Amount-mass-number relationships

Amount-Mass-Number Conversions Involving Elements We begin with amount-mass-number relationships of elements. As Figure 3.2 shows, convert mass (in grams) or number of entities (atoms or molecules) to amount (mol) first. For molecular elements, Avogadro s number gives molecules per mole. 

Figure 3.3 Amount-mass-number relationships for compounds. Use the...

Figures. Summary of amount-mass-number relationships in a chemical equation. Start at any box (known) and move to any other (unknown) by using the conversion factor on the arrow. As always, convert to amount (mol) first.

A particularly convenient way to use this mass-number relationship is to measure amounts in grams that are numerically equal to molecular masses. If, for instance, you were to carry out your experiment with 36.5 g of HC1 and 28.0 g of ethylene, you could be certain that you have the correct 1 1 number ratio of reactant molecules. 

Amount-Mass-Number Conversions Involving Compounds Only one new step is needed to solve amount-mass-number problems involving compounds we need the chemical formula to find the molar mass and the amount of each element in the compound. The relationships are shown in Figure 3.3, and Sample Problems 3.4 and 3.5 apply them. 

This balanced equation can be read as 4 iron atoms react with 3 oxygen molecules to produce 2 iron(III) oxide units. However, the coefficients can stand not only for the number of atoms or molecules (microscopic level) but they can also stand for the number of moles of reactants or products. So the equation can also be read as 4 mol of iron react with 3 mol of oxygen to produce 2 mol ofiron(III) oxide. In addition, if we know the number of moles, the number of grams or molecules may be calculated. This is stoichiometry, the calculation of the amount (mass, moles, particles) of one substance in the chemical equation from another. The coefficients in the balanced chemical equation define the mathematical relationship between the reactants and products and allow the conversion from moles of one chemical species in the reaction to another. 

Figure 3.3 Summary of the mass-mole-number relationships for elements. The amount (mol) of an element is related to its mass (g) through the molar mass (jU in g/mol) and to its number of atoms through Avogadro s number (6.022x10 atoms/mol). For elements that occur as molecules, Avogadro s number gives molecules per mole.

Figure 3.8 Summary of the mass-mole-number relationships in a chemical reaction. The amount of one substance in a reaotion is related to that of any other. Quantities are expressed in terms of grams, moles, or number of entities (atoms, molecules, or formula units). Start at any box in the diagram (known) and move to any other box (unknown) by using the information on the arrows as conversion factors. As an example, if you know the mass (in g) of A and want to know the number of molecules of B, the path involves three calculation steps ...

In this chapter, you learned how to balance simple chemical equations by inspection. Then you examined the mass/mole/particle relationships. A mole has 6.022 x 1023 particles (Avogadro s number) and the mass of a substance expressed in grams. We can interpret the coefficients in the balanced chemical equation as a mole relationship as well as a particle one. Using these relationships, we can determine how much reactant is needed and how much product can be formed—the stoichiometry of the reaction. The limiting reactant is the one that is consumed completely it determines the amount of product formed. The percent yield gives an indication of the efficiency of the reaction. Mass data allows us to determine the percentage of each element in a compound and the empirical and molecular formulas. 

The mole (mol) is the amount of a substance that contains the same number of particles as atoms in exactly 12 grams of carbon-12. This number of particles (atoms or molecules or ions) per mole is called Avogadro s number and is numerically equal to 6.022 x 1023 particles. The mole is simply a term that represents a certain number of particles, like a dozen or a pair. That relates moles to the microscopic world, but what about the macroscopic world The mole also represents a certain mass of a chemical substance. That mass is the substance s atomic or molecular mass expressed in grams. In Chapter 5, the Basics chapter, we described the atomic mass of an element in terms of atomic mass units (amu). This was the mass associated with an individual atom. Then we described how one could calculate the mass of a compound by simply adding together the masses, in amu, of the individual elements in the compound. This is still the case, but at the macroscopic level the unit of grams is used to represent the quantity of a mole. Thus, the following relationships apply ... 

We saw in Section 3.3 that the coefficients in a balanced equation tell the numbers of moles of substances in a reaction. In actual laboratory work, though, it s necessary to convert between moles and mass to be sure that the correct amounts of reactants are used. In referring to these mole-mass relationships, we use the word stoichiometry (stoy-key-ahm-uh-tree from the Greek stoicheion, "element," and metron, "measure"). Let s look again at the reaction of ethylene with HC1 to see how stoichiometric relationships are used. 

For work in the laboratory, it s necessary to weigh reactants rather than just know numbers of moles. Thus, it s necessary to convert between numbers of moles and numbers of grams by using molar mass as the conversion factor. The molar mass of any substance is the amount in grams numerically equal to the substance s molecular or formula mass. Carrying out chemical calculations using these relationships is called stoichiometry. 

If, in a ratio of amounts of substance, both of the two numbers of entities are traceable to numbers of carbon-12 atoms, and if the ratio between the entities is obtained by an appropriate measurement, the measurement is perfectly true to the concept of that SI unit. Calling that relationship traceable to SI is thereby reasoned and should be considered correct. Just as for mass measurements, the realization of amounts of sub-... 

In this chapter, you have learned about the relationships among the number of particles in a substance, the amount of a substance in moles, and the mass of a substance. Given the mass of any substance, you can now determine how many moles and particles make it up. In the next chapter, you will explore the mole concept further. You will learn how the mass proportions of elements in compounds relate to their formulas... 

You can get the same kind of information from a balanced chemical equation. In Chapter 4, you learned how to classify chemical reactions and balance the chemical equations that describe them. In Chapters 5 and 6, you learned how chemists relate the number of particles in a substance to the amount of the substance in moles and grams. In this section, you will use your knowledge to interpret the information in a chemical equation, in terms of particles, moles, and mass. Try the following Express Lab to explore the molar relationships between products and reactants. 

The concentration of a very small quantity of a substance in the human body, or in the environment, can be expressed in parts per million (ppm) and parts per billion (ppb). Both parts per million and parts per billion are usually mass/mass relationships. They describe the amount of solute that is present in a solution. Notice that parts per million does not refer to the number of particles, but to the mass of the solute compared with the mass of the solution. 

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