Chemistry: A Self-Teaching Guide - Post R., Snyder C., Houk C.C. 2020


Mole Concept

Just as a dozen is 12 and a gross is 144, a mole of any kind of particle is 6.022 × 1023 of the particles. The weight of a dozen eggs is not the same as the weight of a dozen oranges. Likewise, the weight of a mole of atoms of one element is not the same as the weight of a mole of atoms of another element. The weight of a mole of any kind of particle or unit, expressed in grams, is numerically the same as the weight of one of the individual particles or units, expressed in atomic mass units (amu).

The following are three examples of the mole concept.

1. From the table of atomic weights, the atomic weight of hydrogen is given as 1.008. This means that one H atom has a weight equal to 1.008 amu. It also means that the weight of 1 mole of H atoms is 1.008 grams. The weight of a single H atom is 1.674 × 10−24 grams. That is, 1.008 grams is the total weight of 6.022 × 1023 H atoms; therefore, the weight of one H atom is 1.008 grams divided by 6.022 × 1023, which gives 1.674 × 10−24 grams.

2. The formula H2 for elementary hydrogen means that each hydrogen molecule consists of two H atoms. The weight of two H atoms is 2 × 1.008 amu = 2.016 amu. The weight of 1 mole of H2 molecules is, therefore, 2.016 grams. The weight of a single H2 molecule is 3.348 × 10−24 grams.

3. The formula Image for a nitrate ion means that the ion consists of one nitrogen atom and three oxygen atoms (together with an additional electron that gives the ion its charge but does not contribute significantly to the weight within the range of our precision limits here). The weight of a nitrate ion is, therefore, the weight of one nitrogen atom plus the weight of three oxygen atoms, or 62.01 amu (to the nearest hundredth). The weight of 1 mole of nitrate ions is, therefore, 62.01 grams, and the weight of an individual nitrate ion is 1.03 × 10−22 grams.

In the past, problems involving chemical reactions have been called mass—mass, mass—volume, or volume—volume problems and have been solved using algebraic ratios or proportions. We feel the solution of these problems using the mole concept is superior and fosters a better understanding of what goes on in a reaction than ratio/proportion solving.

The problem solving presented here uses solely the mole concept when we are dealing with chemical reactions. A chemist, chemical engineer, or metallurgist uses this technique to answer very important questions, such as how much raw material will be required to produce a specified quantity of product. Management then uses the cost of those materials and labor, along with other production costs, to determine the price of the product.

OBJECTIVES

After completing this chapter you will be able to calculate the weight or number of moles of any reactant or product that will be used up (if a reactant) or produced (if a product) given a completely balanced chemical equation, a table of atomic weights, and a specified quantity (weight or moles) of any one reactant or product.

Image Remember, a mole is 6.022 × 1023 (Avogadro's number) particles such as atoms, ions, or molecules. The weight of this number of particles is expressed in grams. A mole of hydrogen ions (H+) contains how many hydrogen ions? _______ How much do they weigh? ________ (Calculate answers in this chapter to the nearest hundredth unless otherwise indicated.)

Answer: 6.022 × 1023; 1.01 grams

Image Unless otherwise stated, the term mole means the same as the term gram-mole. A gram-mole is the weight of 6.022 × 1023 particles expressed in grams. A gram-mole of atoms is equivalent to the atomic weight expressed in grams.

One mole of carbon atoms (C) weighs how many grams? ________. The atomic weight of carbon is how many grams? _______

Answer: 12.01; 12.01

Image One mole of the element lead (Pb) contains _________________ atoms and weighs _____________________________.

Answer: 6.022 × 1023; 207.2 grams

Image How many atoms of carbon and sulfur are needed to make one molecule of carbon disulfide (CS2)? ________________

Answer: one atom of C and two atoms of S

Image In calculations, the abbreviation mol means mole or moles. To make 1 mol of carbon disulfide (CS2) molecules requires how many moles of carbon atoms and sulfur atoms? __________________

Answer: 1 mol of C and 2 mol of S

Image One mole of carbon tetrachloride (CCl4) requires how many moles of C atoms and how many moles of Cl atoms? ____________

Answer: 1 mol of C and 4 mol of Cl

Image Since 4 moles of Cl atoms and 1 mole of C atoms make up 1 mole of CCl4, what does 1 mole of CCl4 molecules weigh? _____________

Answer: 153.81 grams (Remember to express the answer in grams.)

Image Half a mole of H2SO4 weighs how many grams?

Answer: ImageImage

Image Thirty-six grams of H2O represent how many moles? ___________

Answer: Image

Image Nine grams of H2O represent how many moles? _________

Answer: Image

Image One formula weight of methyl alcohol (CH3OH) is 32.05 grams. Half a gram of CH3OH represents how many moles (to the nearest thousandth)? __________

Answer: Image

Image A mole of Na atoms is 22.99 grams. A mole of Cl atoms is 35.45 grams. A mole of NaCl molecules is 58.44 grams. Which weighs more, a mole of Cl atoms or a mole of Na atoms? ____________

Answer: a mole of Cl atoms

Now that you understand what a mole of a substance is, let's apply the concept to some reactions.

Image In the balanced reaction Zn + 2HCl → H2 + ZnCl2, when zinc metal reacts with hydrochloric acid, hydrogen gas and zinc chloride are the products. How many moles of HCl are needed to produce 1 mole of ZnCl2? _____________

Answer: 2

Image Suppose that in the previous reaction, only half a mole of Zn was available. How many moles of ZnCl2 could be produced? __________ How many moles of HCl would be used up? __________

Answer: ½; 1

Image Suppose that only ⅓ mole of Zn was available. How many moles of ZnCl2 would be produced? __________ How many moles of HCl would be used up? _________

Answer: ⅓; ⅔

Image The reaction 2KClO3 → 2KCl + 3O2 is often used in the laboratory to produce oxygen gas. In this reaction, 2 moles of KClO3 are required to produce 2 moles of KCl and 3 moles of O2. If 2 moles of KClO3 are reacted until completely consumed, how much oxygen (O2) by weight would be produced? (Remember that oxygen gas exists as a diatomic molecule and that 3 moles of O2 molecules weighs the same as 6 moles of O atoms.) ________________________

Answer: Image

Image Express the following weights to the nearest tenth.

1. 2 moles of KClO3 weigh __________ grams.

2. 2 moles of KCl weigh __________ grams.

3. 3 moles of O2 weigh __________ grams.

Answer: (a) 245.1; (b) 149.1; (c) 96.0

Image If only 122.6 grams of KClO3 are available, how many moles of KCl and O2 would be produced? (First, convert grams of KClO3 to moles of KClO3.)

· moles of KCl = ____________________________

· moles of O2 = ____________________

Answer: Image

2 mol KClO3 produced 2 mol KCI and 3 mol O2 (from frame 16)

∴ 1 mol KClO3 will produce 1 mol KCI and 1.5 mol O2 (Throughout this book, we will use the symbol ∴ for the word “therefore.”)

Image If only 122.6 grams of KClO3 are available, how many grams of KCl and O2 would be produced (to the nearest tenth)?

· grams of KCl = ______________

· grams of O2 = ______________

Answer: From frame 18, 1 mol KCI and 1.5 mol O2 are produced.

Image

Image If only 24.5 grams of KClO3 are available, how many moles of KClO3 are available?

Answer: Image

Image If only 24.5 grams of KClO3 are available, how many moles of KCl and O2 would be produced? (First convert grams of KClO3 to moles of KClO3 as you did in frame 18.)

· mol KCl ________________

· mol O2 ________________

How many grams of O2 would be produced (to the nearest tenth)? ____________

Answer:

Image

Image 2Fe + 3Cl2 → 2FeCl3

1. 2 moles of of Fe weighs __________ grams.

2. 3 moles of of Cl2 weighs __________ grams.

3. 2 moles of of FeCl3 weighs __________ grams.

Answer: (a) 111.70; (b) 212.70; (c) 324.40

Image How many moles of iron (Fe) and chlorine gas (Cl2) are required to produce 32.44 grams of FeCl3? (First convert grams of FeCl3 to moles of FeCl3.)

· moles of Fe _________________

· moles of Cl2 _____________________

Answer: Image

1 mol Fe and 1.5 mol Cl2 will produce 1 mol FeCl3

∴ 0.20 mol FeCl3 will require 0.20 mol Fe and 0.30 mol Cl2

Image In the reaction 2H2 + O2 → 2H2O, if 360.4 grams of water are produced, how many moles of H2 and of O2 are required? How many grams of O2 are required?

1. moles of H2 ____________________

2. moles of O2 ________________

3. grams of O2 ___________________

Answer:

Image

LIMITING REACTANT

For many real-life chemical reactions, one or more of the reactants is limited in quantity. For example, when a car burns 1 gallon of gasoline, the gasoline reacts with oxygen from the air and, while the engine runs, produces chemical reaction products, such as CO (carbon monoxide) and H2O, as well as some others. After the gallon of gasoline is all used up, there is still plenty of oxygen in the air. In fact, after a whole tank full of gasoline is burned, there is still plenty of oxygen in the air. The limiting reactant in this case is the gasoline. It is completely consumed in the reaction.

Image For the reaction C + O2 → CO2, only 3 grams of carbon (C) are available, but there is plenty of oxygen.

1. Which reactant is the limiting reactant, C or O2? ____________

2. How many grams of CO2 could be produced? ______________

Answer:

1. C

2. Image

Image Only 4.01 grams of methane (CH4) are available for the reaction CH4 + 2O2 → CO2 + 2H2O. There is plenty of oxygen.

1. Which reactant is the limiting reactant? ______________

2. How many grams of H2O will be formed? ___________

Answer:

1. CH4

2. 9.01 g H2O

The weight of 1 mol CH4 = 12.01 g + (4 × 1.01 g) = 16.05 g

Image

1 mol CH4 will produce 2 mol H2O∴0.25 mol CH4 will produce 0.5 mol H2O

Image

Image For the following reaction, 18.02 grams of water are produced and all of the silane (SiH4) is used up, although oxygen is still available after the reaction: SiH4 + 2O2 → SiO2 + 2H2O.

1. How many moles of silane (SiH4) are used up? _________

2. What is the limiting reactant? __________

Answer: (a) 0.50 mol SiH4; (b) silane (SiH4)

Image After the following reaction, all of the oxygen is used up in the reaction vessel and 60.09 grams of SiO2 are produced. The reaction is SiH4 + 2O2 → SiO2 + 2H2O.

1. What weight of silane (SiH4) was used up? _______________

2. Which do you think is the limiting reactant? ___________________

Answer: (a) 32.13 g SiH4; (b) Since the oxygen was all used up, it is the limiting reactant. We can assume that some silane still exists in the reaction vessel.

You have just learned how to use the mole concept to solve problems that deal with chemical reactions. You would be able to tell a producer of vinyl chloride how much chlorine would be needed to prepare 1 million pounds of vinyl chloride or a headache remedy producer how much salicylic acid is needed to produce 10 million pounds of acetylsalicylic acid (aspirin), provided you know the formulas of the reactants and the products and their combining ratios as indicated in a balanced chemical equation.

Understanding the mole concept is of utmost importance. You will encounter its use frequently in any chemistry course and in the chapters that follow in this book.

SELF-TEST

This self-test is designed to show how well you have mastered this chapter's objectives. Correct answers and review instructions follow the test. Round answers to the nearest hundredth.

1. How many moles of each atom are in

1. 1.00 moles of CH4. ______________

2. 1.00 moles of H3PO4. _____________________

3. 2.00 moles of glucose (C6H12O6). ___________

2. How many moles of each atom are in

1. 1.50 moles of NH3. ______________

2. 2.00 moles of H2CO3. _____________________

3. 1.00 moles of sucrose (C12H22O11). ___________

3. Express the following weights to the nearest tenth.

1. 4.0 moles of C2H6 weigh ________ grams.

2. 4.0 moles of C3H8 weigh ________ grams.

3. 4.0 moles of C4H10 weigh ________ grams.

4. Express the following weights to the nearest tenth.

1. 1.8 moles of O3 weigh ________ grams.

2. 3.2 moles of NO2 weigh ________ grams.

3. 5.6 moles of HNO3 weigh ________ grams.

5. Express the following moles to the nearest hundredth.

1. 44.2 grams of Cl2 is equal to ______ moles of Cl2.

2. 541.0 grams of S8 is equal to ______ moles of S8.

3. 65.7 grams of H2O is equal to ______ moles of H2O

6. Express the following moles to the nearest hundredth.

1. 11.3 grams of H2 is equal to ______ moles of H2.

2. 755.0 grams of P4 is equal to ______ moles of P4.

3. 89.9 grams of CH2O is equal to ______ moles of CH2O

7. Consider the following balanced reaction for the burning of glucose (C6H12O6):

Image

Determine the mole-to-mole ratio that is incorrect:

Image

8. Consider the following balanced reaction for the decomposition of ammonia (NH3) to nitrogen and hydrogen gas: 2NH3 → N2 + 3H2

Determine the mole-to-mole ratio that is incorrect:

Image

9. Using the balanced equation for the reaction of hydrochloric acid with magnesium hydroxide, determine the amount of water produced if 4.5 moles of HCl are completely reacted.

10. Using the balanced equation for the combustion of glucose in question 7, determine the amount (number of moles) of C6H12O6 required to produce 18.0 moles of CO2.

11. Iron metal reacts with oxygen to produce iron(III) oxide, commonly known as rust. If 2.40 moles of iron are completely reacted with excess oxygen, how much iron(III) oxide, in grams, is produced?

12. Consider the balanced equation in question 11. How many grams of iron are required to produce 10.7 grams of Fe2O3?

13. In the following reaction, 4 moles of oxygen (O2) molecules are completely consumed to produce water. There is still some hydrogen left in the reaction vessel after the reaction.

Image

1. How many moles of water (H2O) are formed?______________________

2. What weight of water is formed?_____________

3. Which reactant is the limiting reactant?_____________

14. In the following reaction, 16.02 grams of methyl alcohol (CH3OH) are burned in open air:

Image

1. How many moles of oxygen (O2) are used up?_______

2. How many grams of water (H2O) are formed?_____

3. Which reactant is the limiting reactant?___________

ANSWERS

Compare your answers to the self-test with those given below. If you answer all questions correctly, you are ready to proceed to the next chapter. If you miss any, review the frames indicated in parentheses following the answers. If you miss several questions, you should probably reread the chapter carefully.

1.

1. 1.00 mol C and 4.00 mol H

2. 3.00 mol H, 1.00 mol P, and 4.00 mol O

3. 12.00 mol C, 24.00 mol H, and 12.00 mol O (frames 4—6)

2.

1. 1.50 mol N and 4.50 mol H

2. 4.00 mol H, 2.00 mol C, and 6.00 mol O

3. 12.00 mol C, 22.00 mol H, and 11.00 mol O (frames 4—6)

3. In order to get the mass in grams, multiply the amount of moles by the formula weight of the substance: (grams of substance = moles of substance × formula weight of substance)

1. 120.3 g C2H6

2. 176.4 g C3H8

3. 232.5 g C4H10 (frames 8—24)

4. In order to get the mass in grams, multiply the amount of moles by the formula weight of the substance: (grams of substance = moles of substance × formula weight of substance)

1. 86.4 g O3

2. 147.2 g NO2

3. 352.9 g HNO3 (frames 8—24)

5. In order to get the moles of substance, divide the grams of substance by the formula weight of the substance: (moles of substance = grams of substance/formula weight of substance)

1. 0.62 mol Cl2

2. 2.11 mol S8

3. 3.65 mol H2O (frames 8—24)

6. In order to get the moles of substance divide the grams of substance by the formula weight of the substance: (moles of substance = grams of substance/formula weight of substance)

1. 5.61 mol H2

2. 6.09 mol P4

3. 2.99 mol CH2O (frames 8—24)

7. Image (frames 13—15)

8. Image (frames 13—15)

9. The balanced reaction 2HCl + Mg(OH)2 → 2H2O + MgCl2 shows that for every 2 moles of HCl used, there are 2 moles of water produced. Therefore, 4.5 moles of HCl yields 4.5 moles of water. (frames 13—15)

10. The balanced reaction C6H12O6 + 6O2 → 6H2O + 6CO2 shows that for every 1 mole of glucose used, 6 moles of carbon dioxide are produced. Therefore, producing 18.0 moles of CO2 requires 3.0 moles of glucose. (frames 13—15)

11. Image

Image (frames 18—24)

12. Image (frame 18—24)

13. 1 mol O2 produces 2 mol H2O.

1. ∴ 4 mol O2 produces 8 mol H2O.

2. Image

3. O2 (frames 13—16, 28)

14. Image

2 mol CH3OH uses 3 mol O2 and produces 4 mol H2O.

1. ∴ 0.50 mol uses 0.75 mol O2 and produces 1 mol H2O.

2. Image.

3. CH3OH is the limiting reactant, since there is plenty of oxygen left after the reaction (the reaction takes place in open air). (frames 18—21, 25—27)