Calculations Using Molar Mass

Note The term molecular weight is deprecated because weight is the gravitational force on an object that varies with geographical location. Historically, the term has been used to denote the molar mass calculated using isotope averaged atomic masses for the constituent elements. 

The information obtained in the course of calculating the molar mass is used to determine the mass percent of H in decane. 

Using the molar mass, calculate the moles of all weighed samples. The moles of substances are converted to molarities by dividing by the volume (in liters) of the solution. Molarities may also be determined from pipet or buret readings using the dilution equation. (If a buret is used, one of the volumes is calculated from the difference between the initial and final readings.) The dilution equation may be needed to calculate the concentration of each reactant immediately after all the solutions are mixed. 

The molar masses of elements are determined by using mass spectrometry to measure the masses of the individual isotopes and their abundances. The mass per mole of atoms is the mass of an individual atom multiplied by the Avogadro constant (the number of atoms per mole). However, there is a complication. Most elements occur in nature as a mixture of isotopes we saw in Section B, for instance, that neon occurs as three isotopes, each with a different mass. In chemistry, we almost always deal with natural samples of elements, which have the natural abundance of isotopes. So, we need the average molar mass, the molar mass calculated by taking into account the masses of the isotopes and their relative abundances in typical samples. All molar masses quoted in this text refer to these average values. Their values are given in Appendix 2D. They are also included in the periodic table inside the front cover and in the alphabetical list of elements inside the back cover. 

Molar mass distributions of PDADMAC were also determined by fractionation using dioxane/methanol system [144] and from sedimentation velocity measurements in 1 m NaCl solution [134]. The molar mass calculations were based on the s-M relation [134] ... 

Determine the molar mass of calcium oxalate. Use the mass of calcium oxalate and its molar mass to find the amount (in mol) of calcium oxalate. Write the net ionic equation for the formation of calcium oxalate. From the coefficients in the net ionic equation, find the amount of oxalate ions (in mol). Calculate the mass of oxalate ions from the amount of oxalate ions (in mol) and the molar mass. Calculate the mass percent of oxalate ions in rhubarb leaves from the mass of the leaves and the mass of the oxalate ions present. 

The calculation of copolymer molar mass averages and so on, and copolymer polydispersity D is done as in conventional GPC calculations using the copolymer molar mass calculated from Eq. (3). 

Calculate the mass in grams of one formula unit of AICI3. Start with molar mass and use the inverse of Avogadro s number as a conversion factor. 

For most practical purposes we are interested in the masses of reactants and products, because those are the quantities that are directly measured. In this case, the molar masses (calculated from a table of atomic masses) are used to convert the number of moles of a substance (in moles) to its mass (in grams), as illustrated by Example 2.6. Sometimes, however, we are also interested in knowing the number of molecules in a sample. The mole allows us to convert easily from mass to numbers of molecules as follows ... 

Conversion factors constructed from molarities can be used in stoichiometric calculations in very much the same way conversion factors from molar mass are used. When a substance is pure, its molar mass can be used to convert back and forth between the measurable property of mass and moles. When a substance is in solution, its molarity can be used to convert between the measurable property of volume of solution and moles of solute. 

The term molar mass is used all the time in chemical calculations, so you need to know what it means. First, it is a mass, so it has units of mass, commonly the gram. Second, it concerns the mole (Avogadro s number). Whether you re dealing with elements or compounds, the molar... 

Equation (6-52) generally will be used here. An apparent molar mass A/app can be defined as a molar mass calculated from experimental data at finite concentrations from an equation applicable to infinite dilution only ... 

The SEC curves of these polyethers show low molar masses, calculated by using polystyrene standards. 

Often, size exclusion chromatograms (SEC) (compare section 11.7, Size Exclusion Chromatography) of polymers under study are expressed as differential representations of molar mass dispersity. The chromatographic retention volumes are directly transformed into the molar masses. This approach renders useful immediate information about tendencies of molar mass evolution in the course of building or decomposition polyreactions but the absolute values of molar mass can be only rarely extracted from it. As a rale, polystyrene calibrations are applied for molar mass calculation so that one deals with the polystyrene equivalent molar masses, not with the absolute values. The resulting dispersity (distribution) functions may be heavily skewed because the linear part of the calibration dependence for the polymer under study may exhibit well different slope compared with the polystyrene calibration, which was employed for the transformation of retention volumes into molar masses. 

Molar mass is useful for chemical calculations because it provides a connection between a quantity that is easy to measure (mass) and one that is conceptually important (moles). Another readily measured quantity is volume. When we work with aqueous solutions, we often use volume in calculations rather than mass. It should not be surprising, therefore, that we would want to define quantities that will help us relate a volume measurement to the number of moles. 

Mass-to-mass calculations use the mole ratio and the molar masses of the given and unknown substances. 

You should take time at this point to look at each type of stoichiometric conversion and make note that in every t3q>e, you must begin with a correctly balanced chemical equation. It is important to remember that without a balanced equation, you will not have an accurate molar ratio and will not be able to calculate the correct molar mass to use in your conversions. 

Fig. 3 illustrates the sequence of steps required for the calculation of and values of representative compounds from the volume increments given in Tables 1 and 2 and the volumes of Table 8. More complex examples (NAD", NADPH2, CoASAc, heme b) are described in [94D1, 97D2, 2001D2]. For the calculation procedure, the empirical and structural formulae as well as the value for the molar mass are used. 

The second term in brackets in equation 36 is the separative work produced per unit time, called the separative capacity of the cascade. It is a function only of the rates and concentrations of the separation task being performed, and its value can be calculated quite easily from a value balance about the cascade. The separative capacity, sometimes called the separative power, is a defined mathematical quantity. Its usefulness arises from the fact that it is directly proportional to the total flow in the cascade and, therefore, directly proportional to the amount of equipment required for the cascade, the power requirement of the cascade, and the cost of the cascade. The separative capacity can be calculated using either molar flows and mol fractions or mass flows and weight fractions. The common unit for measuring separative work is the separative work unit (SWU) which is obtained when the flows are measured in kilograms of uranium and the concentrations in weight fractions. 

As you will see shortly, the formula of a compound can be used to determine the mass percents of the elements present. Conversely, if the percentages of the elements are known, the simplest formula can be determined. Knowing the molar mass of a molecular compound, it is possible to go one step further and find the molecular formula. In this section we will consider how these three types of calculations are carried out. 

---