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Chapter 4: Problem 52

Determine the amount of reaction (in moles) that takes place for each process $$ \frac{1}{2} \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s}) \longrightarrow \mathrm{FeO}(\mathrm{s})+\frac{1}{4} \mathrm{O}_{2}(\mathrm{~g}) $$ (a) \(2 \mathrm{~mol} \mathrm{O}_{2}\) forms (b) \(0.824 \mathrm{~mol} \mathrm{Fe}_{2} \mathrm{O}_{3}\) reacts (c) \(1.34 \mathrm{~g} \mathrm{FeO}\) forms

Short Answer

Expert verified
(a) 4 mol, (b) 0.824 mol, (c) 0.009325 mol.

Step by step solution

01

Determine Moles from Stoichiometry (Part a)

For part (a), we start with the formation of \(2 \text{ mol } \mathrm{O}_2\). From the balanced equation, for every \(\frac{1}{4} \text{ mol } \mathrm{O}_2\) formed, \(\frac{1}{2} \text{ mol } \mathrm{Fe}_2\mathrm{O}_3\) reacts. Therefore, for \(2 \text{ mol } \mathrm{O}_2\):\[\frac{2}{\frac{1}{4}} \times \frac{1}{2} = 4 \text{ mol } \mathrm{Fe}_2\mathrm{O}_3\] Thus, 4 moles of \(\mathrm{Fe}_2\mathrm{O}_3\) react.
02

Direct Mole Relation (Part b)

For part (b), we have \(0.824 \text{ mol } \mathrm{Fe}_2\mathrm{O}_3\) reacting directly as given. Therefore, the amount of reaction is simply the same, since we have \(\frac{1}{2} \text{ mol } \mathrm{Fe}_2\mathrm{O}_3\) reacting in this stoichiometry.Hence, 0.824 moles of reaction takes place.
03

Convert Grams to Moles (Part c)

For part (c), first we need to convert grams of \(\mathrm{FeO}\) to moles. The molar mass of \(\mathrm{FeO}\) is approximately 71.85 g/mol. From the equation:\[\text{Moles of } \mathrm{FeO} = \frac{1.34 \text{ g}}{71.85 \text{ g/mol}} \approx 0.01865 \text{ mol}\]According to the equation, for every \(1 \text{ mol } \mathrm{FeO}\) formed, \(\frac{1}{2} \text{ mol } \mathrm{Fe}_2\mathrm{O}_3\) reacts: \[0.01865 \text{ mol } \times \frac{1}{2} \approx 0.009325 \text{ mol}\]Thus, the reaction extent is approximately 0.009325 moles.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Chemical Reactions
Chemical reactions describe how substances change during a chemical process. They are expressed using chemical equations that show the reactants (starting materials) and products (end results). In the given exercise, the equation is balanced, meaning that the number of atoms of each element is the same on both sides.
Balanced equations follow the law of conservation of mass, ensuring mass is neither created nor destroyed. This provides a clear roadmap for understanding how much of each substance is involved. In our example, for every \(\frac{1}{2}\) mole of \(\mathrm{Fe}_2\mathrm{O}_3\) reacting, \(1\) mole of \(\mathrm{FeO}\) and \(\frac{1}{4}\) mole of \(\mathrm{O}_2\) is formed.
  • Reactants are the substances you start with. Here, it's \(\mathrm{Fe}_2\mathrm{O}_3\).
  • Products are what you end up with, like \(\mathrm{FeO}\) and \(\mathrm{O}_2\) in this case.
Understanding the relationships between reactants and products is crucial for predicting how much of each substance you'll need or produce in an experiment.
Molar Mass
Molar mass is a vital concept for calculating amounts of substances in chemical reactions. It represents the mass of one mole of a substance, typically expressed in grams per mole (g/mol).
To find the molar mass, sum the atomic masses of all atoms in a molecule, which you can find on the periodic table. For example:
  • The molar mass of \(\mathrm{FeO}\) is calculated by adding the atomic masses of iron (Fe) and oxygen (O), giving approximately 71.85 g/mol.
Molar mass acts as a bridge, translating between grams and moles. When you're given mass in grams, you can use molar mass to convert it to moles, a step crucial in stoichiometric calculations.
In the exercise, the molar mass of \(\mathrm{FeO}\) helps convert 1.34 g of \(\mathrm{FeO}\) into moles, making it possible to determine the amount of reaction occurring.
Conversion of Grams to Moles
Converting grams to moles is essential for solving stoichiometry problems. This conversion allows you to translate a measurable quantity (mass) into a countable quantity (moles), which is used in chemical equations.
Here鈥檚 how you do it:
  • Identify the mass of the substance in grams.
  • Use the molar mass (from the periodic table) to convert grams to moles using the formula: \[\text{Moles} = \frac{\text{grams}}{\text{molar mass in g/mol}}\]
In the step-by-step solution, 1.34 g of \(\mathrm{FeO}\) is converted to moles using its molar mass (71.85 g/mol), resulting in approximately 0.01865 moles.
This conversion reveals how much of a reactant is involved, allowing you to use stoichiometry to find out other amounts in the reaction. It simplifies the complex process of transformation in reactions.

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Most popular questions from this chapter

You want to heat the air in your house with natural gas, \(\mathrm{CH}_{4}\). Assume your house has \(275 \mathrm{~m}^{2}\) (about \(2800 \mathrm{ft}^{2}\) ) of floor area and that the ceilings are \(2.50 \mathrm{~m}\) (about \(8 \mathrm{ft}\) ) from the floors. The air in the house has a molar heat capacity of \(29.1 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\). (The number of moles of air in the house can be found by assuming that the average molar mass of air is \(28.9 \mathrm{~g} / \mathrm{mol}\) and that the density of air at these temperatures is \(1.22 \mathrm{~g} / \mathrm{L}\). ) Calculate what mass of methane you have to burn to heat the air from \(15.0^{\circ} \mathrm{C}\) to \(22.0^{\circ} \mathrm{C}\)

Chloromethane, \(\mathrm{CH}_{3} \mathrm{Cl}\), arises from microbial fermentation and is found throughout the environment. It is also produced industrially and is used in the manufacture of various chemicals and has been used as a topical anesthetic. Calculate how much energy is required to convert \(92.5 \mathrm{~g}\) liquid to a vapor at its boiling point, \(-24.09^{\circ} \mathrm{C}\). (The heat of vaporization of \(\mathrm{CH}_{3} \mathrm{Cl}\) is \(21.40 \mathrm{~kJ} / \mathrm{mol}\).)

The specific heat capacity of benzene, \(\mathrm{C}_{6} \mathrm{H}_{6},\) is 1.74 J \(\mathrm{g}^{-1} \mathrm{~K}^{-1}\). Calculate its molar heat capacity.

A diamond can be considered a giant all-carbon supermolecule in which almost every carbon atom is bonded to four other carbons. When a diamond cutter cleaves (splits) a diamond, carbon-carbon bonds must be broken. Is the cleavage (splitting) of a diamond endothermic or exothermic? Explain.

Acetic acid, \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H},\) is made industrially by the reaction of methanol and carbon monoxide. \(\mathrm{CH}_{3} \mathrm{OH}(\ell)+\mathrm{CO}(\mathrm{g}) \longrightarrow \mathrm{CH}_{3} \mathrm{COOH}(\ell)\) $$ \Delta_{\mathrm{r}} H^{\circ}=-135.3 \mathrm{~kJ} / \mathrm{mol} $$ If you produce \(1.00 \mathrm{~L}\) acetic acid \((d=1.044 \mathrm{~g} / \mathrm{mL})\) by this reaction, calculate how much energy is transferred out of the system.
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