/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 99 An iron bar weighed \(664 \mathr... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

An iron bar weighed \(664 \mathrm{~g}\). After the bar had been standing in moist air for a month, exactly one-eighth of the iron turned to rust \(\left(\mathrm{Fe}_{2} \mathrm{O}_{3}\right)\). Calculate the final mass of the iron bar and rust.

Short Answer

Expert verified
The final mass of the iron bar and rust is 699.4 grams.

Step by step solution

01

Understanding the Conversion

Initially, the iron bar weighs 664 grams. Out of this, one-eighth has oxidized to form rust, which is Fe₂O₃ (Iron (III) oxide). Our task is to calculate the final mass combining the remaining iron and the rust.
02

Calculating the Mass of Rust

Determine the mass of one-eighth of the iron that turned to rust. So, \[\text{Mass of oxidized iron} = \frac{664}{8} = 83 \text{ grams}\]
03

Understanding the Chemical Reaction

Iron oxidizes according to the reaction: \[4\mathrm{Fe} + 3\mathrm{O}_2 \rightarrow 2\mathrm{Fe}_2\mathrm{O}_3\]From this, you can see that 4 moles of Fe react to form 2 moles of Fe₂O₃.
04

Moles and Molar Mass Conversion

Convert grams of iron to moles using iron's molar mass (approximately 56 g/mol):\[\mathbf{Moles~of~iron} = \frac{83}{56} \approx 1.48 \text{ moles}\]
05

Calculating Moles of Fe₂O₃

With the reaction stoichiometry, for every 4 moles of Fe, 2 moles of Fe₂O₃ are produced. So:\[\text{Moles of}~\mathrm{Fe}_2\mathrm{O}_3 = \left(\frac{1.48}{4}\right) \times 2 = 0.74 \text{ moles}\]
06

Converting Moles of Fe₂O₃ to Grams

Calculate the mass of 0.74 moles of Fe₂O₃ using its molar mass (approximately 160 g/mol):\[\text{Mass of}~\mathrm{Fe}_2\mathrm{O}_3 = 0.74 \times 160 = 118.4 \text{ grams}\]
07

Calculating Final Mass

The final mass of the iron bar (after rust formation) is the sum of the remaining iron and rust. The remaining iron (after oxidation) is:\[664 - 83 = 581 \text{ grams}\]Thus, the total (iron + rust) is:\[581 + 118.4 = 699.4 \text{ grams}\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Chemical Reactions
A chemical reaction is a process where substances, also known as reactants, are transformed into different substances called products. The changes occur at the molecular level and involve the making and breaking of chemical bonds. In the context of rust formation, the iron from the bar reacts with oxygen in the moist air to form iron oxide, commonly seen as rust.
This reaction is classified as an oxidation reaction, where the iron ( Fe ) loses electrons to oxygen ( O_2 ). The chemical reaction that describes rust formation is:
  • 4Fe + 3Oâ‚‚ → 2Feâ‚‚O₃
This equation shows that four iron atoms react with three oxygen molecules to produce two units of iron oxide. Remember, chemical reactions like this need to be balanced to ensure that the number of each atom on the reactants side equals the number in the products.
Stoichiometry
Stoichiometry is a branch of chemistry that deals with the measurement and calculation of elements in chemical reactions. It helps predict the amount of products that can form from given reactants. In the rust formation, stoichiometry tells us the ratios in which molecules and atoms react.
For instance, using the balanced equation for rust formation
  • 4Fe + 3Oâ‚‚ → 2Feâ‚‚O₃
we see that 4 moles of iron react with 3 moles of oxygen to form 2 moles of iron oxide. This ratio helps us calculate specific amounts—such as how much rust results from a certain amount of iron. In calculations, we use these mole ratios to determine the moles of rust formed from moles of iron, converting between substances in a reaction.
Molar Mass
Molar mass is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). It serves as a bridge between chemical equations and laboratory measurements. For rust formation, we consider the molar masses of iron and iron(III) oxide.
Iron (Fe) has a molar mass of approximately 56 g/mol, while iron(III) oxide (Fe₂O₃) has a molar mass of about 160 g/mol. These values are crucial when converting grams to moles in our calculations. For example, if you have 83 grams of oxidized iron, you convert it to moles using iron's molar mass:
  • Moles of iron = 83 g / 56 g/mol ≈ 1.48 moles
Analyzing these conversions is vital to understand how much of each substance is involved in a reaction.
Oxidation of Iron
The oxidation of iron is a specific chemical process where iron atoms lose electrons, reacting to form iron oxide. It involves the exposure of iron to oxygen over time, often accelerated in humid conditions, leading to rust.
The process is an example of oxidation, a key type of redox (reduction-oxidation) reaction. In this case, iron is oxidized and oxygen is reduced, forming rust:
  • 4Fe + 3Oâ‚‚ → 2Feâ‚‚O₃
This reaction explains the transformation observed in the exercise, where one-eighth of the iron bar was converted to rust. Understanding oxidation helps us comprehend why iron tarnishes and how to mitigate these effects in practical applications.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

(a) A research chemist used a mass spectrometer to study the two isotopes of an element. Over time, she recorded a number of mass spectra of these isotopes. On analysis, she noticed that the ratio of the taller peak (the more abundant isotope) to the shorter peak (the less abundant isotope) gradually increased with time. Assuming that the mass spectrometer was functioning normally, what do you think was causing this change? (b) Mass spectrometry can be used to identify the formulas of molecules having small molecular masses. To illustrate this point, identify the molecule which most likely accounts for the observation of a peak in a mass spectrum at: 16 amu, \(17 \mathrm{amu}, 18 \mathrm{amu},\) and 64 amu. (c) Note that there are (among others) two likely molecules that would give rise to a peak at 44 amu, namely, \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2} .\) In such cases, a chemist might try to look for other pea generated when some of the molecules break apart in the spectrometer. For example, if a chemist sees a peak at 44 amu and also one at 15 amu, which molecule is producing the 44 amu peak? Why? (d) Using the following precise atomic masses: \({ }^{1} \mathrm{H}(1.00797 \mathrm{amu}),{ }^{12} \mathrm{C}(12.00000 \mathrm{amu}),\) and \({ }^{16} \mathrm{O}(15.99491 \mathrm{amu}),\) how precisely must the masses of \(\mathrm{C}_{3} \mathrm{H}_{8}\) and \(\mathrm{CO}_{2}\) be measured to distinguish between them? (e) Every year millions of dollars' worth of gold is stolen. In most cases the gold is melted down and shipped abroad. This way the gold retains its value while losing all means of identification. Gold is a highly unreactive metal that exists in nature in the uncombined form. During the mineralization of gold, that is, the formation of gold nuggets from microscopic gold particles, various elements such as cadmium (Cd), lead (Pb), and zinc (Zn) are incorporated into the nuggets. The amounts and types of the impurities or trace elements in gold vary according to the location where it was mined. Based on this knowledge, describe how you would identify the source of a piece of gold suspected of being stolen from Fort Knox, the federal gold depository.

The annual production of sulfur dioxide from burning coal and fossil fuels, auto exhaust, and other sources is about 26 million tons. The equation for the reaction is $$ \mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g) $$ How much sulfur (in tons), present in the original materials, would result in that quantity of \(\mathrm{SO}_{2} ?\)

What is the molar mass of an atom? What are the commonly used units for molar mass?

Write the symbols used to represent gas, liquid, solid, and the aqueous phase in chemical equations.

Why is the theoretical yield of a reaction determined only by the amount of the limiting reagent?

See all solutions

Recommended explanations on Chemistry Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.