Masses and Numbers of Particles

The mole concept provides the bridge between mass and number of particles. To illustrate how this bridge works, let s calculate the number of copper atoms in an old copper penny. Such a penny has a mass of about 3 g, and we assume it is 100% copper  

The general procedure for interconverting mass and number of formula units (atoms, molecules, ions, or whatever else is represented by the chemical formula) is summarized in T FIGURE 3.12. 

What number would you use to convert (a) moles of CH4 to grams of CH4 and (b) number of molecules of CH4 to moles of CH4  

A FIGURE 3.12 Procedure for interconverting mass and number of formula units. The 

CHAPTER 3 Stoichiometry Caicuiations with Chemicai Formuias and Equations 

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The collection technique involves the removal of particles from the air stream. The two principal methods are filtration and impaction. Filtrahon consists of collecting particles on a filter surface by three processes—direct interception, inertial impaction, and diffusion (5). Filtration attempts to remove a very high percentage of the mass and number of particles by these three processes. Any size classification is done by a preclassifier, such as an impactor, before the particle stream reaches the surface of the filter. 

Converting Between Moles, Mass, and Number of Particles... 

Example Problem 11-8 illustrated how to find the number of moles of a compound contained in a given mass. Now, you will learn how to calculate the number of representative particles—molecules or formula units—contained in a given mass and, in addition, the number of atoms or ions. Recall that no direct conversion is possible between mass and number of particles. You must first convert the given mass to moles by multiplying by the inverse of the molar mass. Then, you can convert moles to the number of representative particles by multiplying by Avogadro s number. To determine numbers of atoms or ions in a compound, you will need conversion factors that are ratios of the number of atoms or ions in the compound to one mole of compound. These are based on the chemical formula. Example Problem 11-9 provides practice in solving this type of problem. 

Ifwe can determine the number of phosphorus atoms in 1.09 X 10 kg P, we can use the second conversion factor at the bottom of the last page to determine the number of molecules of P4O10. But your production manager doesn t want to know the number of P4O10 molecules that you can make. She wants to know the mass of P40iothat can be made. That means we also need a conversion factor that converts back and forth between any mass of the compound and the number of molecules contained in that mass. The main goal of the first half of this chapter is to develop conversion factors that convert between mass and number of particles. 

You have learned that different kinds of representative particles are counted using the mole. In the last section, you read how to use molar mass to convert among moles, mass, and number of particles of an element. Can you make similar conversions for compounds and ions Yes, you can, but to do so you will need to know the molar mass of the compounds and ions involved. 

Figure 1.39 Summary of interconversions between amount, mass and number of particles... 

Table 6.1 Relationship between diameter, surface area and number of particles per unit mass for idealised spherical particles.

What if you wanted to compare amounts of substances, and you only knew their masses You would probably convert their masses to moles. The Avogadro constant relates the molar amount to the number of particles. Examine the next Sample Problem to learn how to convert mass to number of particles. 

Solve problems converting between mass, amount in moles, and number of particles using Avogadro s number and molar mass. 

Converting from mass to number of particles is the reverse of the operation in the previous problem. This conversion is also shown in Skills Toolkit 3, but this time you are going from right to left and using the bottom conversion factors. 

You will use the mole and molar mass to make conversions among moles, mass, and number of representative particles. 

Visuahzing a mole as a pile of particles, however, is just one way to understand this concept. A sample of a substance has a mass, volume (generally used with gases), and number of particles that is proportional to the chemical amount (measured in moles) of the sample. For example, one mole of oxygen gas (O2) occupies a volume of 22.4 L at standard temperature and pressure (STP 0°C and 1 atm), has a mass of 31.998 grams, and contains about 6.022 X 10 molecules of oxygen. Measuring one of these quantities allows the calculation of the others and this is frequently done in stoichiometry. 

Design a concept map that shows the conversion factors needed to convert between mass, moles, and number of particles. 

Conversions between mass, moles, and the number of particles are summarized in Figure 10.11. Note that molar mass and the inverse of molar mass are conversion factors between mass and number of moles. Avogadros number and its inverse are the conversion factors between moles and the number of representative particles. To convert between moles and the number of moles of atoms or ions contained in the compound, use the ratio of moles of atoms or ions to 1 mole of compound or its inverse, which are shown on the upward and downward arrows in Figure 10.11. These ratios are derived from the subscripts in the chemical formula. 

Figure 1.39 is a summary showing how to interconvert between mass (in g), amount (in mol) and number of particles using molar mass and Avogadro s constant. 

Unfortunately, we cannot count particles—at least, not directly. Instead, we measure masses or other macroscopic quantities. These can be converted into numbers of particles. You already know how to do this conversion with mass, using molar mass as a conversion factor between mass (in grams) and number of particles (in moles) (see Section 7.5). Equation 10.1 can also be interpreted as, Four moles of NH3 molecules react with five moles of O2 molecules to produce four moles of NO molecules and six moles of H2O molecules. ... 

The number of particles in a mole is known as Avogadro s number, named for the nineteenth-century Italian scientist Amedeo Avogadro, whose ideas were crucial in explaining the relationship between mass and numbers of atoms. Avogadro s number—6.022141 79 x lO —is the number of particles in exactiy one moie of a pure substance. For most purposes, Avogadro s number is rounded to 6.022 x 10. ... 

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