Mass and the Mole

A mole always contains the same number of particles however, moles of different substances have different masses. 

Real-World Reading Link When purchasing a dozen eggs, you can pick from several sizes—medium, large, and extra-large. The size of the egg does not affect how many come in the carton. A similar situation exists with the size of the atoms that make up a mole. 

Recall from Chapter 4 that each atom of carbon-12 has a mass of 12 amu. The atomic masses of all other elements are established relative to carbon-12. For example, an atom of hydrogen-1 has a mass of approximately 1 amu, one-twelfth the mass of a carbon-12 atom. The mass of an atom of helium-4 is approximately 4 amu, one-third the mass of one atom of carbon-12. 

Molar Mass How does the mass of one atom relate to the mass of one mole of that atom Recall that the mole is defined as the number of carbon-12 atoms in exactly 12 g of pure carbon-12. Thus, the mass of one mole of carbon-12 atoms is 12 g. Whether you are considering a single atom or Avogadro s number of atoms (a mole), the masses of all atoms are established relative to the mass of carbon-12. The mass in grams of one mole of any pure substance is called its molar mass. 

The molar mass of any element is numerically equal to its atomic mass and has the units g/mol. As given on the periodic table, an atom of iron has an atomic mass of 55.845 amu. Thus, the molar mass of iron is 

This relationship can be used to convert between mass and moles. 

A roll of copper wire has a mass of 848 g. How many moles of copper are in the roU Use the atomic mass of copper given on the periodic table to apply a conversion factor to the mass given in the problem. 

Note that the conversion factor is arranged so that g Cu cancel, leaving only mol Cu, the desired quantity. 

Use the molar mass of calcium to apply a conversion factor to the number of moles given in the problem. According to the periodic table, the atomic mass of calcium is 40.078 amu, so the molar mass of calcium is 40.078 g. 

You can find atomic masses on the periodic table, but notice that the values shown are not exact integers. For example, you ll find 12.011 amu for carbon, 1.008 amu for hydrogen, and 4.003 amu for helium. These differences occur because the recorded values are weighted averages of the masses of all the naturally occurring isotopes of each element. 

Relate the mass of an atom to the mass of a mole of atoms. 

Calculate the number of moles in a given mass of an element and the mass of a given number of moles of an element. 

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The final step in the problem is to combine the given mass and the moles we found to give the molar mass. This will require the conversion of the milligrams given into grams. 

The key to any reaction experiment is moles. The numbers of moles may be calculated from various measurements. A sample may be weighed on a balance to give the mass, and the moles calculated with the formula weight. Or the mass of a substance may be determined using a volume measurement combined with the density. The volume of a solution may be measured with a pipet, or calculated from the final and initial readings from a buret. This volume, along with the molarity, can be used to calculate the moles present. The volume, temperature, and pressure of a gas can be measured and used to calculate the moles of a gas. You must be extremely careful on the AP exam to distinguish between those values that you measure and those that you calculate. 

All weighed samples are converted to moles by using the molar mass, and the moles are divided by the volume of the volumetric flask in liters to yield molarity. 

SUI "Relative Atomic Mass and the Mole A Concrete Analogy to Help Students Understand These Abstract Concepts/ ]. Chem. Educ.,... 

Explain the relationship between average atomic mass and the mole. 

A 9.386 M aqueous solution of sulfuric acid has a density of 1.5091 g cm. Calculate the molality, the percentage by mass, and the mole fraction of sulfuric acid in this solution. 

A basic question raised in the chemical laboratory is, How much product will be formed from specific amounts of starting materials (reactants) Or in some cases we might ask the reverse question How much starting material must be used to obtain a specific amount of product To interpret a reaction quantitatively, we need to apply our knowledge of molar masses and the mole concept. Stoichiometry is the quantitative study of reactants and products in a chemical reaction. 

Interpret Data Using your data, determine the mass and the moles of copper produced. Calculate the moles of iron used, and determine the whole-number iron-to-copper mole ratio and percent yield. 

Now we ve reduced our original question to something that looks a lot more like the previous examples What mass of CO2 is produced by the complete combustion of 2659 g of CsHis Use molar masses and the mole ratio firom the balanced equation to set up the calculation ... 

These limitations are overcome in modem chemistry through the introduction of two extremely important concepts the atomic mass and the mole. 

A mole of a substance is defined as Avogadro s number of molecules of the substance. Thus a mole of water, H O, is the quantity of water containing N H2O molecules. The molecular mass of water (the sum of the atomic masses of the atoms in the molecule 2 x 1.00797 -f- 1 x 15.9994, from Table 4-1) is 18.0153. From the definitions of atomic masses and the mole we see that a mole of water is 18.0153 g. 

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