Atom-to-mass conversions

Atoms-to-Mass Conversion Helium (He) is an unreactive noble gas often found in underground deposits mixed with methane. The mixture is separated by cooling the gaseous mixture until all but the helium has liquefied. A party balloon contains 5.50 X 10 atoms of helium gas. What is the mass, in grams, of the helium ... 

Conversions from mass to atoms and atoms to mass So far, you have learned how to convert mass to the number of moles and the number of moles to mass. You can go one step further and convert mass to the number of atoms. Recall the jellybeans you were selling at the candy sale. At the end of the day, you find that 550 g of jellybeans are left unsold. Without counting, can you determine how many jellybeans this is You know that one dozen jellybeans has a mass of 35 g and that 1 dozen contains 12 jellybeans. Thus, you can first convert the 550 g to dozens of jellybeans by using the conversion factor that relates dozens and mass. 

To convert the mass of the iron bar to the number of moles of iron, use the mass of 1 mol of iron atoms as a conversion factor. 

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. 

Unfortunately, natural carbon always contains carbon-13 atoms as well as carbon-12 atoms, so the conversion factor shown above is not very useful. We need a conversion factor that relates mass and moles of natural carbon instead. Because the average mass of the atoms in natural carbon (12.011 u) is slightly greater than the mass of each carbon-12 atom (12 u), the mass of a mole of natural carbon atoms has a mass slightly greater than the mass of a mole of carbon-12 atoms (12.011 g compared to 12 g). The following conversion factor can be used to convert between mass of natural carbon and number of moles of carbon atoms. 

The atomic mass of C is 12.01 amu therefore, 1 mole C = 12.01 g C. This equality provides the needed gram-to-mole conversion factor. 

The notions of Avogadro s number and molar mass enable us to carry out conversions between mass and moles of atoms and between the number of atoms and mass and to calculate the mass of a single atom. We will employ the following unit factors in the calculations ... 

The change in mass when one mole of 235U undergoes fission is found by recognizing that the conversion from u to grams and atoms to moles both require Avogadro s number ... 

We need to know the relative numbers of each type of atom to write the formula, so we must convert the masses of the elements to moles of atoms to get the empirical formula. We carry out the conversion by using the atomic masses of the elements. 

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