THE CONCEPT OF MOLE

The molar mass of a substance is equal to the molecular weight of that substance. The molecular weight (formula weight) of water is 18 amu. Since this is the molar mass, we can express it as 18 grams/mol. 

Calculate the mass of one molecule of sodium hydroxide (NaOH). 

Ans We know that the formula weight of sodium hydroxide is 40 g/mol. 

We also know that one mole of NaOH contains Avogadro number of molecules. So the mass of the NaOH molecule can be found by the following method  

Calculate the number of moles in 109.5 grams of hydrogen chloride. 

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The concept of mole fraction of a component used in Equation (4.1) is a convenient measure of concentration when dealing with trace quantities and dilute solutions, often experienced in environmental systems. This is especially the case with transport phenomena and equilibrium between phases, where it results in simple quantitative expressions. The phenomena of interest when dealing with the exchange of odorous compounds and oxygen between wastewater and a sewer atmosphere are, in this respect, relevant examples. 

The concept of moles is extremely useful for determining how much of one substance you need to complete a chemical reaction with another substance. For example, the balanced equation for the reaction of zinc with hydrochloric acid is given below. Note I m not suggesting you actually try this reaction. It s a bit violent, and it s always a risk doing such a reaction with a strong acid. 

The concepts of weight % and volume fo are self-explanatory. However, the concept of mole % or mole fraction should be described more fully so that its meaning is clearly understood. Basically, the mole fraction represents the fraction of molecules in the system that are of a given kind. This foUows at once from the fact that one mole of any gas contains the same niunber of molecules. For example, suppose a system craitainB one mole of CH and two moles of ObHa, In this system the mole fraction of CH is % and that of OgHe is %. It is also true that % Of the molecules are CH molecules and % are GzHg molecules. 

The answer is D. This question tests your understanding of the concept of mole. The student is preparing a solution using calcium hydroxide. The formula of calcium hydroxide is Ca(OH)2. The formula weight of calcium hydroxide is 74.1 grams/mol. Here, the student added two moles of it. So the answer is 74.1 x 2 = 148.2 g. 

By definition, the mole fraction is related to the concept of mole, which in turn is related to the molecular weight. We thus have the following correlation ... 

In the above equation, Aq is a pre-exponential factor, which can be weakly temperature dependent. The formulation of the Arrhenius law was giveu a physical justification by Van t Hoff in the same year of 1889. (Incidentally, Van t Hoff was the first recipient of the Nobel Prize in Chemistry ) The pre-exponential factor Aq is related to the concept of an attempt frequency of a chemical reaction, particularly when the reaction occurs in the liquid state, which is in a state of perpetual Brownian motion. Indeed, the Arrhenius law is directly related to the concept of moles of chemical species that were expounded by another contemporary chemist, Ostwald (Figure 11.2). 

Ostwald, who initially had strong philosophical opposition to the atomic theory, was converted to the concept of moles as the fundamental constituent of matter, following Perrin s historical experiments on the Brownian motion [3],... 

Another way to state this is to use the concept of mole fraction. In a mixture of two... 

When chemical reactions are of interest it is convenient to work in terms of an alternative description, one involving the concept of mole. By defini-... 

Biomass, e.g., the cells that are formed in this example, is another example of a material whose structure firequently is so complex that the concepts of moles and molecular weight caimot be employed. The atomic ratios of the elements in a specific kind of cell often are constant. However, live cells are constantly growing and dividing, so the molecular weight is not constant firom cell to cell. 

Consider two distinct closed thermodynamic systems each consisting of n moles of a specific substance in a volnme Vand at a pressure p. These two distinct systems are separated by an idealized wall that may be either adiabatic (lieat-impemieable) or diathermic (lieat-condncting). Flowever, becanse the concept of heat has not yet been introdnced, the definitions of adiabatic and diathemiic need to be considered carefiilly. Both kinds of walls are impemieable to matter a permeable wall will be introdnced later. 

Space time ST is equal to the residence time in a plug flow reactor only if the volumetric flowrate remains constant throughout the reactor. The residence time depends on the change in the flowrate through the reactor, as well as V/u. The change in u depends on the variation in temperature, pressure, and the number of moles. The concept of SV with conversions in the design of a plug flow reactor is discussed later in this chapter. 

A number of groups have criticized the ideas of Dauben and Noyce, especially the concept of PDC. Kamernitzsky and Akhrem, " in a thorough survey of the stereochemistry of addition reactions to carbonyl groups, accepted the existence of SAC but not of PDC. They point out that the reactions involve low energies of activation (10-13 kcal/mole) and suggest that differences in stereochemistry involve differences in entropies of activation. The effect favoring the equatorial alcohols is attributed to an electrostatic or polar factor (see also ref. 189) which may be determined by a difference in the electrostatic fields on the upper and lower sides of the carbonyl double bond, connected, for example, with the uncompensated dipole moments of the C—H bonds. The way this polar effect is supposed to influence the attack of the hydride is not made clear. 

We now have the foundation for applying thermodynamics to chemical processes. We have defined the potential that moves mass in a chemical process and have developed the criteria for spontaneity and for equilibrium in terms of this chemical potential. We have defined fugacity and activity in terms of the chemical potential and have derived the equations for determining the effect of pressure and temperature on the fugacity and activity. Finally, we have introduced the concept of a standard state, have described the usual choices of standard states for pure substances (solids, liquids, or gases) and for components in solution, and have seen how these choices of standard states reduce the activity to pressure in gaseous systems in the limits of low pressure, to concentration (mole fraction or molality) in solutions in the limit of low concentration of solute, and to a value near unity for pure solids or pure liquids at pressures near ambient. 

What Do We Need to Know Already This chapter develops the concepts of physical equilibria introduced in the context of thermodynamics (Chapters 6 and 7) and assumes a knowledge of intermolecular forces (Sections 5.1-5.5). The compositions of some of the solutions discussed are expressed in terms of mole fraction (Section 4.8). 

We developed the concept of the mole In terms of pure chemical substances, but many chemical reactions take place In solution. To treat solution reactions quantitatively, we need ways to apply the mole concept to solutions. A substance used to dissolve solutes Is a solvent, and a pure substance dissolved In solution Is a solute. Most of the time, the solvent Is a liquid and Is present In much larger quantities than any solutes. 

Sections 2- and 3- describe how to use the relationships among atoms, moles, and masses to answer how much questions about individual substances. Combining these ideas with the concept of a balanced chemical equation lets us answer how much questions about chemical reactions. The study of the amounts of materials consumed and produced in chemical reactions is called stoichiometry. 

The system is ideal, with equilibrium described by a constant relative volatility, the liquid components have equal molar latent heats of evaporation and there are no heat losses or heat of mixing effects on the plates. Hence the concept of constant molar overflow (excluding dynamic effects) and the use of mole fraction compositions are allowable. 

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. 

Applying Concepts Write the equation for the reaction of oxalic acid (H2C204) with NaOH. What is the ratio of moles of NaOH to moles of H2C204 ... 

When reporting the molar conductivity data, the species whose amount is given in moles should be indicated. Often, a fractional molar conductivity corresponding to one mole of chemical equivalents (called a val) is reported. For example, for sulphuric acid, the concentration c can be expressed as the normality , i.e. the species H2S04 is considered. Obviously, A(H2S04) = 2A( H2S04). Consequently, the concept of the equivalent conductivity is often used, defined by the relationship... 

In thermodynamics the state of a system is specified in terms of macroscopic state variables such as volume, V, temperature, T, pressure,/ , and the number of moles of the chemical constituents i, tij. The laws of thermodynamics are founded on the concepts of internal energy (U), and entropy (S), which are functions of the state variables. Thermodynamic variables are categorized as intensive or extensive. Variables that are proportional to the size of the system (e.g. volume and internal energy) are called extensive variables, whereas variables that specify a property that is independent of the size of the system (e.g. temperature and pressure) are called intensive variables. 

Background This experiment uses the concept of continuous variation to determine mass and mole relationships. Continuous variation keeps the total volume of two reactants constant, but varies the ratios in which they combine. The optimum ratio would be the one in which the maximum amount of both reactants of known concentration are consumed and the maximum amount of product(s) is produced. Since the reaction is exothermic, and heat is therefore a product, the ratio of the two reactants that produces the greatest amount of heat is a function of the actual stoichiometric relationship. Other products that could be used to determine actual molar relationships might include color intensity, mass of precipitate formed, amount of gas evolved, and so on. 

The concept of substance activity was derived by Gilbert N. Lewis in 1907 from the laws of equilibrium thermodynamics and is described in detail in the text entitled Thermodynamics and the Free Energy of Chemical Substances by Lewis and Randell (1923). In a homogeneous mixture, each component has a chemical potential (jjl), which describes how much the free energy changes per mole of substance added to the system. The chemical potential of water (pw) in a solution is given by... 

The DP of the polymers too was independent of the quantity of monomer and of the amount of catalyst solution added, but increased with decreasing temperature from 103 at -35° to 2.8 x 103 at -98°, giving a linear Arrhenius plot with EDP - -1.3 kcal/mole. These observations indicate that the DP is controlled by transfer reactions, and it seems likely that under the conditions of these experiments the most important of these is monomer transfer. The fact that the DP was independent of conversion is difficult to interpret since the polymer was precipitated during the reaction and therefore the concept of monomer concentration is ambiguous if the growing chain ends remained in the unreacted monomer its concentration would remain effectively constant. 

Our goal in this chapter is to assist you in learning the concepts of gases and gas laws. Be sure that you know how to properly use your calculator and, if you need to, refer to Chapter 3 on the mole concept. It s especially true with gas law problems that the only way to master them is to Practice, Practice, Practice. 

The same mole ratio, a/d, can also be found by simply balancing the common element in the formulas of A and D. Thus, the ratio, a/d, is the same as the ratio QS/QK seen in the equation for a gravimetric factor derived in Section 3.6.3 (Equation (3.12)) and is used to convert the weight of one substance to the weight of another, just as we described in Chapter 3 was the purpose of the gravimetric factor. Thus the concept of a gravimetric factor is based on stoichiometry. 

The rapid acceptance of the association theory was accompanied by an equally rapid dropping of the high molecular weight or polymer concept. Olby (31) has stated that three developments made the theory attractive as an explaination for the behavior of polymers. First, he sates, was Alfred Werner s introduction of the concept of two kinds of combining forces—Hauptvalenzen or primary valence forces, and Nebenvalenzen or secondary forces (32). When applied to cellulose, proteins, or rubber, the mole-... 

The bulk polymerization of acrylonitrile in this range of temperatures exhibits kinetic features very similar to those observed with acrylic acid (cf. Table I). The very low over-all activation energies (11.3 and 12.5 Kj.mole-l) found in both systems suggest a high temperature coefficient for the termination step such as would be expected for a diffusion controlled bimolecular reaction involving two polymeric radicals. It follows that for these systems, in which radicals disappear rapidly and where the post-polymerization is strongly reduced, the concepts of nonsteady-state and of occluded polymer chains can hardly explain the observed auto-acceleration. Hence the auto-acceleration of acrylonitrile which persists above 60°C and exhibits the same "autoacceleration index" as at lower temperatures has to be accounted for by another cause. 

A further difficulty is the distinction between a concept and an operation, for example in the definition of ion exchange capacity. Operationally, "the ion exchange capacity of a soil (or of soil-minerals in waters or sediments) is the number of moles of adsorbed ion charge that can be desorbed from unit mass of soil, under given conditions of temperature, pressure, soil solution composition, and soil-solution mass ratio" (Sposito, 1989). The measurement of an ion exchange capacity usually involves the replacement of (native) readily exchangeable ions by a "standard" cation or anion. 

The number of molecules passing in each direction from vapour to liquid and in reverse is approximately the same since the heat given out by one mole of the vapour on condensing is approximately equal to the heat required to vaporise one mole of the liquid. The problem is thus one of equimolecular counterdiffusion, described in Volume 1, Chapter 10. If the molar heats of vaporisation are approximately constant, the flows of liquid and vapour in each part of the column will not vary from tray to tray. This is the concept of constant molar overflow which is discussed under the heat balance heading in Section 11.4.2. Conditions of varying molar overflow, arising from unequal molar latent heats of the components, are discussed in Section 11.5. 

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