Converting moles to atoms

Empirical formulas can also be calculated from the mass of each element in a sample of a compound. Analysis of a sample of a compound shows that it contains 1.179 g Na and 0.821 g S. You could calculate the percent of each element from these numbers, but that s not necessary. The mass of each element is converted directly to moles for the empirical formula. From the table of atomic masses, we find the molar masses are 22.99 g for Na and 32.07 g for S. 

To convert masses to moles or vice versa, we use the molar mass of the substance. Molar mass has the same numeric value as the number of atomic mass units in a formula unit, but it is expressed in units of grams per mole. For example, the molar mass of water is 18.0 g/mol because the formula mass of water is 18.0 amu/molecule. Because molar mass is a ratio, it can be used as a factor in problem solving. 

Converting Particles to Moles Zinc (Zn) is used as a corrosion-resistant coating on iron and steel. It is also an essential trace element in your diet. Calculate the number of moles of zinc that contain 4.50 x 10 atoms. 

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

You are given the number of atoms of helium and must find the mass of the gas. First, convert the number of atoms to moles, then convert moles to grams. 

Now that you have practiced conversions between mass, moles, and representative particles, you probably realize that the mole is at the center of these calculations. Mass must always be converted to moles before being converted to atoms, and atoms must similarly be converted to moles before calculating their mass. Figure 10.8 shows the steps to follow as you complete these conversions. In the Example Problems, two steps were used to convert either mass to moles to atoms, or atoms to moles to mass. Instead of two separate steps, these conversions can be made in one step. Suppose you want to find out how many atoms of oxygen are in 1.00 g of oxygen. This calculation involves two conversions— mass to moles and then moles to atoms. You could set up one equation like this. 

Strategy Use Avogadro s number to convert from moles to atoms and from atoms to moles. 

One result of this apparently simple concept is that the atomic weight can be used to interconvert grams and moles. Since the units of atomic weight, as defined earlier, include both grams and moles, it can be used as a conversion factor to convert grams to moles, and vice versa. The dimensional analysis would appear as follows for the conversion from grams to moles ... 

To find the number of atoms in the sample, you must first determine how many moles are in 4.77 g lead. According to data from the periodic table, the molar mass of lead is 207.2 g/mol. Apply a conversion factor to convert mass to moles. 

Strategy First (1), convert the masses of the three elements to moles. Knowing the number of moles (n) of K, Cr, and O, you can then (2) calculate the mole ratios. Finally (3), equate the mole ratio to the atom ratio, which gives you the simplest formula. 

Our task is to estimate the volume occupied by one atom of lithium. As usual, the mole is a convenient place to begin the calculations. Visualize a piece of lithium containing one mole of atoms. The molar mass, taken from the periodic table, tells us the number of grams of Li in one mole. The density equation can be used to convert from mass to volume. Once we have the volume of one mole of lithium, we divide by the number of atoms per mole to find the volume of a single atom. 

Table 2 gives the compositions of the same four clay samples in atomic percent. The atomic percent is defined as the number of atoms of an element per unit volume divided by the number of atoms per unit volume of the substance containing the element. This is similar to mole fraction when the atomic percent is converted to fractional value. 

The relationship above gives a way of converting from grams to moles to particles, and vice versa. If you have any one of the three quantities, you can calculate the other two. This becomes extremely useful in working with chemical equations, as we will see later, because the coefficients in the balanced chemical equation are not only the number of individual atoms or molecules at the microscopic level, but also the number of moles at the macroscopic level. 

CH O. For the sake of simplicity, assume that you have a total of 100 g of this mystery compound. Therefore, you have 40.0 g of Ccirbon, 6.7 g of hydrogen, and 53.3 g of oxygen. Convert each of these masses to moles by using the gram atomic masses of C, H, and O ... 

Solution To convert the mass of carbon dioxide to moles of C atoms, we use the molar mass of carbon dioxide (44.01 g-mol-1) and the stoichiometric relation 1 mol C — 1 mol C02 ... 

Note that the subscripts in a molecular formula represent the number of atoms in a molecule. Since a molecule of CuS04 has four oxygen atoms, the relative mass of oxygen must be multiplied by four and added to the relative mass of one copper atom and one sulfur atom to find the relative mass of a mole of CuS04, copper sulfate molecules. Two atoms of potassium, four atoms of oxygen, and one atom of chromium must be accounted for in potassium chromate, K2Cr04. Students should calculate the mass of one mole of each of the molecules needed, convert each to 0.1 mole (multiply by... 

The law of multiple proportions, in its historical form, is somewhat contusing, but we can understand it better by determining the empirical formulas of the nitrogen oxides. Following the procedure of Table 2-2, we convert the masses of N and O contained in 100 g of each compound to moles as shown in Table 2-5. The mole ratios then indicate the relative numbers of N and O atoms in one molecule ... 

The transformation was called an homologation reaction because essentially it consisted in going from one alcohol to an alcohol containing one carbon atom more than the starting material (Wender, Levine, and Orchin, 14). Tertiary alcohols reacted most rapidly, secondary alcohols less rapidly and primary alcohols only very slowly. It was of considerable importance to ascertain whether the olefin intermediate was essential and for this purpose, methanol and benzyl alcohol, neither of which can dehydrate to an olefin, were used in the reaction. Both compounds, contrary to other primary alcohols, reacted quite rapidly and gave the homologous alcohol of the methanol converted, about 40 mole per cent went to ethanol and with benzyl alcohol, a 30% yield of 2-phenylethanol was secured. In both examples, however, reduction products were also present of the methanol converted, 8 mole per cent went to methane and from benzyl alcohol, a 50 to 60% yield of toluene was secured. The conversion of methanol to methane appears to be the only case in which an appreciable quantity of hydrocarbon is secured from a purely aliphatic alcohol. The behavior of benzyl alcohol and its derivatives will be discussed later. 

The Avogadro constant is the factor that converts the relative mass of individual atoms or molecules, expressed in atomic mass units, to mole quantities, expressed in grams. 

The first step is to use the molar mass to convert grams of carbon to moles of carbon. Once the moles are obtained, Avogadro s number can be used to calculate the number of atoms. 

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