Representative particles, 321 convert

Why is it not possible to convert between the mass of a substance and the number of representative particles, as represented by double-arrow 4 of the diagram ... 

Convert moles to number of representative particles and number of representative particles to moles. 

For more practice converting from moles to representative particles, go to Supplemental Practice Problems in Appendix A. 

Explain bow you can convert from tbe number of representative particles of a substance to moles of that substance. 

Just as you cannot make a direct conversion from the mass of jellybeans to the number of jellybeans, you caimot make a direct conversion from the mass of a substance to the number of representative particles in that substance. You must first convert the mass to moles by multiplying by a conversion factor that relates moles and mass. Can you identily the conversion factor The number of moles must then be multiplied by a conversion factor that relates the number of representative particles to moles. That conversion factor is Avogadro s number. 

Now that you have learned about and practiced conversions between mass, moles, and representative particles, you can see that the mole is at the center of these calculations. Mass must always be converted to moles before being converted to atoms, and atoms must similarly be converted to moles before calculating their mass. Figure 11-5 shows the steps to follow as you work with these conversions. 

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 can convert between moles and number of representative particles by multiplying the known quantity by the proper conversion factor. Example Problem 10.1 further illustrates the conversion process. 

Challenge Convert each given mass to number of representative particles. Identify the type of representative particle, and express the number in scientific notation. 

Figure 10.8 The mole is at the center of conversions between mass and particles (atoms, ions, or molecules). In the figure, mass is represented by a balance, moles by a bag of particles, and representative particles by the contents that are spilling out of the bag. Two steps are needed to convert from mass to representative particles or the reverse. 

Now that you have practiced conversions between mass, moles, and representative particles, you probably realize that the mole is at the center of these calculations. Mass must always be converted to moles before being converted to atoms, and atoms must similarly be converted to moles before calculating their mass. Figure 10.8 shows the steps to follow as you complete these conversions. In the Example Problems, two steps were used to convert either mass to moles to atoms, or atoms to moles to mass. Instead of two separate steps, these conversions can be made in one step. Suppose you want to find out how many atoms of oxygen are in 1.00 g of oxygen. This calculation involves two conversions— mass to moles and then moles to atoms. You could set up one equation like this. 

You have learned that different kinds of representative particles are counted using the mole. In the last section, you read how to use molar mass to convert among moles, mass, and number of particles of an element. Can you make similar conversions for compounds and ions Yes, you can, but to do so you will need to know the molar mass of the compounds and ions involved. 

Conversions between mass, moles, and the number of particles are summarized in Figure 10.11. Note that molar mass and the inverse of molar mass are conversion factors between mass and number of moles. Avogadros number and its inverse are the conversion factors between moles and the number of representative particles. To convert between moles and the number of moles of atoms or ions contained in the compound, use the ratio of moles of atoms or ions to 1 mole of compound or its inverse, which are shown on the upward and downward arrows in Figure 10.11. These ratios are derived from the subscripts in the chemical formula. 

Fig. 11. Variation of heat-transfer coefficient, where O represents experimental results at 100 kPa , 500 kPa 0, 1000 kPa and , 2000 kPa, of pressure (23) for (a) a 0.061-mm glass—CO2 system (Group A particles) and (b) a 0.475-mm glass—N2 system (Group B and D particles). To convert kPa to psi,...

Electrostatic Interaction. Similarly charged particles repel one another. The charges on a particle surface may be due to hydrolysis of surface groups or adsorption of ions from solution. The surface charge density can be converted to an effective surface potential, /, when the potential is <30 mV, using the foUowing equation, where -Np represents the Faraday constant and Ai the gas law constant. 

The diametei of average mass and surface area are quantities that involve the size raised to a power, sometimes referred to as the moment, which is descriptive of the fact that the surface area is proportional to the square of the diameter, and the mass or volume of a particle is proportional to the cube of its diameter. These averages represent means as calculated from the different powers of the diameter and mathematically converted back to units of diameter by taking the root of the moment. It is not unusual for a polydispersed particle population to exhibit a diameter of average mass as being one or two orders of magnitude larger than the arithmetic mean of the diameters. In any size distribution, the relation ia equation 4 always holds. 

When a distribufion of particle sizes which must be collected is present, the aclual size distribution must be converted to a mass distribution by aerodynamic size. Frequently the distribution can be represented or approximated by a log-normal distribution (a straight line on a log-log plot of cumulative mass percent of particles versus diameter) wmich can be characterized by the mass median particle diameter dp5o and the standard statistical deviation of particles from the median [Pg.1428]

In this equation, the (1/r2) term represents the electrostatic repulsion force on the a-particle by the gold atom nucleus. The (y/r) term converts the total velocity change (Av) into the y-component of the velocity change (Av ). The proportionality constant 7.311 X 1(T20 m3/s accounts for the charges of the particles and the time interval used. 

The data chain of the collected atoms can be converted to a one-dimensional composition-depth profile. The depth profile shows an average concentration of solute within the aperture, and there is always a possibility that the chemical information from the selected area is a convolution of more than one phase, as indicated diagrammatically in Figure 1.5, which represents the analysis of a FIM specimen containing second phase particles and also an interface across which there is a change of composition. 

Figure 8B shows the characteristic theoretical and practical collection efficiency curve. The x-axis may be plotted as particle diameter, in which case a series of curves at ever-decreasing sizes representing different stages of the impactor would exist. Converting the data to the square root of Stokes number overlays each of the particle size curves. The characteristic Stokes number for circular jets is 0.22. 

For a reaction represented by A(g) + bB(s) —> produc1(g), derive the relation between time (t) of reaction and fraction of B converted (/B), if the particle is spherical with an initial radius R0, and the Ranz-Marshall correlation for kAg(R) is valid, where R is the radius at t. Other assumptions are given above. 

If the particles do not have the same residence time and are not all of the same size, we must average with respect to both t and R, to obtain the fraction converted at the reactor outlet. This double averaging is represented by 1 - fB, and may be obtained by... 

Sum Distribution. A cumulative presentation of equivalent diameters, which converts the density distribution curve to a plot that represents percentages of particles which are smaller than a given equivalent diameter D. 

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