Molar concentration definition

Within the scope of the original definition, a very wide variety of ionomers can be obtained by the introduction of acidic groups at molar concentrations below 10% into the important addition polymer families, followed by partial neutralization with metal cations or amines. Extensive studies have been reported, and useful reviews of the polymers have appeared (3—8). Despite the broad scope of the field and the unusual property combinations obtainable, commercial exploitation has been confined mainly to the original family based on ethylene copolymers. The reasons for this situation have been discussed (9). Within certain industries, such as flexible packaging, the word ionomer is understood to mean a copolymer of ethylene with methacrylic or acryhc acid, partly neutralized with sodium or zinc. 

From the definition v = (l/V)(d /dt) find the rate of reaction in terms of molar concentration for the case in which the system volume V is not constant (Reference 44). 

Chemists often indicate the concentration of a substance in water solution in terms of the number of moles of the substance dissolved per liter of solution. This is called the molar concentration. A one-molar solution (1 M) contains one mole of the solute per liter of total solution. a two-molar solution (2 M) contains two moles of solute per liter, and a 0.1-molar solution (0.1 M) contains one-tenth mole of solute per liter. Notice that the concentration of water is not specified, though we must add definite amounts of water to make the solutions. 

In general, no matter what the route, certain characteristics will predispose a material to have local effects (and, by definition, if not present, tend to limit the possibility of local effects). These factors include pH, redox potential, high molar concentration, and the low flexibility and sharp edges of certain solids. These characteristics will increase the potential for irritation by any route and, subsequent... 

A small amount of the substance is accurately weighed, dissolved and made up carefully in a volumetric flask. to a definite volume, e.g. 100 ml. From the known relative molecular mass (RMM) of the compound it is possible to calculate the molar concentration of the solution ... 

The pH values produced by 1 mol dm-3 solutions of HC1 and NaOH, i.e. 0 and 14 respectively, define the practical range in which activity coefficients of H + (aq) and OH-(aq) may be ignored for general purposes, and subsidiary definitions of pH and pOH may be used pH = —logi0[H+] and pOH = —logi0[OH-]. The square brackets indicate the molar concentration of the species enclosed as a ratio to the standard molar concentration of I mol dm-3. 

The definitions of concentrations, velocities, and fluxes in Tables I, II, III may be used to rewrite this equation in terms of molar concentrations and molar fluxes ... 

The exact definition of the equilibrium constant given by IUPAC requires it to be defined in terms of fugacity coefficients or activity coefficients, in which case it carries no units. This convention is widely used in popular physical chemistry texts, but it is also common to find the equilibrium constant specified in terms of molar concentrations, pressure or molality, in which cases the equilibrium constant will carry appropriate units. 

In applying a rate equation to a situation where the volume of a given reaction mixture (i.e. the density) remains constant throughout the reaction, the treatment is very much simplified if the equation is expressed in terms of a variable X, which is defined as the number of moles of a particular reactant transformed per unit volume of reaction mixture (e.g. Cao Ca) at any instant of time t. The quantity X is very similar to a molar concentration and has the same units. By simple stoichiometry, the moles of the other reactants transformed and products generated can also be expressed in terms of x, and the rate of the reaction can be expressed as the rate of increase in X with time. Thus, by definition,... 

The derivation of the law of mass action from the second law of thermodynamics defines equilibrium constants K° in terms of activities. For dilute solutions and low ionic strengths, the numerical values of the molar concentration quotients of the solutes, if necessary amended by activity coefficients, are acceptable approximations to K° [Equation (3)]. However, there exists no justification for using the numerical value of a solvent s molar concentration as an approximation for the pure solvent s activity, which is unity by definition.76,77... 

The results in Table 2.4 are also relevant to preparative scale reactions. Adapting the definition of selectivities (Equation 2.10) for the reaction shown in Scheme 2.21 by rearranging Equation 2.14 gives a definition of S for competing methanolysis and aminolysis (Equation 2.17). Although the molar concentration of methanol in almost pure solvent is high (24.7 M), the major product is amide even when the concentration of m-nitroaniline is only 10-2 M (Table 2.4), and S is calculated from Equation 2.17 to be over 8000 very high yields are predicted for reactions in more concentrated solutions of m-nitroaniline. In contrast, under the same conditions, the less basic amine o-nitroaniline has an S value of only 6 [44] ... 

The preceding sections have used standard molar concentration units for RNA and ions, indicated by brackets or the abbreviation M. Thermodynamic definitions of interaction coefficients are made in terms of molal units, abbreviated m, the moles of solute per kilogram of solvent water. Molal units have the convenient properties that the concentration of water is a constant 55.5 m regardless of the amount ofsolute(s) present, and the molality of one solute is unaffected by addition of a second solute. For dilute solutions, M and m units are interchangeable. We use molal units for the thermodynamic derivations in this section, and indicate later (Section 3.1) the salt concentrations where a correction for molar-molal conversion is required. 

Molality and molarity are each very useful concentration units, but it is very unfortunate that they sound so similar, are abbreviated so similarly, and have such a subtle but crucial difference in their definitions. Because solutions in the laboratory are usually measured by volume, molarity is very convenient to employ for stoichiometric calculations. However, since molarity is defined as moles of solute per liter of solution, molarity depends on the temperature of the solution. Most things expand when heated, so molar concentration will decrease as the temperature increases. Molality, on the other hand, finds application in physical chemistry, where it is often necessary to consider the quantities of solute and solvent separately, rather than as a mixture. Also, mass does not depend on temperature, so molality is not temperature dependent. However, molality is much less convenient in analysis, because quantities of a solution measured out by volume or mass in the laboratory include both the solute and the solvent. If you need a certain amount of solute, you measure the amount of solution directly, not the amount of solvent. So, when doing stoichiometry, molality requires an additional calculation to take this into account. 

Consider the definition of partial pressure Partial pressures of perfect gases are the pressures that each species would exert if it were alone in the system. Therefore the presence of another gas has no effect on the equilibrium constant and on the equilibrium molar concentrations (e.g., mol/cm3) of species so long as the gases are perfect. 

SOLUBILITY OF PRECIPITATES A large number of reactions employed in qualitative inorganic analysis involve the formation of precipitates. A precipitate is a substance which separates as a solid phase out of the solution. The precipitate may be crystalline or colloidal, and can be removed from the solution by filtration or by centrifuging. A precipitate is formed if the solution becomes oversaturated with the particular substance. The solubility (5) of a precipitate is by definition equal to the molar concentration of the saturated solution. Solubility depends on various circumstances, like temperature, pressure, concentration of other materials in the solution, and on the composition of the solvent. 

Hie chemical reaction rate is usually dependent on the molar concentrations of the reactants and not on their mass fractions, because it depends on the chance of collision of molecules. However, here the definition of in terms of mass fractions is preferred, because it can readily be incorporated into mass balances. A definition in terms of moles or molar concentrations might invite the use of mole balances instead of mass balances. Since, contrary to conservation of mass, there is no such thing as conservation of moles (because one molecule might divide into several molecules, or several might condense into one), the use of mole balances is strongly dissuaded. More information concerning the definition of conversion can be found elsewhere [2]. 

We can avoid these conversion factors that relate the different rate expressions, by defining the rate in terms of an equivalent concentration instead of the molar concentration. If X is the number of equivalents per liter that reacted in a time t, then dX/dt is a convenient expression of the reaction rate. However, the definition of equivalent must be made explicit. 

To do the conversion, first convert the molar concentration to mass concentration by multiplying it by the molecular mass (MM). Thus, [C] (MM) is the corresponding mass concentration. By definition, the number of equivalents is equal to the mass divided by the equivalent mass (eq. mass). Therefore, the equivalent concentration, [C]e , is... 

The total molar concentration of active sites per imit mass of catalyst is equal to the number of active sites per imit mass divided by Avogadro s number and will be labeled C, (mol/g-cat.) The molar coneentration of vacant sites, C , is the number of vacant sites per imit mass of eatalyst divided by Avogadro s number. In the absence of catalyst deactivation we assume that the total concentration of active sites remains constant. Some further definitions include ... 

In practice we frequently measure the rate of change of the molar concentration of the components. Since by definition, cf. (1.6),... 

Some teachers, including myself, believe that the concept of normality adds an unnecessary extra level of complication, not to mention a new definition, to titration problems. We ask our students to remember that when we define M as the molar concentration of the ions in the acid solution, we really mean that it is equal to the molarity of the solution, multiplied by the number of moles of H+ ions that it yields per mole. In this way, a 2.0 M solution of H,SO, would have an M value of 4.0 M. A 2.0 M solution of H3P04 would have an Ma value of 6.0 M. The same concept applies to bases, so a 4.0 M solution of Ca(OH)2would have an Mb value of 8.0 M. 

Most volumetric calculations are based on two pairs of simple equations that are derived from definitions of the millimole, the mole, and the molar concentration. For the chemical species A, we may write... 

The second pair is derived from the definition of molar concentration. That is,... 

With an arbitrary definition of KNaX as equal to unity, thus establishing a reference half reaction, the equilibrium constant for any other half reaction can be determined from measured selectivity coefficients. The Gapon equation can be readily implemented in this manner. Implementation of the Vanselow equation, however, requires modification of the general equilibrium models to account for the more complex dependence of mole fractions on the molar concentrations. An example ion-exchange calculation using the half reaction approach to represent the Gapon equation is presented in Appendix 2. 

We should recall that the thermodynamic definition of K is in terms of activities. In dilute solutions, the activity of the (nearly) pure H2O is essentially 1. The activity of each dissolved species is numerically equal to its molar concentration. Thus the ionization constant of a weak acid, K, does not include a term for the concentration of water. 

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