Grams counting molecules

The meaning of a chemical formula was discussed in Chapter 5, and we learned how to interpret formulas in terms of the numbers of atoms of each element per formula unit. In this chapter, we will learn how to calculate the number of grams of each element in any given quantity of a compound from its formula and to do other calculations involving formulas. Formula masses are presented in Section 7.1, and percent composition is considered in Section 7.2. Section 7.3 discusses the mole—the basic chemical quantity of any substance. Moles can be used to count atoms, molecules, or ions and to calculate the mass of any known number of formula units of a substance. Section 7.4 shows how to use relative mass data to determine empirical formulas, and the method is extended to molecular formulas in Section 7.5. 

Fig. 7.24 illustrates in four graphs how the optimum linear velocity, optimum d /L. optimum, column length, optimum dimensionless loading, resulting plate count, yield, cycle time, cost per gram (S/g) and production rate (kg/yr) vary with the product diffusivity for a 30 cm ID column. This result allows comparison of the added difficulty of separating proteins and small molecules by looking at the sole etFect of the diffusion coefficient. As the diffusion coefficient increases ... 

It is not necessary for every molecule of a compound to be radioactive for us to use the radioactivity as a measure of concentration (and, thereby, determine reaction rates, and so on). All that is necessary is that the sample contain enough radioactive molecules to count accurately and that we know the specific activity of the compound. Specific activity (S.A.) refers to the amount of radioactivity per unit amount of substance. It is, in fact, a way of designating the fraction of the total molecules present that is radioactive. Specific activity may be given in terms of curies per gram (Ci/g), millicuries... 

Atoms, ions, and molecules are very small, so even tiny samples have a huge number of particles. To make counting such large numbers easier, scientists use the same approach to represent the number of ions or molecules in a sample as they use for atoms. The SI unit for amount is called the moie (mol). A mole is the number of atoms in exactly 12 grams of carbon-12. 

In the arithmetic of chemistry, a lot of calculations come down to counting atoms and molecules. The international unit for the amount of substance isn t the kilogram (which is used for mass), it s the mole. Chemists need to think in terms of numbers of particles, and this is what the mole allows. The mole is a very large number 6.022 x 1023. It is the number of carbon-12 atoms in exactly 12.00 grams of that isotope. It is such an important number in chemistry that it has its own special name, Avogadro s number, named after Amadeo Avogadro (1776-1856), one of the most famous early scientists. 

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. 

The efforts in applying mass spectrometry to the measurement of radionuclides are devoted to achieving detection of small numbers of atoms. The crucial question is whether an isotope that has, say, 106 atoms in a gram of solid or liquid can be detected and quantified by MS in the presence of possibly 1021 atoms and molecules of other isotopes, including many with nearly the same mass. For some elements (e.g., Pu), detection limits below 106 atoms have been demonstrated for a variety of sample matrices (soil, water) using several mass spectrometric techniques (Beasley et al., 1998b Oughton et al., 2004 Sahoo et al., 2002). Instrumental detection limits, in terms of counts (i.e., detected ions) per atom, have exceeded 5 counts per hundred atoms under optimum conditions. 

It is interesting to observe the form in which the potential energy factor is expressed in (2 6). Consider the simple example of a reaction. 4 S. The equilibrium constant K = [E I A contains a term The chance that a molecule of. B is in its jth energy state is normally or counting on a gram-molecular basis. 

Mole (mol) (3.4) The particular quantity by which chemists usually choose to count atoms or molecules. The number of particles in one mole is defined as the number of atoms in exaaly 12 grams of C, which is also called Avogadro r number. 

The mole is often referred to as a chemist s unit of quantity. Counting atoms is a difficult process and beyond the scope of most calculators, but measuring the mass of a sample is easy when we can relate the number of atoms in a sample to its mass. This is the unique purpose of the mole. A mole of any substance is its molecular formula weight expressed in grams. Avogadro s number s a universal constant that states the number of molecules in a mole Nq = 6.023 x 10 molecules/mole. One mole (abbreviated mol) of any element (chemical compound) has the same number of chemical particles as one mole of another element (chemical compound). In other words, 1 mole of any compound contains 6.02 x 10 molecules. Review the following problem using the mole concept. 

Unfortunately, we cannot count particles—at least, not directly. Instead, we measure masses or other macroscopic quantities. These can be converted into numbers of particles. You already know how to do this conversion with mass, using molar mass as a conversion factor between mass (in grams) and number of particles (in moles) (see Section 7.5). Equation 10.1 can also be interpreted as, Four moles of NH3 molecules react with five moles of O2 molecules to produce four moles of NO molecules and six moles of H2O molecules. ... 

If you wanted to carry out this reaction, how could you measure the correct numbers of particles of aluminum and iodine Fortunately, you can count particles by measuring mass. Suppose you have a sample of an element, and the mass of the sample in grams is numerically equal to the atomic mass of the element. Scientists have discovered that this mass of an element contains 6.02 X 10 atoms of that element. This number is called Avogadro s number. Avogadro s number of particles is called a mole of particles. The mole is the SI base unit used to measure the amount of a substance and is defined as the number of particles in exactly 12 g of pure carbon-12. For the purpose of dealing with moles, the simplest unit of any substance is called a representative particle. The particle may be an atom, a molecule, a formula unit, or an ion. 

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