Atomic Masses Counting Atoms by Weighing

The value of using atomic masses is that it allows us to count a large number of atoms by weighing a sample of the element. For instance, we can calculate that a small speck of carbon weighing 1.00 mg (1.00 X 10-3 g) contains 5.01 X 1019 carbon atoms ... 

I hapter 1 explained how chemical and physical methods are used to estab-lish chemical formulas and relative atomic and molecular masses. This chapter begins our study of chemical reactions. We start by developing the concept of the mole, which allows us to count molecules by weighing macroscopic quantities of matter. We examine the balanced chemical equations that summarize these reactions and show how to relate the masses of substances consumed to the masses of substances produced. This is an immensely practical and important subject. The questions how much of a substance will react with a given amount of another substance and how much product will be generated are central to all chemical processes, whether industrial, geological, or biological. 

Now let s take similar steps to count atoms of the element carbon. Because of the size and number of carbon atoms in any normal sample of carbon, it is impossible to count the atoms direcdy. Therefore, we want to develop a way of converting from mass of carbon, which we can measure, to the number of carbon atoms. To do this, we will follow steps that are similar to those we followed to count nails by weighing. 

A mole of substance is the amount that contains Avogadro s number (6.022x10 ) of chemical entities (atoms, molecules, or formula units). The mass (in grams) of a mole has the same numerical value as the mass (in amu) of the entity. Thus, the mole allows us to count entitles by weighing them. Using the molar mass (jM., g/mol) of an element (or compound) and Avogadro s number as conversion factors, we can convert among amount (mol), mass (g), and number of entities. The mass fraction of element X in a compound is used to find the mass of X in any amount of the compound. 

Counting Carbon Atoms To count carbon atoms by weighing, we need to know the mass of individual atoms, just as we needed to know the mass of the individual jelly beans. We learned from Chapter 3 that the atoms of a given element exist as isotopes. 

Now that we know the average mass of the carbon atom (12.01 amu), we can count carbon atoms by weighing samples of natural carbon. For example, what mass of natural carbon must we take to have 1000 carbon atoms present ... 

To summarize, we have seen that we can count atoms by weighing if we know the average atomic mass for that type of atom. This is one of the fundamental operations in chemistry, as we will see in the next section. 

Chemists also count atoms by weighing. We know the average masses of atoms, so we can count atoms by defining a unit to represent a larger number of atoms. Chemists have chosen the mole (mol) as the unit for counting atoms. The mole is a unit for counting just as a dozen or a ream or a gross is used to count ... 

This definition of the mole establishes a relationship between mass (grams of carbon) and number of atoms (Avogadro s number). This relationship, as we will see shortly, allows us to count atoms by weighing them. 

From the measured mass of a sample of a pure substance, we can calculate the amount of substance (called simply the amount in this book). The SI base unit for amount is the mole (Sec. 1.1.1). Chemists are familiar with the fact that, although the mole is a counting unit, an amount in moles is measured not by counting but by weighing. This is possible because one mole is defined as the amount of atoms in exactly 12 grams of carbon-12, the most abundant isotope of carbon (Appendix A). One mole of a substance has a mass of Mr grams, where Mr is the relative molecular mass (or molecular weight) of the substance, a dimensionless quantity. 

If we want to know the number of atoms in anything of substantial size, we need another method besides direct counting. One such method involves the mole concept, which relates the mass of a sample of an element to the number of atoms within it, so that we can determine the number of atoms by weighing. 

Molar Mass Counting Atoms by Weighing Them... 

To count atoms by weighing them, we need one other conversion factor—the mass of 1 mol of atoms. For the isotope carbon-12, we know that the mass of 1 mol of atoms is exactly 12 grams, which is numerically equivalent to carbon-12 s atomic mass in atomic mass units. Since the masses of all other elements are defined relative to carbon-12, the same relationship holds for all elements. 

Chemists report numbers of atoms, ions, and molecules in terms of a unit called a mole. A mole is the analog of the wholesaler s dozen. A dozen could be defined as the number of soda cans in a twelve pack carton supplied by a wholesaler. Even if you could not open the carton to count the number of cans inside, you could find out how many cans are in a dozen by weighing the carton and dividing the mass of the carton by the mass of one can. A similar approach is used to define a mole (abbreviated mol) ... 

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