Molar mass as conversion factor

A chemical equation tells us the relations between the amounts (in moles) of each reactant and product. By using the molar masses as conversion factors, we can express these relations in terms of masses. 

Let s use for our example a colorless liquid whose composition is 84.1% carbon and 15.9% hydrogen by mass. Arbitrarily taking 100 g of the substance to make the calculation easier, we find by using molar masses as conversion factors that the 100 g contains ... 

You use molar masses as conversion factors in the same way you use Avogadro s number. The right side of Skills Toolkit 3 shows how the amount in moles relates to the mass in grams of a substance. Suppose you must find the mass of 3.50 mol of copper. You will use the molar mass of copper. By checking the periodic table, you find the atomic mass of copper, 63.546 amu, which you round to 63.55 amu. So, in calculations with copper, use 63.55 g/mol. 

Consider as an example the mole fraction of hydrochloric acid (HCI) in the aqueous solution shown in Figure 15-15. For every 100 grams of solution, 37.5 g would be HCI and 62.5 g would be H2O. To convert these masses to moles, you would use the molar masses as conversion factors. 

Given the chemical equation Na2C03(aqf) + Ca(OH)2 —> 2NaOH(at/) + CaC03(s), determine to two decimal places the molar masses of all substances involved. Then, write the molar masses as conversion factors. 

A Both the density and the molar mass of Pb serve as conversion factors. 

If we want an amount other than 1 mol, we use the molar mass as a conversion factor from the stated number of moles to the mass required ... 

Now that we know how many moles of ethylene we have (0.536 mol), we also know from the balanced equation how many moles of HC1 we need (0.536 mol), and we have to do a mole-to-gram conversion to find the mass of HC1 required. Once again, the conversion is done by calculating the molecular mass of HC1 and using molar mass as a conversion factor ... 

The problem gives the number of moles of NaHC03 and asks for a mole-to-mass conversion. First, calculate the formula mass and molar mass of NaHC03. Then use molar mass as a conversion factor, and set up an equation so that the unwanted unit cancels. 

We need to calculate the amount of methyl tert-bu tyl ether that could theoretically be produced from 26.3 g of isobutylene and compare that theoretical amount to the actual amount (32.8 g). As always, stoichiometry problems begin by calculating the molar masses of reactants and products. Coefficients of the balanced equation then tell mole ratios, and molar masses act as conversion factors between moles and masses. 

Next, find how many moles of ethyl alcohol are in 40.0 g by using molar mass as a conversion factor ... 

We therefore need to find how many grams of diethyl ether are in 0.435 mol, using molar mass as the conversion factor ... 

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 you measure 165 g of manganese on a balance, you will have the 3.00 moles of manganese you need for the reaction. The reverse conversion—from mass to moles—also involves the molar mass as a conversion factor, but it is the inverse of the molar mass that is used. Can you explain why ... 

Suppose you need to measure a certain number of moles of a compound for an experiment. First, you must calculate the mass in grams that corresponds to the necessary number of moles. Then, that mass can be measured on a balance. In Example Problem 11-2, you learned how to convert the number of moles of elements to mass using molar mass as the conversion factor. The procedure is the same for compounds except that you must first calculate the molar mass of the compound. 

Imagine that the experiment you are doing in the laboratory produces 5.55 g of a compound. How many moles is this To find out, you calculate the molar mass of the compound and determine it to be 185.0 g/mol. The molar mass relates grams and moles, but this time you need the inverse of the molar mass as the conversion factor. 

Use the inverse of molar mass as the conversion factor to calculate moles. 

Determine the moles of the given substance using a mass-to-mole conversion. Use the inverse of the molar mass as the conversion factor. 

Most chemical reactions that occur on the earth s surface, whether in living organisms or among inorganic substances, take place in aqueous solution. Chemical reactions carried out between substances in solution obey the requirements of stoichiometry discussed in Chapter 2, in the sense that the conservation laws embodied in balanced chemical equations are always in force. But here we must apply these requirements in a slightly different way. Instead of a conversion between masses and number of moles, using the molar mass as a conversion factor, the conversion is now between solution volumes and number of moles, with the concentration as the conversion factor. 

For pure liquids and solids, as we have seen, the most convenient measurable property is mass. It is very easy to measure the mass of a pure solid or liquid, and we can convert between that and the number of particles it represents using the molar mass as a conversion factor. 

Between this chapter and Chapter 10, we have now seen three different ways to convert between a measurable property and moles in equation stoichiometry problems. The different paths are summarized in Figure 13.10 in the sample study sheet on the next two pages. For pure liquids and solids, we can convert between mass and moles, using the molar mass as a conversion factor. For gases, we can convert between volume of gas and moles using the methods described above. For solutions, molarity provides a conversion factor that enables us to convert between moles of solute and volume of solution. Equation stoichiometry problems can contain any combination of two of these conversions, such as we see in Example 13.8. 

A mole of substance is the amount that contains Avogadro s number (6.022x10 ) of chemical entities (atoms, molecules, or formula units). The mass (in grams) of a mole has the same numerical value as the mass (in amu) of the entity. Thus, the mole allows us to count entitles by weighing them. Using the molar mass (jM., g/mol) of an element (or compound) and Avogadro s number as conversion factors, we can convert among amount (mol), mass (g), and number of entities. The mass fraction of element X in a compound is used to find the mass of X in any amount of the compound. 

Just as you could not make a direct conversion from the mass of jelly beans to the number of jelly beans, you cannot make a direct conversion from the mass of a substance to the number of representative particles of that substance. You must first convert mass to moles by multiplying by a conversion factor that relates moles and mass. That conversion factor is the molar mass. The number of moles must then be multiplied by a conversion factor that relates the number of representative particles to moles. For this conversion, you use will use Avogadros number. This two-step process is shown in Example Problem 10.4. 

You are given 2.50 mol of ( 3115)25 and must convert the moles to mass using the molar mass as a conversion factor. The molar mass is the sum of the molar masses of all the elements in ( 3115)25. 

You are given the moles of the reactant, CI2, and must determine the mass of the product, NaCI. You must convert from moles of CI2 to moles of NaCI using the mole ratio from the equation. Then, you need to convert moles of NaCI to grams of NaCI using the molar mass as the conversion factor. 

Step 2 Calculate the number of moles of each element in the compound. Remember, an empirical formula tells us which elements are present and the simplest whole-number ratio of their atoms. This ratio is also a mole ratio. Use the molar masses of these elements as conversion factors to convert to moles. 

Step 3 Calculate the number of moles of each element present in the sample. Use molar mass as a conversion factor. 

We use the mole ratio from the balanced equation and the molar mass of SO2 as conversion factors to convert to grams of SO2. 

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