Mole and Molar Mass

The Mole, Molar Mass, and Mole-Gram Conversions... 

Formulating models A nuclear model of mass can provide a simple picture of the connections between the mole, molar mass, and the number of representative particles in a mole. 

The three most common problems that involve the mole, molar mass, and numbers of atoms, as they apply to elements, are discussed in the three following sections. As each problem is put forth, keep in mind that the methods used to solve them will also be applied to compounds later in the chapter. Each problem is discussed in greater detail here to ensure that you understand the principles. 

Discuss the relationships that exist between the mole, molar mass, and Avogadros number. 

Relationship between moles, molar mass and the mass of substance... 

Interpret the equation for a reaction that produces copper from copper ore in terms of moles, molar masses, and masses of reactants and products. 

The molar volume, 22.4 L/mol, is used as a conversion factor to convert grams per liter to grams per mole (molar mass) and also to convert liters to moles. The two conversion factors are... 

For purposes of chemical bookkeeping, it is unnecessary to know the isotopic molar masses and isotopic distributions of the elements. All we need to know is the mass of one mole of an element containing its natural composition of isotopes. These molar masses usually are included in the periodic table, and they appear on the inside front and back covers of this textbook. 

As emphasized in Section 2-, many of the calculations in chemistry involve converting back and forth among the mass of a substance, the number of moles, and the number of atoms and/or molecules. These calculations are all centered on the mole. The connections shown in Figure apply to chemical compounds as well as to atoms of pure elements. Molar mass and Avogadro s number provide links between mass of a sample, the number of moles, and the number of molecules. 

The chemicai formuia identifies the ions that are present in the finai soiution. The formula also tells us how many moles of each ion are present in one moie of the sait. Use mass, molar mass, and volume to calculate molarity. 

First, we must identify the chemistry. This is an acid-base titration in which hydrogen phthalate anions (the acid) react with OH (the base). We use the molar equality of acid and base at the stoichiometric point together with the equations that link moles with mass and volume. 

Strictly speaking, the terms molar mass and molecular weight refer to different quantities. Molar mass is the mass of one mole of polymer molecules and measured in g/mol, whereas molecular weight is dimensionless and refers to the weight (mass) of a single polymer molecule measured as multiples of the atomic mass unit u. The numerical values of both quantities are identical. Usually, no such strict distinction is made in the literature, and also in this contribution both terms will be used as synonyms for the strict term molar mass. 

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. 

Specification with regard to mass fractions, mole fractions, molar masses and degrees of polymerization... 

Note that our multiparameter LFER Eq. 5-20 includes two terms that contain a volume term (a quantitative measure of the volume of one mole molecules) as a size parameter ( vdW, size -terms). This Vi value can be the molar volume, Vn of the compound (derived from the molar mass and the density of the compound, see Chapters 3 and 4), or it can be an estimated entity (see Box 5.1). Therefore, we denote this term as Vt and not Vl. We will, however, use the term molar volume even if we refer to estimated Vt values. 

To calculate the molality of a solution prepared by dissolving 10.5 g of sodium chloride in 250 g of water, we convert the mass of sodium chloride to moles of NaCl (by dividing the mass by the molar mass) and divide it by the mass of water in kilograms ... 

When a 2.36-g sample of phosphorus was burned in chlorine, the product was 10.5 g of a phosphorus chloride. Its vapor took 1.77 times longer to effuse than the same number of moles of C02 under the same conditions of temperature and pressure. What is the molar mass and molecular formula of the phosphorus chloride ... 

Knowing both the mass and the number of moles of insulin, we can calculate the molar mass and hence the molecular mass ... 

The following equation can be used to solve problems involving mass, molar mass, and number of moles ... 

You can use what you now know about the mole to carry out calculations involving molar mass and the Avogadro constant. One mole of any compound or element contains 6.02 x 1023 particles. The compound or element has a mass, in grams, that is determined from the periodic table. 

Use the molar masses and mole ratios (coefficients) to set up the calculation ... 

We can use Avogadro s number as a conversion factor to convert moles to numbers of formula units, and vice versa. We can use the molar mass to convert moles to masses, and vice versa (Figure 7.1). 

The number of moles in a substance can be calculated with the help of its molar mass and mass. The following formula shows the relationship between the number of moles and mass. 

Since the number 16.043 represents the mass of 1 mole of methane molecules, it makes sense to call it the molar mass for methane. However, tradi-A substance s molar mass (molecular tionally, the term molecular weight has been used to describe the mass of 1 weight) is the mass in grams of mole of a substance. Thus the terms molar mass and molecular weight mean... 

In Example 3.6 we found the molecular formula by comparing the empirical formula mass with the molar mass. There is an alternative way to obtain the molecular formula. The molar mass and the percentages (by mass) of each element present can be used to compute the moles of each element present in one mole of compound. These numbers of moles then represent directly the subscripts in the molecular formula. This procedure is illustrated in Example 3.7. 

The MMA homopolymer and the unreacted PVA are removed from the reaction product by the selective extraction method. The grafted branch PMMA is separated from the backbone by oxidative cleavage of all 1,2-glycols of PVA (about 2 mole%) Molar masses of the isolated graft copolymers and the separated branches are osmo-metrically determined, after acetylation of hydroxyl groups in benzene. The diem-ical composition of the graft copolymers is determined frcan the s onification value of the acetylated sample. 

For two molar masses and two temperatures, very nice straight lines were obtained. In the temperature range considered (15 and 25°C), there is no temperature dependence. From the figure we found for the shorter chains (M = 4.2 kg/mole, N = 49) A° to be about 35 m /pmole, whereas for the longer ones (M = 12 kg/mole. N = 140), A = 220 m /pmole. The ratio 220/35 = 6.3 between the two values of A should be compared with the theoretical ratio (140/49) 2 4 g -phe agreement is not perfect but quite reasonable, also considering that the values of N are possibly... 

Determine the formula, the molar mass, and the number of moles in 2.11 g of each of the following compounds. 

When reactants are liquids, they are almost always measured by volume. So, to do calculations involving liquids, you add two more steps to the sequence of mass-mass problems—the conversions of volume to mass and of mass to volume. Five conversion factors—two densities, two molar masses, and a mole ratio—are needed for this type of calculation, as shown in Skills Toolkit 4. 

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