Molecules relationship with mole

Figure 3.4 Summary of the mass-mole-number relationships for compounds. Moles of a compound are related to grams of the compound through the molar mass (jtt in g/mol) and to the number of molecules (or formula units) through Avogadro s number (6.022 XICF molecules/mol). To find the number of molecules (or formula units) in a given mass, or vice versa, convert the information to moles first. With the chemical formula, you can calculate mass-mole-number information about each component element.

This balanced equation can be read as 4 iron atoms react with 3 oxygen molecules to produce 2 iron(III) oxide units. However, the coefficients can stand not only for the number of atoms or molecules (microscopic level) but they can also stand for the number of moles of reactants or products. So the equation can also be read as 4 mol of iron react with 3 mol of oxygen to produce 2 mol ofiron(III) oxide. In addition, if we know the number of moles, the number of grams or molecules may be calculated. This is stoichiometry, the calculation of the amount (mass, moles, particles) of one substance in the chemical equation from another. The coefficients in the balanced chemical equation define the mathematical relationship between the reactants and products and allow the conversion from moles of one chemical species in the reaction to another. 

If a liquid is placed into a sealed container, molecules will evaporate from the surface of the liquid and will eventually establish a gas phase over the liquid that is in equilibrium with the liquid phase. This is the vapor pressure of the liquid. This vapor pressure is temperature dependent, the higher the temperature the higher the vapor pressure. If a solution is prepared, then the solvent contribution to the vapor pressure of the solution depends upon the vapor pressure of the pure solvent, P°soivenb and the mole fraction of the solvent. We can find the contribution of solvent to the vapor pressure of the solution by the following relationship ... 

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 ... 

The relationship above gives a way of converting from grams to moles to particles, and vice versa. If you have any one of the three quantities, you can calculate the other two. This becomes extremely useful in working with chemical equations, as we will see later, because the coefficients in the balanced chemical equation are not only the number of individual atoms or molecules at the microscopic level, but also the number of moles at the macroscopic level. 

Fig. 37. Polymerization of propylene oxide (PO) initiated with the (TPP)AlCl (l,X=Cl)-2-pro-panol (2-PrOH) system in the presence of methylaluminum bis(2,6-di-tert-butyl-4-methyl-phenolate) (3e) ([2-PrOH]o/[PO]o/[l]o=9/200/l) in CH2CI2 at rt. Relationship between p/ TPP ( ) [Mw/Mn (O)] at 100% conversion and the initial mole ratio [3e]o/[l]o-l p and ATtpp Numbers of the molecules of the produced polymer and initiator 1, respectively...

It has now been shown that solution paramagnetism can very often be correlated with association (69, 73, 108, 126), the axial perturbation being produced by other solute molecules. This effect takes place simultaneously with the solvation (73), but very little is so far known about the relative degrees of solvation and of association, or about the relative powers of the two effects to produce a low-lying triplet. Where association is responsible for the paramagnetism, the susceptibility should be strongly concentration-dependent, the exact relationship depending on the number of mole-... 

Atoms and molecules react in specific ratios. In the laboratory, however, chemists work with bulk quantities of materials, which are measured by mass. Chemists therefore need to know the relationship between the mass of a given sample and the number of atoms or molecules contained in that mass. The key to this relationship is the mole. Recall from Section 7.2 that the mole is a unit equal to 6.02 X 1023. This number is known as Avogadro s number, in honor of Amadeo Avogadro (Section 3-3). 

A chemical equation represents the relationship of the reactants and products through a numerical relationship expressed by the coefficients associated with the participants. The coefficients can be interpreted as telling us the number of molecules or moles of materials involved but they also represent the volumes of those participants that are gases, assuming a constant temperature and pressure (T and P). An example of these relationships is as follows ... 

Remember that kinetic energy is 1/2mv1. The Boltzmann constant k is equal to the ideal gas constant R divided by Avogadro s number. Avogadro s number is the number of molecules in a mole, so the Boltzmann constant treats individual molecules, while the ideal gas constant deals with moles of molecules. So, if we use the molecular mass (M), we need to use the ideal gas constant. Also, we re always safest in physics when we stick to SI units, so let s express the molecular mass in units of kg/mol and R in units of J/mol/K. So, on a molar scale, we can recast the relationship between kinetic energy and temperature as ... 

Flory s mathematical relationships for the free energy change that occurs when a solute is mixed with a solvent for the solution phase and the solid phase have been discussed as they apply to collagen assembly by Silver (1987). The free energy of mixing of solute and solvent per mole of molecules is equivalent to the change in chemical potential of a desired state (p)... 

Figure 2. Relationship between the number of moles of ethylene oxide in octyl- or nonyl-phenol polyoxyethylene glycol ether surfactant molecules and the toxicity index of these surfactants in mixtures with (a) paraquat and (b) dalapon on corn plants.

One property of the surfactant molecule recently studied in detail has been the influence of the number of moles of ethylene oxide (EO) in the lipophilic side chain on herbicide penetration and activity. A surfactant with a small number of moles of EO—i.e., 1-5—or a short hydrophilic chain appears to be too nonpolar, whereas one with a large number of moles of EO—i.e., 40—is too large to form layers as efficiently as those with an intermediate number of moles—i.e., 10-20. The relationship between the number of moles of EO in three alkylarylpolyoxyethylene glycol ether surfactants and the toxicity of three different herbicide solutions is illustrated in Figure 3. 

Figure 3. Relationship between the number of moles of ethylene oxide in octylphenol (%), nonylphenol ( ), or laurylphenol ( J) polyoxyethylene glycol ether surfactant molecules and the toxicity index of these surfactants in mixtures with (a) paraquat, (b) dalapon, and (c) amitrole on corn plants. Herbicides applied at 1/64, 10, and 5 lb./ acre, respectively surfactant concentration was 0.005M in all cases. Toxicity index calculated by expressing fresh weight for each treatment as percentage of untreated control and subtracting this value from 100 (58)...

So the chemical equation N2(g) + 3H2(g) -> 2NH3(g) also means that 1 mol of nitrogen molecules reacts with 3 mol of hydrogen molecules to form 2 mol of ammonia molecules. The relationships between moles in a balanced chemical equation are called mole ratios. For example, the mole ratio of nitrogen to hydrogen in the equation above is 1 mol N2 3 mol H2. The mole ratio of hydrogen to ammonia is 3 mol H2 2 mol NH3. 

You have already encountered problems involving moles, molecules, and molar masses earlier in this book. There is still one other relationship that needs to be connected with the mole and that is molar volume. Once you make a connection between moles and volume, mass, and molecules you will be able to solve problems easily. One very helpful mnemonic device to use is the Mole-Go-Round. Some think of this method as a way of cheating the system, but because the SAT II exam does not require you to show work, the Mole-Go-Round is a perfectly acceptable method for achieving better results. 

The frequency with which A molecules in a solution will encounter B molecules is this frequency multiplied by ns, the mole fraction of B. For very dilute solutions ub = Nb/Nb, the ratio of the molecular densities of B to S molecules. But l/Ns, the volume per solvent molecule, can be written as t ab, with y determined by the packing factor for the lattice. By substituting these relationships in Eq, (XV.2.2) we can write for the encounter frequency of A and B in such a lattice s... 

Sn(CH3)3l dissolved in nitrobenzene as a function of concentration of various EPD solvents added (35). In noncoordinating or weakly coordinating solvents, such as hexane, earbon tetrachloride, 1,2-dichloroethane, nitrobenzene, or nitromethane, Sn(CH3)3l is present in an unionized state (tetrahedral molecules). Addition of a stronger EPD solvent to this solution provokes ionization, presumably with formation of trigonal bipju amidal cations [Sn(CH3)3 (EPD)2J. Table II reveals that the molar conductivities at a given mole ratio EPD Sn(CH3)3l are (with the exception of pyridine) in accordance with the relative solvent donicities. No relationship appears to exist between conductivities and the dipole moments or the dielectric constants of the solvents. 

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