times=\mathrm{mol} \mathrm{CO}_{2}\) (c) Suppose you know the number of moles of \(\mathrm{Fe}\) product formed and you want to know the number of moles of \(\mathrm{CO}\) that reacted. What mole ratio would you use in the following equation? \(\mathrm{mol} \mathrm{Fe} \times \overline{\mathrm{F}}=\mathrm{mol}\)

Short answer

The mole ratios used for the chemical reaction would be as follows: (a) mol Fe3O4 * 4 = mol CO, (b) mol Fe3O4 * 4 = mol CO2, and (c) mol Fe * 4/3 = mol CO.

Step-by-step solution

Identify Mole Ratio to Find Mole of CO

Use the provided balanced chemical reaction. It is given as: Fe3O4 + 4CO → 3Fe + 4CO2 The moles ratio of Fe3O4 to CO is 1:4. So, to react with every mole of Fe3O4, four moles of CO are needed. Therefore, the equation becomes: mol Fe3O4 * 4 = mol CO

Identify Mole Ratio to Find Mole of CO2

Again, using the balanced chemical reaction given. The mole ratio of Fe3O4 to CO2 is 1:4 again. This means that for every mole of Fe3O4 reacted, four moles of CO2 are produced. So, the equation becomes: mol Fe3O4 * 4 = mol CO2

Identify Mole Ratio to Find Mole of CO that Reacted Base on Mole of Fe

The chemical reaction also shows that the molar ratio of Fe produced to CO reacted is 3:4. This means that for every three moles of Fe produced, four moles of CO reacts. Using this molar ratio, if the moles of Fe produced are known, the number of moles of CO reacted can be determined from the equation: mol Fe * 4/3 = mol CO

Key concepts

Balanced Chemical Reaction

A balanced chemical reaction is fundamental for understanding the interactions between the reactants and products in any chemical process. In our exercise, the equation \(\mathrm{Fe}_{3}\mathrm{O}_{4}(s)+4 \mathrm{CO}(g) \longrightarrow 3 \mathrm{Fe}(s)+4 \mathrm{CO}_{2}(g)\)is balanced, meaning the number of each type of atom on the reactant side is equal to the number on the product side. This is crucial because it reflects the law of conservation of mass, which states that mass cannot be created or destroyed in a chemical reaction. This balance is achieved by adjusting the coefficients in front of the chemical formulas, which represent the proportions of molecules or moles involved. Understanding this allows us to accurately predict how much of one substance is needed to react fully with another.

Moles of Reactants

Moles are a standard unit in chemistry for counting particles, like atoms or molecules, and they are central to calculating the quantities in reactions. In the balanced equation, we see that one mole of \(\mathrm{Fe}_{3}\mathrm{O}_{4}\) reacts with four moles of \(\mathrm{CO}\). This mole ratio (1:4) guides us in determining how much carbon monoxide is required to completely react with a given amount of iron(III) oxide. This is particularly useful when solving problems requiring precise amounts of reactants to avoid waste or ensure completeness of the reaction. Thus, understanding these mole relations helps in scaling the reaction to any desired magnitude while ensuring that no reactant is left unconverted.

Moles of Products

After knowing how much reactants we started with, figuring out the moles of products formed is the next step. The balanced chemical reaction tells us that one mole of \(\mathrm{Fe}_{3}\mathrm{O}_{4}\) produces four moles of \(\mathrm{CO}_{2}\) and three moles of \(\mathrm{Fe}\). This mole ratio is crucial for calculating the yield of a reaction. If you started with a known quantity of \(\mathrm{Fe}_{3}\mathrm{O}_{4}\), you can directly use these ratios to predict the number of moles of each product formed under complete reaction conditions. This aspect of calculations plays a significant role in industrial chemistry, where maximizing the output of desired products is the primary goal.

Stoichiometry

Stoichiometry is the backbone of chemical quantitative analysis. It involves using the balanced chemical equation to compute the exact amounts of reactants required and products formed in a chemical reaction. By understanding stoichiometry, you can navigate through complex reactions by employing simple arithmetic based on mole ratios. For example, the exercise uses stoichiometry to find out how many moles of \(\mathrm{CO}\) would react with a known amount of \(\mathrm{Fe}_{3}\mathrm{O}_{4}\) or how many moles of \(\mathrm{CO}_{2}\) would be produced. It can also help in calculating leftovers in reactions, optimizing efficiency, and predicting yields, fundamentally ensuring that all components in a chemical system are accounted for and balanced.