Relating Mass to Number of Particles

09 X10 kg P Until we know that, how can we tell how much P4O10 we ll he able to produce Unfortunately, atoms and molecules are so small and numerous that they cannot he counted directly. We need a conversion factor that converts back and forth between any mass of the element and the number of atoms contained in that mass. 

An industrial chemist must be able to calculate the amounts of reactants necessary to run an efficient reaction and predict the amount of product that will form. 

Imagine that you have decided to make a little money for schoolbooks by taking a temporary job doing inventory at the local hardware store. Your first task is to determine how many nails are in a bin filled with nails. There are a lot of nails in the bin, and you do not want to take the time to count them one by one. It would be a lot easier to weigh the nails and calculate the number of nails from the mass. To do this you need a conversion factor that allows you to convert from the mass of the nails in the bin to the number of nails in the bin. 

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Now that you can relate mass to moles, you can also relate mass to number of particles by first converting mass to moles and then using the following relationship. 

What if you wanted to compare amounts of substances, and you only knew their masses You would probably convert their masses to moles. The Avogadro constant relates the molar amount to the number of particles. Examine the next Sample Problem to learn how to convert mass to number of particles. 

Avogadro s number is the number of particles (atoms, molecules,. or formula units) that are in a mole of a substance. In this lab, you will relate a common object to the concept of Avogadro s number by finding the mass and volume of one mole of the object. 

The mole (mol) is the amount of a substance that contains the same number of particles as atoms in exactly 12 grams of carbon-12. This number of particles (atoms or molecules or ions) per mole is called Avogadro s number and is numerically equal to 6.022 x 1023 particles. The mole is simply a term that represents a certain number of particles, like a dozen or a pair. That relates moles to the microscopic world, but what about the macroscopic world The mole also represents a certain mass of a chemical substance. That mass is the substance s atomic or molecular mass expressed in grams. In Chapter 5, the Basics chapter, we described the atomic mass of an element in terms of atomic mass units (amu). This was the mass associated with an individual atom. Then we described how one could calculate the mass of a compound by simply adding together the masses, in amu, of the individual elements in the compound. This is still the case, but at the macroscopic level the unit of grams is used to represent the quantity of a mole. Thus, the following relationships apply ... 

Figure 5 shows the relations between fractions N0/Nz and Nq/Nz (Nz = Nq + Na) on the number of particles-I and particles-II respectively, and the fractions m0/mz(te) and ma/mz(te) of mass of zeolite formed at the end of the crystallization process (by the growth of nuclei-I and nuclei-II, respectively). The rapid increase in the number Ra of particles-II relative to the number of all particles present in the system (particles-I + particles-II) influences very slightly the fraction raQ of their mass in the final product, as well as the numerical value of q, so that m0/mz(te) > raa/mz(te) and q < 4 for Na/Nz < 0.97. This means that particles-I (formed by the growth of nuclei-I), even in small proportions, influence the overall crystallization process much more than particles-II, i.e., m0/raz(te) = 0.95 and mQ/mz(te) = 0.05 for Nq/Nz = 0.52 B0/mz(te) = 0.876 and ma/mz(te) = 0.124 for Ua/Nz = 0.76 B0/m7(te) = 0.646 and ma/mz(te) = 0.354 for Ka/Nz = 0.939 (see Figure 5). A good illustration for the influence of nuclei-I and nuclei-II on the crystallization of zeolites is shown in Figure 6.

In section 5.1, you learned about the average atomic mass of an element. Then, in section 5.2, you learned how chemists group particles using the mole. In the final section of this chapter, you will learn how to use the average atomic masses of the elements to determine the mass of a mole of any substance. You will learn about a relationship that will allow you to relate the mass of a sample to the number of particles it contains. 

The molar mass relates the amount of an element or a compound, in moles, to its mass. Similarly, the Avogadro constant relates the number of particles to the molar amount. 

Now that you have learned how the number of particles, number of moles, and mass of a substance are related, you can convert from one value to another. Usually chemists convert from moles to mass and from mass to moles. Mass is a property that can be measured easily. The following graphic shows the factors used to convert between particles, moles, and mass. Moles are a convenient way to communicate the amount of a substance. 

In this chapter, you have learned about the relationships among the number of particles in a substance, the amount of a substance in moles, and the mass of a substance. Given the mass of any substance, you can now determine how many moles and particles make it up. In the next chapter, you will explore the mole concept further. You will learn how the mass proportions of elements in compounds relate to their formulas... 

You can get the same kind of information from a balanced chemical equation. In Chapter 4, you learned how to classify chemical reactions and balance the chemical equations that describe them. In Chapters 5 and 6, you learned how chemists relate the number of particles in a substance to the amount of the substance in moles and grams. In this section, you will use your knowledge to interpret the information in a chemical equation, in terms of particles, moles, and mass. Try the following Express Lab to explore the molar relationships between products and reactants. 

You now know what a balanced chemical equation tells you in terms of number of particles, number of moles, and mass of products and reactants. How do you use this information Because reactants and products are related by a fixed ratio, if you know the number of moles of one substance, the balanced equation tells you the number of moles of all the other substances. In Chapters 5 and 6, you learned how to convert between particles, moles, and mass. Therefore, if you know the amount of one substance in a chemical reaction (in particles, moles, or mass), you can calculate the amount of any other substance in the reaction (in particles, moles, or mass), using the information in the balanced chemical equation. 

The number of moles, which is represented by n, is used for various calculations in chemistry. The number of moles is related to the number of particles, mass or volume of substances. 

The distribution of aerosols (shown in Figure 2—per unit mass) can also be expressed in terms of the total number of particles, which places greater emphasis on the smaller particles and provides information about the nuclei mode and the process of accumulation. Aerosol concentrations are sometimes expressed in terms of aerosol surface area, which is closely related to visibility impacts. 

Let us look again at the balanced reaction equation above with some actual masses. (From the periodic table, Ca has a RAM of 40 Cl, 35.5 C, 12 O, 16, and H, 1.) If we use these quantities, then because the masses relate to the number of particles, we will have the correct number of each of the different particles to satisfy fully all of the reacting materials. 

Particle-particle interaction is central to a wide range of engineering applications and processing industries. Examples include coagulation, flocculation, dispersion, emulsification, and froth flotation. In these applications, the particle size is small, and the overall particulate behavior is determined by forces associated with the surface properties rather than those related to mass or volume. The surface properties of a particle in a liquid medium are the result of a complex interaction between molecules, atoms, and ions at the particle surface and in the surrounding liquid. If a number of particles are present, interactions also take place between particles at short separation distances, and it is this interaction that is of most interest as it can determine the overall stability or instability of dispersions and/or suspensions. 

Fractal dimension, D is considered as an effective number that characterises the irregular electrode surface. The term has been related to physical quantities such as mass distribution, density of vibrational stages, conductivity and elasticity. If we consider a 2-D fractal picture in its self-similar multi-steps, one can draw various spheres of known radii at various points of its structure and may thus count the number of particles, N inside the sphere by microscope, following relation will then hold good ... 

Taking into account that the subsequent fate of the radicals formed in the reaction (1) depends, in the general case, on the relation between the number of collisions with other particles in the gas phase and with the surface and also on the nature, concentration and reactivity of the surface centers, we utilized the approach proposed in [18] to simulate the heterogeneous-homogeneous oxidation of methane in combination with mass-transfer in the gas-solid system. The reaction space was considered as a gas volume of a varied thickness (L) exposed to a flat surface with a varied concentration of active sites (C). 

The concept of molar mass makes it easy to determine the number of particles in a sample of a substance by simply measuring the mass of the sample. The concept is also useful in relating masses of reactants and products in chemical reactions. 

Solute concentration must be in mok-based units. The number of particles (molecules or ions) is critical here, not the mass of solute. One heain/ molecule will have exactly the same effect on the freezing or boiling point as one light molecule. A mole-based unit, because it is related directly to Avogadro s number, will correctly represent the number of particles in solution. 

Measurements performed at the exhausts of commercial residential heating devices have shown that particulate matter emission is negligible below the detection limit of instruments based on mass measurement. However, there is increasing evidence that the concentration of the "number" of particles (related to their size) rather than their cumulative mass might be responsible for the observed effects of particulate on health and the environment. For these reasons it is important to control the emission of the number of particles of specific sizes, rather than their mass from combustion systems that are widely used, such as residential burners. In particular, the interest should be focused on the ultrafine emitted particles, those with mean sizes below 100 nm that, because of the low sizes, do not contribute massively to mass emission. 

The mass of a particle, m, or the diameter, Dp, can also be used as the independent variable for the mathematical description of the aerosol distribution. We saw in Chapter 8 that these functions are not equal to each other but can be easily related. For example, if the radius Rp is used as an independent variable for the distribution function n (Rp, t), then the concentration of particles dN in the size range Rp to (Rp + dRp) is given by dN = riR(Rp,t) dRp. But the same number of particles is equal to n(v,t)dv, where v = %itRp or dv = 4nRp dRp, so... 

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