Substances with the Mole

Chemists make new substances in a process called synthesis. And a logical question they ask is how much — how much of this reactant do I need to make this much product How much product Ccin I mcike with this much reactant  

To cinswer these questions, chemists must be able to take a balanced chemical equation, expressed in terms of atoms and molecules, and convert it to grams or pounds or tons — some type of unit they can actually weigh out in the lab. The mole concept enables chemists to move from the microscopic world of atoms and molecules to the reed world of grams and kilograms, and it s one of the most importcuit central concepts in chemistry. In this chapter, I introduce you to Mr. Mole. 

In chemistry, you count very large numbers of particles, such as atoms and molecules. To count them efficiently and quickly, you use the count-by-weighing method, which means you need to know how much individual atoms and molecules weigh. Here s where you find the weights  

Atoms Get the weights of the individual atoms on the periodic table — just find the atomic mass number. 

Compounds Simply add together the weights of the individual atoms in the compound to figure the molecular weight or formula weight. (Note Molecular weights refer to covalently bonded compounds, and formula weights refer to both ionic and covalent compounds.) 

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Although the chemical member of the SI base quantities is amount of substance with the mole as the corresponding... 

Solution. 1) The precipitated solid calcium hydroxide Ca(OH)2(s) constitutes a pure substance with the mole fraction a = x = 1 thus, from eqn. (5.33) we... 

All possible titration problems will simply be adding steps before and/or after one of these two mole ratio terms. The problem will begin with the substance with the most information, and proceed through one of these mole ratios to the substance with less information given. 

Anytime the problem deals with the moles and the mass of a substance, you will very, very likely need to know the molar mass (molecular weight) of the substance to complete the problem. 

You use the coefficients from this equation along with the mole value calculated in Step 4 to determine the mole value of the unknown substance you re titrating ... 

In these calculations, you will be converting either from moles of the given substance to grams of the unknown or from grams of the given substance to moles of the unknown. Either way, you will need to use the mole ratio as the mechanism for crossing over from one substance to the next. Other than the step with the mole ratio, these calculations are the same as the calculations from earlier in the chapter that converted mass to moles or moles to mass for a single substance. We ll use the same equation from the sample problem to continue with this example. 

Before continuing, you should take note of a few things. First, because the reaction vessel is 1.00 liters, we can substitute the number of moles for the molarity. Second, because we don t know the equilibrium concentrations of the two known substances (H2 and I2), we must represent the decrease in each substance with the variable x. Finally, the ratio 2 1 written in the A row for HI represents the mole ratio of HI to the other reactants. 

The second, symbol s, is the SI unit of time, defined as the duration of 9,192,631,770 cycles of radiation associated with a specified transition of the cesium atom. The meter, symbol m, is the fundamental unit of length, defined as the distance light travels in a vacuum during 1/299,792,458 of a second. The kilogram, symbol kg, is the mass of a platinum/ iridium cylinder kept at the International Bureau of Weights and Measures at Sevres, France. The unit of temperature is the kelvin, symbol K, equal to 1/273.16 of the thermodynamic temperature of the triple point of water. A more detailed discussion of tern-perature, the characteristic dimension of thermodynamics, is given in Sec. 1.4. The measure of the amount of substance is the mole, symbol mol, defined as the amount of substance represented by as many elementary entities (e.g., molecules)... 

In general, the term SW represents all different forms of work. Work is the product of an intensive variable and a differential of an extensive variable. For example, if the system is displaced by a distance dl under a force F, it performs the work of -Fdl. If dNt moles of substance / with the chemical potential /a, flow from the system to its surroundings, the chemical work of -pdNi occurs. Thus the total work becomes... 

A related, but simpler, way to determine which reactant is limiting is to compare the mole ratio of the substances required by the balanced equation with the mole ratio of reactants actually present. For example, in this case the mole ratio of H2 to N2 required by the balanced equation is... 

For each of the following pairs, choose the substance with the higher positional probability (per mole) at a given temperature. 

The mole is to the amount of substance (or chemical amount) as the gram is to mass. Like other units of the SI system, prefixes can be used with the mole, so it is permissible to refer to 0.001 mol as 1 mmol just as 0.001 g is equivalent to 1 mg. 

The activity coefficient y, is in general a function of pressure and temperature together with the mole fractions of all substances in solution. For an ideal solution y, = 1. The... 

I have deliberately violated this rule in using two different symbols for the volume concentration. The traditional symbol for the volume concentration in units of mol per litre is c. This is a non-SI unit in the sense that it is not derived directly from the base units, but involves a numerical factor as well. It is an SI unit in the sense that it involves legitimate SI units for amount of substance (mol) and volume (dm ). As a laboratory unit of concentration c is going to be with us for a long time. Rather than use this symbol for the SI unit of concentration derived simply from the base units, mol/m, I have introduced the symbol c for the SI base unit concentration. The use of c in the equations avoids both cumbersome numerical factors and confusion with the moles-per-litre concentration. Similarly, I have used A for number of molecules per cubic metre. 

The activity coefficient y, is in general a function of pressure and temperature together with the mole fractions of all substances in solution. For an ideal solution = 1. The standard chemical potential /x is defined as the chemical potential at the hypothetical state for which Yi 1 and jc, —1 (Denbigh, 1981). The product of the mole fraction jr, of a solution component and its activity coefficient y, is defined as the activity, a of the component... 

For a strongly diluted substance, the change of with the mole fraction x is negligible compared to the strongly changing term KT Inx, which in the limit... 

Indifferent Substances The chemical potential of homogeneous mixtures can be applied so that reactions between mixed phases can be treated exactly like reactions between pure substances. As an example the chemical drive Amix for the mixing process of two substances that are indifferent to each other should be determined. Because the conversion numbers va and vb coincide with the mole fractions Xa and Xb, the conversion formula simplifies to... 

The by-products can be easily removed from the product solution leaving the column reactors by multi-step crystallization. After evaporation and crystallization isomaltulose (Palatinose ) is separated by centrifugation and dried. The process yields isomaltulose (Palatinose ) as a free-flowing, non-hygroscopic crystalline substance with one mole crystal water. The mother liquor of the isomaltulose (Palatinose ) crystallization is the only by-product of the process. Because this liquid is used e.g. as feed stuff, the whole isomaltulose (Palatinose ) production process is free of waste products. 

We use the quantitative information inherent in chemical formulas and equations together with the mole concept to predict the amounts of substances consumed or produced in chemical reactions. 

Molar mass with units [g/mol] or [kg/mol], (NOT molecular mass] - because we deal with the moles of substance and NOT with single molecules). The unitless term molecular weight is also accepted by lUPAC. High molar mass is the general, fundamental property of polymers. 

We then use chemical formulas to relate the masses of substances with the numbers of atoms, molecules, or ions they contain, which leads to the crucially important concept of a mole. A mole is 6.022 X 10 objects (atoms, molecules, ions, or whatever). 

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