Using Moles

Why is it important to know how may atoms or molecules are present in any particular mass  

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Thermodynamic Relationships. A closed container with vapor and liquid phases at thermodynamic equiUbrium may be depicted as in Figure 2, where at least two mixture components ate present in each phase. The components distribute themselves between the phases according to their relative volatiUties. A distribution ratio for mixture component i may be defined using mole fractions ... 

Equation (25-2) is frequently used for a kinetic modehng of a burner using mole fractions in the range of 0.15 and 0.001 for oxygen and HC, respectively. The rate constant is generally of the following Arrhenius form ... 

Mole The SI unit of quantity the amount of a pure element or chemical compound that contains the same number of atoms or molecules. It is often simpler to use moles rather than volume or mass when working with gases. Moles are given by... 

Using mole fractions as the driving force, equation 10.35 becomes ... 

To be unambiguous when using moles, we must be specific about which entities (that is, which atoms, molecules, formula units, or ions) we mean. For example, hydrogen occurs naturally as a gas, with each molecule built from two atoms, which is why it is denoted H2. We write 1 mol H if we mean hydrogen atoms or 1 mol H2 if we mean hydrogen molecules. Note that 1 mol H2 corresponds to 2 mol H. 

The component balance for a variable-volume but otherwise ideal batch reactor can be written using moles rather than concentrations ... 

Solution The analysis could be carried out using mole fractions as the composition variable, but this would restrict applicability to the specific conditions of the experiment. Greater generality is possible by converting to concentration units. The results will then apply to somewhat different pressures. The somewhat recognizes the fact that the reaction mechanism and even the equation of state may change at extreme pressures. The results will not apply at different temperatures since k and kc will be functions of temperature. The temperature dependence of rate constants is considered in Chapter 5. 

We do this problem using moles. Eirst, determine the amounts present in the solution before addition of... 

Because we know we are dealing with a buffer solution made from a specific conjugate acid-base pair, we can work directly with the buffer equation. We need to calculate the ratio of concentrations of conjugate base and acid that will produce a buffer solution of the desired pH. Then we use mole-mass-volume relationships to translate the ratio into actual quantities. 

This problem is similar to CONSTILL except that three components benzene, xylene and toluene are considered. Thus, as explained in Sec. 3.3.3.4, each component of the mixture may be expressed by a separate component mass balance. Using mole fractions one balance can be omitted, and replaced by the condition that the sum of the mole fractions must be equal to unity. 

SI (le Systeme International d UniUs) units are used in many countries to express clinical laboratory and serum drug concentration data. Instead of employing units of mass (such as micrograms), the SI system uses moles (mol) to represent the amount of a substance. A molar solution contains 1 mol (the molecular weight of the substance in grams) of the solute in 1 L of solution. The following formula is used to convert units of mass to moles (mcg/mL to pmol/L or, by substitution of terms, mg/mL to mmol/L or ng/mL to nmol/L). 

The van t Hoff equation also has been used to describe the temperature effect on Henry s law constant over a narrow range for volatile chlorinated organic chemicals (Ashworth et al. 1988) and chlorobenzenes, polychlorinated biphenyls, and polynuclear aromatic hydrocarbons (ten Hulscher et al. 1992, Alaee et al. 1996). Henry s law constant can be expressed as the ratio of vapor pressure to solubility, i.e., pic or plx for dilute solutions. Note that since H is expressed using a volumetric concentration, it is also affected by the effect of temperature on liquid density whereas kH using mole fraction is unaffected by liquid density (Tucker and Christian 1979), thus... 

The percent yield calculated by using moles or grams would be the same. 

Compare the required ratio of reactants (using moles) to the available ratio of reactants using partial pressures to find the limiting reactant. 

Another type of gas law problem involves stoichiometry. Gas stoichiometry problems are just like all other stoichiometry problems—you must use moles. In addition, one or more gas laws are necessary. Let s look at a gas stoichiometry problem. What volume, in liters of oxygen gas, collected over water, forms when 12.2 g ofKCl03 decompose according to the following equation ... 

These equations apply to the total mass or mass density of the system, while we use moles when describing chemical reaction. Therefore, whenever we need to solve these equations simultaneously, we must transform our species mass balances into weight fraction when including momentum and total mass-balance equations. 

Protein attachment (i.e., casein and gelatin) to a DE 10 maltodextrin base failed to yield any substantial improvement in hindering lemon oil vapor phase flux using mole ratios of 0,... 

In the present paper we shall use mole/liter for concentration units and seconds for time. Rate constants will then be expressed appropriately. 

We really should use mole fraction, and not concentration, in our description of y and x, but for our work, we will just say that the term concentration refers to the percent of a component that the operator would see in the gas-chromatographic (GC) results, as reported by the lab. The equilibrium constant, assuming the ideal-gas law applies, is defined as... 

The strategy used for this and other redox titrations is outlined in Figure 4.5. As with acid-base titrations, the general idea is to measure a known amount of one substance—in this case, H2C204—and use mole ratios from the balanced equation to find the number of moles of the second substance—in this case, KMn04—necessary for complete reaction. With the molar amount of KMn04 thus... 

This scheme differs from the various systems in use in industry and academia in that it uses the mole instead of the cc(STP) to express the quantity of matter being transported, the pascal rather than the atmosphere or the cm. Hg. to express pressure, the meter rather than the mil, the inch, or the centimeter to express length, and the second rather than the day to express time. Our experience indicates that the existing variety of unit systems leads to confusion and that calculations of related physical properties such as permeabilities, diffusion coefficients, and solubilities are easier using the SI units. More modern measurement systems which detect permeants by means of the electrical currents generated by individual atoms are easier to analyze when one uses moles rather than cc(STP) to express the amount of matter undergoing transport. Applications involving the transport of mixed permeant species are also easier to deal with on a molar basis. Conversion tables between the SI units and customary units are provided on the SRM certificate and in the appropriate standards documents (4, 5). ... 

Glazes can be prepared by combining a particular number of molecules of each ingredient. This can be accomplished using moles, which Activity 4.2 allows you to do. 

The main reason chemists use moles is because individual molecules are just too small to deal with on an individual basis. So, we gather 6.02 x 1023 of them together into a mole, and use that as our working unit in chemistry. So what is the mass of one mole of carbon Well, the system is set up so that the molar mass (expressed in g/mol) of an element is equal to its atomic mass (expressed in amu). 

We can also analyze the part of n versus a isotherm at large a. When the film s area is very large, the surfactant molecules are sufficiently far apart that we can assume that their behavior is ideally dilute. In this case, the activity in Eq. (50) can be written in the usual ideally dilute solution approximation, a = c = n/a, d Inc = dn/n. We use moles/area for the interfacial concentration. Equation (50) then becomes... 

The apolar contribution to AS0, ASap, is better characterized than AHap. The value of Tt has been shown to be a universal temperature for all processes involving the transfer of an apolar surface into water and has a value of 112°C (Murphy et al., 1990). At this temperature the AS0 of transfer, ASf, represents the mixing entropy of the process. The universal value of Tt was determined using mole fraction concentration units, so that the liquid transfer ASf takes on a value of zero. The value of Tt remains the same using the local standard state of Ben-Naim (i.e., molar concentration units) (Ben-Naim, 1978), but the value of Ais increased by R ln(55.5), where R is the gas constant and 55.5 is the molarity of water. 

A Heat is evolved from the substance as it cools, so the heat change will be negative, eliminating choices C and D. Data in the table are given using moles, so the first step is to convert the mass of water to moles ... 

This is best achieved by using mole fraction, x, to define the composition of the phases. 

Figure 32.2 Solution made up of solvent + solute comprises a solution whose composition can be defined using mole fractions, xsolvent and xs0iute (which sum to 1). Above any solution exists a vapour (gas) usually composed almost exclusively of (volatile) solvent molecules, since the solute(s) are normally involatile and therefore do not, themselves, exert or contribute to the vapour pressure over the solution. Temperature T is constant. P is the vapour pressure.

Percentages are similar except that they add up to 100 (instead of 1). Thus if we defined the various components in terms of their weight percent = % age of component 1 present in mixture, then we would only need to define this for (c — 1) of the components since weight % for component c = 100 - [sum of weight percentages of components 1 to (c — 1). The same is of course true when we use mole fractions. 

It is common not to use mole fraction as the measure of concentration in solutions, but rather to express the concentration of species in terms of molalities or molarities. The former is defined as the number of moles in a kg of solvent and the latter is defined as the number of moles per liter of solution (- concentration). Since the molality is obviously temperature independent, it is the normal concentration measure used, and our convention for activity coefficient is now ps = p + F / ln ysxs for the solvent where the subscript s signifies solvent and ys - 1 when xs - 1, and for the solute p, = pf + RTlnyimi where y, - 1 as m, - 0. If there is more than one component, then the concentrations of all solutes must fall to zero simultaneously if the formula is to have any meaning, and it would be more correct to write y -> 1 as xs - 1. (Different symbols were recommended by the IUPAC for the activity coefficients, i.e., fi, yi and y, or yx, ym>, and yc>, when the concentration is expressed by mole fraction, molality and amount concentration (molarity), respectively, however, mostly y is used.)... 

Chemists rarely use the number of particles to communicate how much of a substance they have. Instead, they use moles. 

The "other" balance (a tie component) and the CO2 balance are independent equations. We will use mole balances since all of the compositions are in mole fractions. 

Since the temperature and pressure are constant throughout, volume balances can be used (mole fraction is the same as volume fraction). The balances could be made in moles and then converted to the basis of 1000 m3. 

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