Problem 91 - Chemistry: An Atoms-Focused Approach

Question

How many moles of \(\mathrm{O}_{2}\) are consumed in the conversion of one mole of \(\mathrm{FeCO}_{3}\) to each of the following compounds? Assume \(\mathrm{CO}_{2}\) is also produced. (a) \(\mathrm{Fe}_{2} \mathrm{O}_{3} ;\) (b) \(\mathrm{Fe}_{3} \mathrm{O}_{4}\)

Step-by-Step Solution

Answer

Question: Determine the number of moles of O₂ consumed when one mole of FeCO₃ is converted to (a) Fe₂O₃ and (b) Fe₃O₄. Answer: (a) In the conversion of one mole of FeCO₃ to Fe₂O₃, there are ¾ moles of O₂ consumed. (b) In the conversion of one mole of FeCO₃ to Fe₃O₄, there are 1/6 moles of O₂ consumed.

Step 1: Write balanced chemical equations for the conversions

First, let's write the balanced chemical equations for converting one mole of \(\mathrm{FeCO}_{3}\) to each of the following compounds. For the conversion of \(\text{FeCO}_3\) to \(\text{Fe}_2 \text{O}_3\): \(\text{FeCO}_3 + \text{O}_2 \rightarrow \text{Fe}_2 \text{O}_3 + \text{CO}_2\) For the conversion of \(\text{FeCO}_3\) to \(\text{Fe}_3 \text{O}_4\): \(3\text{FeCO}_3 + \text{O}_2 \rightarrow \text{Fe}_3 \text{O}_4 + 3\text{CO}_2\) Now let's balance these chemical equations. (a) \(2\text{FeCO}_3 + \cfrac{3}{2}\text{O}_2 \rightarrow \text{Fe}_2 \text{O}_3 + 2\text{CO}_2\) (b) \(3\text{FeCO}_3 + \cfrac{1}{2}\text{O}_2 \rightarrow \text{Fe}_{3}\text{O}_{4} + 3\text{CO}_2\)

Step 2: Find the moles of \(\text{O}_2\) consumed in each conversion

Now, we will use stoichiometry to determine the number of moles of \(\text{O}_2\) consumed for each of the conversions. (a) In the balanced chemical equation, \(2\text{FeCO}_3\) react with \(\cfrac{3}{2}\text{O}_2\). Since we're considering one mole of \(\text{FeCO}_3\), we can use a simple ratio to find the moles of \(\text{O}_2\) required. Moles of \(\text{O}_2 =\cfrac{1\cdot (\cfrac{3}{2})}{2}=\cfrac{3}{4}\) moles So, there are \(\cfrac{3}{4}\) moles of \(\mathrm{O}_{2}\) consumed in the conversion of one mole of \(\mathrm{FeCO}_{3}\) to \(\mathrm{Fe}_{2} \mathrm{O}_{3}\). (b) In the balanced chemical equation, \(3\text{FeCO}_3\) react with \(\cfrac{1}{2}\text{O}_2\). Since we're considering one mole of \(\text{FeCO}_3\), we can use a simple ratio to find the moles of \(\text{O}_2\) required. Moles of \(\text{O}_2 =\cfrac{1\cdot (\cfrac{1}{2})}{3}=\cfrac{1}{6}\) moles So, there are \(\cfrac{1}{6}\) moles of \(\mathrm{O}_{2}\) consumed in the conversion of one mole of \(\mathrm{FeCO}_{3}\) to \(\mathrm{Fe}_{3} \mathrm{O}_{4}\).

Key Concepts

Chemical Equations

Chemical equations are a way to represent chemical reactions using symbols for the substances involved. They show the conversion of reactants into products. For example, in our exercise,

• the conversion of \( \text{FeCO}_3 \) to \( \text{Fe}_2 \text{O}_3 \) can be represented by the equation: \( \text{FeCO}_3 + \text{O}_2 \rightarrow \text{Fe}_2 \text{O}_3 + \text{CO}_2 \).
• For \( \text{Fe}_3 \text{O}_4 \), it starts as: \( 3\text{FeCO}_3 + \text{O}_2 \rightarrow \text{Fe}_3 \text{O}_4 + 3\text{CO}_2 \).

These formulas show which substances start the reaction (reactants) and which substances are produced (products). Each formula within the equation is significant because it indicates the specific chemical makeup of the substances involved in the reaction. When writing chemical equations, it's crucial that they accurately reflect what occurs during the reaction. This can sometimes involve balancing the equation, which ensures that the amount of atoms for each element are the same on both sides of the equation.

Moles Calculation

Moles are a standard unit of measurement in chemistry that represent a specific number of molecules or atoms, precisely \(6.022 \times 10^{23}\) (Avogadro's number). Calculations involving moles allow chemists to quantify substances based on the number of particles rather than their mass.
In the context of our exercise, we were asked to determine how many moles of \(\text{O}_2\) are used when converting one mole of \(\text{FeCO}_3\) into other compounds.
When using stoichiometry, which is the calculation of reactants and products in chemical reactions, we're essentially using ratios derived from the balanced chemical equation to find out mole relationships.

• For example, in the conversion to \( \text{Fe}_2 \text{O}_3 \), the balanced equation allows us to calculate that \(\frac{3}{4}\) moles of \(\text{O}_2\) are consumed for every mole of \(\text{FeCO}_3\).
• Similarly, the conversion to \( \text{Fe}_3 \text{O}_4 \) requires \(\frac{1}{6}\) moles of \(\text{O}_2\) per mole of \(\text{FeCO}_3\).

This calculation is fundamental in chemical reactions to understand how reactants are consumed and products are formed based on the mole ratios from the balanced equation.

Balanced Reactions

Balanced reactions are essential in chemistry because they obey the Law of Conservation of Mass, which states that mass is neither created nor destroyed in a chemical reaction. This means the number of atoms for each element must be the same on both the reactant and product sides of the chemical equation.
Balancing involves altering the coefficients that precede each chemical formula, never the subscripts within the formulas.
Let's consider our exercise:

• For the reaction converting \( \text{FeCO}_3 \) to \( \text{Fe}_2 \text{O}_3 \), the balanced equation is \(2\text{FeCO}_3 + \frac{3}{2}\text{O}_2 \rightarrow \text{Fe}_2 \text{O}_3 + 2\text{CO}_2\).
• For \( \text{Fe}_3 \text{O}_4 \), it is \(3\text{FeCO}_3 + \frac{1}{2}\text{O}_2 \rightarrow \text{Fe}_3\text{O}_4 + 3\text{CO}_2\).

To balance these equations, notice how the number of atoms for iron (Fe), carbon (C), and oxygen (O) are kept equal on both sides. Balancing chemical reactions ensures that the resulting equation accurately represents what happens during a chemical process, which is crucial for accurate stoichiometric calculations.