Mass calculating numbers

Mass-mole-number calculations often involve atoms yvithin a compound as well as the compound itself. The chemical formula provides the link between moles of a compound and the number of moles of the compound s individual elements ... 

The measured NMR signal amplitude is directly proportional to the mass of adsorbate present, and the NMR signal versus pressure (measured at a fixed temperature) is then equivalent to the adsorption isotherm (mass of adsorbate versus pressure) [24-25]. As in conventional BET measurements, this assumes that the proportion of fluid in the adsorbed phase is significantly higher than the gaseous phase. It is therefore possible to correlate each relaxation time measurement with the calculated number of molecular layers of adsorbate, N (where N = 1 is monolayer coverage), also known as fractional surface coverage. 

Once you know the mass or number of molecules in 1 mol, you merely have to multiply to get the mass or number of molecules in any other given number of moles. Sometimes the calculation is easy enough to do in your head. 

The radius of the peptide molecule can be calculated from the molecular mass, Avogadro number, and the partial specific volume. 

The number of decimal places one should employ in mass calculations depends on the purpose they are used for. In the m/z range up to about 500 u, the use of isotopic mass with four decimal places will provide sufficient accuracy. Above, at least five decimal places are required, because the increasing number of atoms results in an unacceptable multiplication of many small mass errors. Beyond 1000 u, even six decimal places should be employed. However, the final results of these calculations may be reported with only four decimal places, because this is sufficient for most applications. If mass accuracies of significantly less than 1 mmu are to be expected, the use of six decimal places becomes necessary in any case. 

From a knowledge of the molecular mass, the number of molecules, Z, in the unit cell can be calculated. Examples of these calculations are in the questions at the end of the chapter. 

Divide the given mass of solute by the number of moles calculated in Step 4. This is your molecular mass, or number of grams per mole, from which you can often guess the identity of the mystery compound. 

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. 

Because one mole of any substance is a specific number of molecules (1 mol things = 6.02 x 1023 things from Chapter 2), the relative numbers of moles undergoing reaction are the same as the relative numbers of molecules. Because of the relationship of molecules to moles, the equation above can be interpreted in terms of masses calculated directly from the Periodic Table (H = 1,0 = 16, N = 24, all in g/mol). 

The approximate molar mass, calculated from the gas density data, is 89 g/mol. The empirical formula, calculated from the percentage composition data, is C2H3O with the empirical formula unit mass of 43.0. The exact molar mass must be (2)(43) = 86.0 g/mol since this is the only multiple of 43.0 (whole-number multiple) reasonably close to the approximate molecular formula of 89 g/mol. The molecule must be the equivalent of 2 empirical formulas CqHgO. 

Calculations Molar volume = -j —Volume— — Number or moles MV = V/n Densi = Vofume D= m/V Molar mass = Sum of molar masses of the atoms in the compound or Molar mass = -f-j—Mass,. j— Number or moles M= m/n... 

In Section 10.1, we learned to calculate the number of moles of any substances involved in a chemical reaction from the number of moles of any other substance. We can solve problems that include mass calculations by simply changing the masses to moles or the moles to masses, as discussed in Chapter 7. In Figure 10.2, these conversions have been added to those shown in Figure 10.1. 

The ideal gas law can be used to calculate the number of moles of gas in a sample of known mass. The number of grams divided by the number of moles in the sample yields the molar mass. 

Dividing both numbers of moles by 7.40 yields 1.00 mol C and 1.50 mol H. Multiplying both of these by 2 yields the empirical formula C2H3. The empirical formula mass is thus 27.0 amu. The number of empirical formula units in 1 mol can be calculated by using 110 amu for the molecular mass. The number must be an integer. 

Calculate either mass with molar mass or number with Avogadro s number given an amount in moles. 

A graphing calculator can run a program that calculates the numbers of protons, electrons, and neutrons given the atomic mass and numbers for an atom. For example, given a calcium-40 atom, you will calculate the numbers of protons, electrons, and neutrons in the atom. 

Multiply the calculated number of moles of helium by the conversion factor that relates mass of helium to moles of helium, molar mass. 

Example Problem 11-8 illustrated how to find the number of moles of a compound contained in a given mass. Now, you will learn how to calculate the number of representative particles—molecules or formula units—contained in a given mass and, in addition, the number of atoms or ions. Recall that no direct conversion is possible between mass and number of particles. You must first convert the given mass to moles by multiplying by the inverse of the molar mass. Then, you can convert moles to the number of representative particles by multiplying by Avogadro s number. To determine numbers of atoms or ions in a compound, you will need conversion factors that are ratios of the number of atoms or ions in the compound to one mole of compound. These are based on the chemical formula. Example Problem 11-9 provides practice in solving this type of problem. 

You are given 35.6 g AICI3 and must calculate the number of Al + ions, the number of Cl ions, and the mass in grams of one formula unit of AICI3. Molar mass, Avogadro s number, and ratios from the chemical formula are the necessary conversion factors. The ratio of AP+ ions to CE ions in the chemical formula Is 1 3. Therefore, the calculated numbers of ions should be in that ratio. The mass of one formula unit in grams should be an extremely small number. 

In the formula for a hydrate, the number of water molecules associated with each formula unit of the compound is written following a dot for example, Na2CO3T0H2O. This compound is called sodium carbonate decahydrate. In the word decahydrate, the prefix deca- means ten and the root word hydrate refers to water. Decahydrate means that ten molecules of water are associated with one formula unit of compound. The mass of water associated with a formula unit must be included in molar mass calculations. Hydrates are found with a variety of numbers of water molecules. Table 11-1 lists some common hydrates. 

Does the chemical equation tell you anything about the masses of the reactants and products Not directly. But as you learned in Chapter 11, the mass of any substance can be determined by multiplying the number of moles of the substance by the conversion factor that relates mass and number of moles, which is the molar mass. Thus, the mass of the reactants can be calculated in this way. 

What about the reactant sulfur, which you know is in excess How much of it actually reacted You can calculate the mass of sulfur needed to react completely with 1.410 mol of chlorine using a mole-to-mass calculation. The first step is to multiply the moles of chlorine by the mole ratio of sulfur to chlorine to obtain the number of moles of sulfur. Remember, the unknown is the numerator and the known is the denominator. 

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 ... 

Calculate the mass or number of moles of each component in a mixture given the percent (or fraction) composition, and the reverse, and compute the average molecular weight. 

Eqs (1.30) and (1.31) can be used to calculate number-average molar mass... 

Once /z-and thus a value for the puckering coordinate at the minimum of the well-is obtained, it is possible to extract some structural information about the molecule in the ground state, such as the ring dihedral angle. A number of papers have appeared in which dihedral angles are reported where neither geometric information nor the details of the reduced mass calculation are given. In some cases the reduced mass has been assumed by comparison with p s calculated for other... 

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