The mole is used so commonly in chemistry to measure the amount of an element or compound that it is sometimes elevated to the level of a concept. In fact, it is just a definition, in the same way that the term ream is defined as 500 sheets of paper or a dozen is defined as 12. Because the mole is part of the everyday language of chemistry we must become entirely familiar with its use. We begin with its origin in atomic weights.
In the 18th and 19th centuries, chemists began to explore weight relationships between the elements. During that period, combining weights were determined. (The term mass is preferred, but we will frequently use weight and mass interchangeably.) Let's pretend that we are working in a 19th-centruy lab and have just carried out a reaction between zinc and sulfur. Specifically, we mixed 65 grams of elemental zinc with 40 grams of elemental sulfur and heated them in a crucible for several hours. We then dissolved the excess sulfur in methylene chloride. The material that remained after the excess sulfur has been removed showed no sign of elemental zinc and weighed 97 grams.
Thus, in this reaction the combining weights of zinc and sulfur are 65 g and 32 g. The significance of these combining weights became clear in the early 1800's when Dalton proposed that all matter consists of atoms and that reactions involve the combinations of these atoms in whole number ratios. Dalton also assumed that all atoms of the same element have the same mass (an assumption we now know is incorrect).
If we know that one atom of sulfur combines with one atom of zinc in forming the compound zinc sulfide, we can assume that if 32 g of sulfur react with 65 g of zinc, then an atom of zinc is 65/32 times heavier than an atom of sulfur. The following chemical equation represents this reaction:
Zn + S → ZnS
In this equation the symbols for the elements are used to represent the elemental forms, and the compound is written as ZnS to indicate that there is a one to one ratio of zinc and sulfur atoms. We can read the equation as "One atom of elemental zinc reacts or combines with one atom of elemental sulfur to form the compound zinc sulfide."
Suppose that it were true that one atom of zinc combines with two atoms of sulfur. Which of the following represents this reaction?
Assuming that the same weights of each element--65 g zinc and 32 g sulfur--were consumed in this reaction of one atom of zinc with two atoms of sulfur, what would be the combining weight of sulfur?
Atoms of different elements combine with sulfur (and other elements) in different ratios. For example, silicon combines with two sulfur atoms (the formula of silicon sulfide is SiS2); two atoms of sodium combine with one atom of sulfur (the formula of sodium sulfide is Na2S). Thus, it is important to determine the ratio of atoms in each compound. We will not pursue this here, but methods such as the use of the combining volumes of gases can provide this kind of information.
So, let us assume that eventually we put together a list of relative weights of atoms, such as the following:
Because hydrogen is the lightest element, let us assign it a weight of 1. Calculate the combining weights of the other elements relative to hydrogen. Your table should now look like this:
According to your new table, how much heavier is an atom of carbon than an atom of boron?
What mass of silver contains the same number of atoms as 12 g of carbon?
What mass of silver contains the same number of atoms as 6 g of carbon?
Near the beginning of the 20th century, mass spectrometers, which allowed chemists to determine the mass of individual atoms, were produced. Several important observations followed the use of this instrument. First, it is was found that not all atoms of the same element have the same mass. (This is why we have used the phrase "average atom" above.) Atoms of the same element that have different masses are called isotopes. For example, there are two important isotopes of boron; both have 5 protons in the nucleusRemember that the nucleus of the atom contains protons, which are positively charged, and neutrons, which have no charge. These two nuclear particles are sometimes called nucleons and they have almost identical masses. The number of protons in the nucleus is called the atomic number of the element. This number distinquishes one element from another. For example, two elements, such as boron and nitrogen, could have the same number of neutrons or they could have the same number of electrons, but boron will always have 5 protons in the nucleus and nitrogen will always have 7 protons in the nucleus., but one has 5 neutrons in the nucleus while the other has 6 neutrons. The sum of the number of protons and neutrons in the nucleus is called the mass number of the isotope. This number is designated as a superscript before the symbolChemists use a type of shorthand to write and talk about the different elements. The element is represented by its chemical symbol, usually the first or first two letters in the element's name. For example, the symbol for fluorine is F, that for carbon is C. Sometimes the first two letters of the element's Latin name are used; such as Au for gold (from aurus) and Pb for lead (from plumbus). of the element. For example, the isotope of boron with 6 protons is designated as 11B.
The electron is the other particle in the atom that is of great interest to the chemist. The electrons are outside of the nucleus, they are negatively charged, and they have a much smaller mass than either the proton or the neutron. The charge on an electron is equal to, but opposite in sign, to the charge on a proton. Consequently, in a neutral atom the number of electrons is equal to the number of protons.
|57 - 71||72
|89 - 103||104
Which of the following isotopes has 6 protons and 7 neutrons in the nucleus?
Naturally occurring chlorine is made up of two isotopes, one with two more neutrons that the other. If the lighter isotopes has a mass number of 35, what is the correct symbol of the other isotope?
An isotope of some element has 70 neutrons in its nuclues and a mass number of 120. What is the element?
After the discovery of isotopes and a means for accurate measurement of the relative mass of these isotopes, it was decided that the mass of the 12C isotope should be defined as exactly 12.0000 atomic mass units (amu).
How would you define one amu?
Protons and neutrons have very nearly the same mass. The mass of the electron is about 2000 times less than that of a proton or neutron.
What is the approximate mass of a proton (and a neutron) in amu units?
What is the approximate mass of one 13C atom?
What is the approximate mass of two atoms of 29Si?
Suppose that it was decided to design a new system of atomic weights in which a 12C atom no longer weighed 12 amu, but rather the mass of a 12C atom would be defined as 1.00 amu. In this system, what would be the mass of a 16O atom?
Naturally-occuring carbon is 99% 12C and 1% 13C. If you had 99 12C atoms and one 13C atom, what would be the mass of the 99 12C atoms and the one 13C atom?
Now, determine the averageAn average, also called a mean, is calculated by dividing the sum of all of the data points in a set of values by the number of values. Suppose you had the following set of numbers that represent the length of time, in seconds, that you can hold your breath under water: 24, 29, 26, 28, and 28. The sum of these 5 numbers is 135, which we divide by 5 to get 27 s. This number is a better representation of the amount of time you are able to hold your breath than any of the individual numbers. mass of these one hundred atoms.
Sometimes, we may want to take a weighted average. Actually, all averages are weighted, but for an ordinary average every value in the set has the same weighting. For example, in the set above, each value counts 20% (one-fifth) toward the average. Indeed, we could determine the average by doing the calculation as follows:
0.20 x 24 + 0.20 x 29 + 0.20 x 26 + 0.20 x 28 + 0.20 x 28 =
4.8 + 5.8 + 5.2 + 5.6 + 5.6 = 27 s
Suppose that while you were measuring the times, you felt that the 24 second value was not a particularly good value. Perhaps this value was obtained while your brother did a cannonball in front of you. Likewise, one of the 28 second values was obtained when your chemistry teacher was walking by and probably was not a really representative value (you were trying to stay under water as long as possible). Because you don't want to exclude these values entirely, you decide to weight them differently. Perhaps you decide to weight the 24 second value only 5% (0.05) and one of the 28 second values you weight only 10% (0.10). These two points therefore contribute 15% (0.15) to the average. You want the weighting of the other values to be equal to one another so each of the other 3 must have a weighting of (100-15)/3 = 28.3%. Now your calculation will look like this:
0.05 x 24 + 0.283 x 29 + 0.283 x 26 + 0.15 x 28 + 0.283 x 28 =
1.2 + 8.2 + 7.4 + 4.2 + 7.9 = 28.9 s
Certainly, the different weightings have affected the mean.
A glance at a periodic chart will show you that the atomic mass of carbon is given as 12.01. Notice also, that there are no units on the atomic masses given on the chart. You now realize that every atomic mass shown on the periodic chart is an average for a large number of isotopes.
Let's try the calculation of the atomic mass of argon for which there are three naturally occuring isotopes: 36Ar, 38Ar, and 40Ar. The percentages of these isotopes are: 0.34%, 0.07%, and 99.58%, respectively. Calculate the atomic mass of argon. Hint: a) You can choose the correct answer without having to use your calculator, and b) This is where you use the weighted average.
Chlorine exists as two isotopes: 35Cl with a mass of 34.97 and 37Cl with a mass of 36.95. The atomic weight of chlorine is 35.453. What is the percentage of each of the isotopes?
We now have two different interpretations of the atomic masses: 1) they represent the mass of the average atom of an element in amu's, given the convention that the mass of 12C is exactly 12 amu, and 2) they represent the relative combining masses of the elements.
Perhaps we should expand on the second interpretation. If you wanted to make the compound carbon dioxide from carbon and oxygen you first need to know that the formula of this compound is CO2. The subscripts after the symbol for each element give the ratio of atoms present in the compound. In the case of CO2, the subscript 2 for oxygen tells us that two oxygen atoms are present for every one atom of carbon (the absence of a subscript for carbon is equivalent to a subscript of 1). Next, you must find the atomic masses of carbon and oxygen--12 and 16, respectively. If the formula of the compound were CO, then you would merely need to combine 12 g of carbon with 16 g of oxygen in order to get the same number of atoms of each element. Or, you could combine 1.2 g of carbon with 1.6 g of oxygen, or you could combine 1.0 pound of carbon with 16/12 = 1.33 pound of oxygen, or 3.5 tons of carbon with 3.5 x 16/12 = 4.7 tons of oxygen. But, the formula of carbon dioxide is CO2, which tells us that we need twice as many oxygen atoms as carbon atoms. Therefore, if we want to use 12 g of carbon we must use 2 x 16 = 32 g of oxygen. If we want to start with 4 g of carbon then we must use 4 x (16/12) x 2 = 10.7 g of oxygen. Notice that the ratio of the atomic masses and the number of atoms of each element always play a role in the calculation.
If you happen to have one pound of carbon, how many pounds of oxygen will be required to make CO2?
If the compound SO2 contains 32 g of sulfur, how many grams of oxygen does it contain?
Problem Twenty One
What is the ratio of the number of atoms in 16 ounces of sulfur to the number in 1 ounce of hydrogen?
Problem Twenty Two
If the compound NH3 contains 6 g hydrogen how many grams of nitrogen are also present?
Problem Twenty Three
How many grams of hydrogen contain the same number of atoms as 12.01 grams of carbon?
It should now be clear that the atomic weights in the periodic chart are numbers that can be used to determine the ratio of the number of atoms in various amounts of the elements. The weights (masses) represent the average mass of an atom of the element in atomic mass units. So far, we have no idea of the value of an atomic mass unit in a unit of mass, such as grams, with which we are familiar.
Chemists usually weigh elements and compounds in grams, and it is, therefore, of particular interest to know the actual number of atoms in an amount of an element equal to its atomic mass in grams. In other words, how many atoms are present in 12.01 grams of carbon, in 1.008 grams of hydrogen, or in 32.04 grams of sulfur? We know, of course, that the number of atoms in each of these quantities is the same. But what is the number? This number has been determined experimentally in a number of different ways and turns out to be an extremely large number-- 6.022 x 1023. It is known as Avogadro's number, in honor of the Italian chemist.
Problem Twenty Four
Which of the following statements expresses the significance of the number 6.02 x 1023?
Problem Twenty Five
How many atoms are present in 24 grams of carbon?
Avogadros's number, 6.022 x 1023, is also called a mole, in the same way that 500 sheets of paper is called a ream, or 144 is referred to as a gross.
Problem Twenty Six
How many ping-pong balls are there in a mole of ping-pong balls and what would their molar mass be if one ping-pong ball weighs 1.0 g?
Are you saying that we can have a mole of anything? Sure, can't you have a dozen pencils, a dozen ducks, a dozen bricks? However, we normally use the term mole in dealing with atomic particles--atoms, ions, molecules.
Problem Twenty Seven
How many atoms are present in 31 g of phosphorus?
Let's try some questions that compare terms like ream or gross or dozen with mole.
Problem Twenty Eight
If one ream of paper weighs 1.0 pounds, how many reams are there in 300 pounds of paper?
Problem Twenty Nine
How many moles of carbon are there in 500 g of carbon?
As the head chick in the hen-house, you have responsibility for 100 eggs, which weigh a total of 1.00 x 104 g. How many dozen eggs do you have under your wings and how much does a dozen weigh?
Problem Thirty One
Your Zork particle counter has just informed you that there are 3 x 1020 atoms of radon in your basement. How many moles of radon is this?
Problem Thirty Two
In order to do well in your favorite course (well, chemistry, what else?) you have ordered 20 gross of pencils. How many pencils will you get?
Problem Thirty Three
Your lab partner is staring out the window as usual when he suddenly exclaims, "Gadzooks! There are 1 x 10-23 moles of dogs running down the street!" Could he be right for a change?
Problem Thirty Four
How many moles of atoms are there in 24 grams of carbon?
Problem Thirty Five
How many grams of calcium must be weighed out in order to obtain a sample containing 3 moles of atoms?
Problem Thirty Six
What is the weight of an average atom of calcium?
Now that we know how to determine the mass of an atom in grams, we can figure out the relationship between amu's and grams.
Problem Thirty Seven
First, calculate the mass of a 12C atom in grams.
Problem Thirty Eight
An amu is defined as 1/12 of the mass of a 12C atom. Determine the mass of one amu in grams.
The Mole and Compounds
We have already found that the formula of a compound represents the ratio of the atoms of the various elements in the compound. For example, magnesium chloride has the formula MgCl2, which reveals that the compound contains two chlorine atoms for every magnesium atom.
Problem Thirty Nine
In the compound Fe2O3, how many atoms are present for every two iron atoms?
The subscripts in formulas can also be interpreted in terms of moles. If there are two atoms of chlorine for every atom of magnesium in MgCl2, then there must also be two moles of chlorine atoms for every one mole of magnesium. Or, if we prefer, we can say that for every 12 x 1023 atoms of chlorine there are 6 x 1023 atoms of magnesium.
The formula for barium hydroxide is Ba(OH)2. The parentheses indicate that for every barium ion there are two hydroxide ions (OH- is the hydroxide ion). How many moles of oxygen are present with one mole of barium?
We can now calculate the molar mass (sometimes also called the formula weight) of a compound. This is the mass of one mole of the compound and can be determined by simply adding the atomic masses of each of the elements (taking into account the number of each) in the compound. For barium hydroxide, we need to add the atomic weight of barium, two times the atomic weight of oxgyen, and two times the atomic weight of hydrogen. So, this would be 137 + (2 x 16) + (2 x 1) = 171 g. Thus, one mole of Ba(OH)2 has a mass of 171 g.
Problem Forty One
How much barium hydroxide must be weighed out in order to obtain 0.10 mole?
Problem Forty Two
A student weighs out a sample of 20 g of barium hydroxide. How many moles of barium hydroxide is this?
Problem Forty Three
Calculate the molar mass of Cu2O.
Problem Forty Four
A 5 x 10-3 mole sample of Cu2O is required. What weight is required?
In addition to the formulas that we have used above, which are called empirical formulas, there are several formulas that are used for molecular compounds. Before we define the molecular formula let's be sure we are clear about the meaning of the empirical formula. The empirical formula gives the simplest whole number ratio of the number of atoms (moles) of the each of the elements in the compound. The empirical formula is the only formula used for ionic compounds - compounds that contain charged atoms (ions). There are also compounds that do not contain ions. The atoms in these compounds are held together by covalent bonds. Many of these compounds contain molecules, the building blocks of a molecular compound. Benzene, an interesting molecular compound, contains molecules that have six carbon atoms attached to one another in a hexagonal ring. Each carbon has one hydrogen attached to it. The structural formula (the name tells you that the formula gives the structure of the molecule) is shown below:
[Note: this is not an electron-dot formula (yes, yet another kind of formula), which you will learn about in your discussion of bonding. This structural formula simply shows which atoms are connected.] As you can see, each molecule of benzene contains six carbons and six hydrogens. The molecular formula of benzene therefore is written C6H6.
The molecular weight or molar mass of benzene is entirely analogous to the formula weight, which is derived from the empirical formula.
Problem Forty Five
Calculate the molecular weight of benzene.
Problem Forty Six
A 78 g sample of benzene contains how many moles of benzene molecules?
It is important to understand that the empirical formula of benzene is CH, which indicates the one to one mole ratio of carbon to hydrogen. The molecular formula, C6H6, gives the number of each atom in one molecule of the compound.
We sometimes need to convert a formula, be it empirical or molecular, to the weight percentageThe use of percentages is very common in science. The word comes from the Latin, per centum, meaning by the hundreds, and means per hundred parts. For example, if we have a class that is 40% women, we know that out of every hundred students, 40 of them are women. If a sample is 40% carbon then for every hundred parts (grams, pounds, tons, whatever), 40 of them are carbon. In order to determine the amount of an element from its percentage, you must first convert the percentage to its decimal equivalent (40% = 0.40) and then multiply that number by the weight. The amount of carbon in 50 grams of benzene (92% carbon) is 0.92 x 50 g = 46 g. of the elements. For example, benzene is 92% carbon and 8% hydrogen. In order to determine the percentage from the formula we first obtain the molar mass from the empirical formula. For benzene, the molar mass is 13 g. The percent of carbon in that 13 g is:
12 g/13 g x 100 = 92 %
Problem Forty Seven
Determine the percentage of oxygen in acetic acid, which has the empirical formula CH2O.
Calculation of Empirical Formula from Percent Composition
The conversion of experimental composition data to empirical formula is an important step in determining the identity of a substance. Suppose that we have a sample of a heavy pale yellow crystalline material that has the experimentally determined composition: 59.0% Ba, 13.5% S, and 27.4% O. We need to convert this percent composition data to an empirical formula, which will tell us the relative number of moles of barium, sulfur and oxygen in the substance. The key to this conversion lies in the understanding of the phrase "relative number of moles of barium, sulfur and oxygen in the substance." If we want the number of moles of each we must know the mass of each element in some amount of the substance and then we must convert each of thoses masses to moles.
In fact, we can choose any amount of the substance and convert it to the mass of each of the elements. If we choose 100 grams of the substance it makes the problem a little easier because we can do the first part of the math in our heads.
Problem Forty Eight
For example, if we have a 100 g sample of the substance and it contains 59.0% barium, what mass of barium is present?
Likewise, in this same sample we have 13.5 g sulfur and 27.4 g oxygen. In order to convert these masses to moles we must divide each by their atomic mass.
Ba 59.0 g/ 137.33 g/mol = 0.430 mol
S 13.5 g/ 32.07 g/mol = 0.421 mol
O 27.4 g/16.00 g/mol = 1.71 mol
We could at this point write the empirical formula as Ba0.430S0.421O1.71, but we know that the empirical formula should be expressed in whole numbers. Consequently, we divide each of the subscripts by the smallest one (0.421), which gives us subscripts of 1.02, 1.00, and 4.06. These still are not whole numbers, but because these numbers have been derived from experimental data, which contain errors, we can not expect the numbers to come out to exact whole numbers. The numbers appear close enough to 1, 1, and 4 to allow us to safely round them off. Hence, the empirical formula of the substance is BaSO4.
Problem Forty Nine
Determine the empirical formula of a compound that contains 10.0% C, 0.84% H, and 89.1% Cl.
In some cases the numbers will not come close to whole numbers and we must then multiply each by some number that will produce a set of whole numbers. The following is such a case.
Determine the empirical formula of a compound with percent composition data of Fe, 69.9%, O 30.1%.
Problem Fifty One
Determine the empirical formula of a compound with the percent composition of 50.04% C, 5.59% H, and 44.37% O.
The compound in the drill question has an empirical formula of C3H4O2. If this were also the molecular formula the compound would have a molecular weight of 3 x 12 + 4 x 1 + 2 x 16 = 72 g/mole. If, in fact, the compound has a molecular weight of 144 g/mole, then the molecular formula must be some multiple of the empirical formula; that is, the subscripts must be multiplied by some whole number. The number, in this case, is 2, and the molecular formula is C6H8O4.
Problem Fifty Two
How many moles of the molecular compound C6H8O4 are there in a 10 g sample of the compound?
Problem Fifty Three
How many molecules are there in this sample?
Problem Fifty Four
How many moles of carbon are present in this sample?
Problem Fifty Five
The empiricial formula of chloroform is CHCl3 and its molar mass is 119. What is the molecular formula of chloroform?
Problem Fifty Six
What is the weight of one molecule of chloroform?
Problem Fifty Seven
How many moles of chloroform are present in 1 mg of the sample [mg = milligram = 10-3 g]?
Problem Fifty Eight
How many moles of chlorine are present in this 1 mg sample of CHCl3?
Problem Fifty Nine
What weight of chlorine is present in this 1 mg sample?
What mass of chloroform is required to provide 1 x 1025 atoms of hydrogen?
Moles in Solution
Solutions are homogeneous mixtures of two or more substances. We will restrict our discussion to solutions that contain only two substances: a solute, the substance present in the smallest amount, and the solvent, the substance present in the greatest quantity. One of the important characteristics of a solution is its concentration: the relative amount of solute in the solution. There are a number of ways to express concentration--weight percent, molarity, molality, and mole fraction--but we will concentrate (no pun intended) on molarity.
Molarity is defined as the number of moles of solute per liter of solution. If we dissolve 1.0 mole of NaCl in enough water to make a total of one liter of solution, we will have a 1.0 molar solution of NaCl in water. Molarity is usually designated with a capital M.
Problem Sixty One
Which of the following describes how you would make up a 1.0 M NaCl solution in water?
- a) Add 58 g of NaCl to a liter of water and then mix carefully
- b) Add 58 g of NaCl to a beaker, add water and mix, and then continue to add water (and mix) until a total volume of 1.0 liter as been reached.
- c) Add 5.8 g of NaCl to a beaker, add enough water to dissolve the NaCl. Then transfer the solution to a graduated cylinder and add enough water, while mixing, to reach a volume of 100 mL.
Problem Sixty Two
If 50 mL of a solution contains 5.8 g NaCl, what is the molarity of the solution?
Problem Sixty Three
George prepares one liter of a 0.05 M NaCl solution. Jack, a good friend of Mary, came to lab late and needs 50 mL of a 0.05 M NaCl solution for a titration. Mary suggests that Jack ask George for 50 mL of his solution. Jack hesitates to use George's solution because he says that if he takes 50 mL he will not have a 0.05 M solution. He will have 0.05 mole of NaCl in 0.050 L, says Jack, which will make the solution a 1 M solution. What should Mary say?
The previous question emphasizes the fact that no matter how much of a solution you have, the concentration remains the same. Let's go through Mary's reasoning (answer b) again with a different amount of the 0.05 M solution. If we start with 1 liter of the solution and take from it 100 mL, we have taken a tenth of the solution. That tenth will contain a tenth of the original amount of solute (0.05 moles); that is, the 100 mL will contain 0.005 moles of solute. But, that 0.005 moles will be present in a total of 100 ml (0.1 L). Thus, the molarity, which is just moles per liter, will be:
0.005 moles/0.1 L = 0.05 M
Problem Sixty Four
How many moles of solute will be present in 310 mL of the 0.05 M NaCl solution?
Problem Sixty Five
What volume of a 0.05 M NaCl solution will be required to obtain 2 x 10-3 moles of NaCl?
Problem Sixty Six
How many moles of solute will be present in 310 mL of the 0.05 M NaCl solution?
Problem Sixty Seven
How many moles of acetic acid are there in 100 mL of a 0.60 M solution?
Problem Sixty Eight
If 10 mL of a 0.60 M acetic acid solution is diluted to 55 mL, what is the molarity of the resulting solution?
Problem Sixty Nine
How many mL of a 12 M stock solution of HCl must be used to prepare 100 mL of a 0.10 M HCl solution?
The Mole and Chemical Reactions
Although the quantitative aspects of chemical reactions will be studied in the module on Stoichiometry, we will introduce the idea that substances react in certain mole ratios. For every reaction there is an equation that expresses the mole ratio between the reactants and products. We have looked at a few simple equations early in this module; let's look at a few more from our new vantage point of the mole.
Aluminum reacts with sulfur to form aluminum sulfide as shown below:
2 Al + 3 S → Al2S3
The substances on the left side of the arrow are the reactants, those on the right side are the products. Every equation must obey the Law of Conservation of Mass, which means that all of the aluminum atoms on the left must be converted to aluminum atoms in some form on the right if the reaction goes to completion. The same is true, of course, of the sulfur. In order to balance an equation, we must, therefore, simply make certain that the number of atoms of each element is the same on both sides. In this sense, a chemical equation is like a mathematical equation; there must be an equality between the number of atoms.
Methane (CH4) reacts with elemental oxygen, which exists as O2 molecules, to form CO2 and water. Which of the following is a balanced equation for this reaction?
Problem Seventy One
Aluminum metal reacts with HCl to form elemental hydrogen (H2) and AlCl3. Write a balanced equation for this reaction.
Problem Seventy Two
Balance the following "equation."
Na2CO3 + HCl → H2CO3 + NaCl
What do the coefficients in from of the substances in the balanced equation mean? For example, what do the 2, the 3 and the 1 (there is an implied 1 in front of Al2S3) mean in the following equation?
2 Al + 3 S → Al2S3
We have already encountered one interpretation: Two atoms of aluminum combine with 3 atoms of aluminum to make aluminum sulfide. Notice that in this sentence we did not specify how much aluminum sufide was produced because we can not say one molecule of aluminum sulfide - the compound does not exist in molecular form. It is very convenient to use the mole to interpret equations. Thus, for this equation we can say: Two moles of aluminum combine with three moles of sulfur to make one mole of aluminum sulfide.
Problem Seventy Three
Verbalize the following equation:
H2 + Cl2 → 2 HCl
The language in our statements above should make it clear that the coefficients in front of each substance in a chemical equation represent the relative number of moles of each involved in the reaction. For example, in the equation:
H2 + Cl2 → 2 HCl
The coefficients, which are 1, 1, and 2, tell us that if we start the reaction with one mole of H2 and one mole of Cl2, we will get two moles of HCl when the reaction is complete. Or, for the reaction:
Fe2(CO3)3 → Fe2O3 + 3 CO2
we know that if we start the reaction with one mole of Fe2(CO3)3 we will get one mole of Fe2O3 and three moles of CO2 when the reaction is complete.
But, what if we start with some other amount, say 0.15 mole of Fe2(CO3)3 ? Certainly, the same mole ratio applies no matter how much we start with. That is, we will get three times as many moles of CO2 as the number of moles of Fe2(CO3)3 that we start with. Thus, if we start with 0.15 mole of Fe2(CO3)3, we will get:
0.15 mol Fe2(CO3)3 x 3 mole CO2 /1 mole Fe2(CO3)3 = 0.45 mole CO2
Problem Seventy Four
How many moles of Fe2(CO3)3 must we start the reaction with if we want 1.8 mol of CO2 when the reaction has gone to completion?
Elemental nitrogen and hydrogen, both of which exist as diatomic molecules (N2 and H2), react to form ammonia, according to the equation:
N2 + 3 H2 → 2 NH3
Problem Seventy Five
If 1.0 mole of H2 is consumed during the reaction, how many moles of ammonia are formed?
In the problem above, and in many other such problems, it is convenient to divide all of the coefficients by the coefficient of the substance in question. In the above case, we could divide all coefficients by the 3 in front of H2 to get the equation:
1/3 N2 + H2 → 2/3 NH3
This equation makes it clear that every mole of H2 will be converted to two-thirds mole of NH3.
Try the same approach with the reaction of ethane with O2 as shown below:
2 C2H6 + 7 O2 → 4 CO2 + 6 H2O
Problem Seventy Six
How many moles of CO2 are formed as a result of the reaction of 2 moles of O2?
Problem Seventy Seven
If 1.0 mole ethane is mixed with 5.0 mole O2 and the 1.0 mole ethane is completely consumed during the reaction, how many moles of O2 will be left at the end of the reaction?