Reference molar concentration

Molar concentrations are used so frequently that a symbolic notation is often used to simplify its expression in equations and writing. The use of square brackets around a species indicates that we are referring to that species molar concentration. Thus, [Na ] is read as the molar concentration of sodium ions. ... 

Chiral nematic Hquid crystals are sometimes referred to as spontaneously twisted nematics, and hence a special case of the nematic phase. The essential requirement for the chiral nematic stmcture is a chiral center that acts to bias the director of the Hquid crystal with a spontaneous cumulative twist. An ordinary nematic Hquid crystal can be converted into a chiral nematic by adding an optically active compound (4). In many cases the inverse of the pitch is directiy proportional to the molar concentration of the optically active compound. Racemic mixtures (1 1 mixtures of both isomers) of optically active mesogens form nematic rather than chiral nematic phases. Because of their twist encumbrance, chiral nematic Hquid crystals generally are more viscous than nematics (6). 

Pore dijfusion in fluid-filled pores. These pores are sufficiently large that the adsorbing moleciile escapes the force field of the adsorbent surface. Thus, this process is often referred to as macropore dijfusion. The driving force for such a diffusion process can be approximated by the gradient in mole fraction or, if the molar concentration is constant, by the gradient in concentration of the diffusing species within the pores. 

Note that the brackets, [ ], refer to the concentration of the species. K,p is the solubility product constant hence [Cu " ] and [OH] are equal to the molar concentrations of copper and hydroxyl ions, respectively. The K p is commonly used in determining suitable precipitation reactions for removal of ionic species from solution. In the same example, the pH for removal of copper to any specified concentration can be determined by substituting the molar concentration into the following equation ... 

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). 

Equiactive close ratios, ratios of molar concentrations of drug (usually agonists) that produce the same response in a given system also referred to as EMR and EPMR see Chapter 10.2.3. 

The condition for the pressure or molar concentration to remain constant in such a system is that there should be no net transference of molecules. The process is then referred to... 

The inlet methanol molar concentration was determined by the mass of catalyst, S/C ratio, and W/F ratio. Here, steam-to-carbon (S/C) ratio is defined as the ratio of steam molecules per carbon atom in the reactant feed and W/F ratio as the amount of catalyst loading into the channel divided by the amount of methanol molar flow rate. For more information on the design parameters, physical properties, and operating conditions, refer to Jung et al. [12]. 

Approximation refers to the bringing together of the substrate molecules and reactive functionalities of the enzyme active site into the required proximity and orientation for rapid reaction. Consider the reaction of two molecules, A and B, to form a covalent product A-B. For this reaction to occur in solution, the two molecules would need to encounter each other through diffusion-controlled collisions. The rate of collision is dependent on the temperature of the solution and molar concentrations of reactants. The physiological conditions that support human life, however, do not allow for significant variations in temperature or molarity of substrates. For a collision to lead to bond formation, the two molecules would need to encounter one another in a precise orientation to effect the molecular orbitial distortions necessary for transition state attainment. The chemical reaction would also require... 

Figure 5.7. When the initial and inlet conditions admit a linear-mixture basis, the molar concentration vector c of length K can be partitioned by a linear transformation into three parts a reaction-progress vector of length NT , a mixture-fraction vector of length Nmf and 0, a null vector of length K — Nr — Nmf. The linear transformation matrix depends on the reference...

When the solution is dilute enough to approximate the activity coefficients to 1 (reference state solute at infinite dilution), activities can then be replaced by molar fractions (dimensionless quantities), but in solution they are generally replaced by molar concentrations ... 

Since the second complex contains two molecules of drug, therefore, we refer to it as dimer complex. Keeping in view the milli molar concentration of the metal ion present in the cell, possibility of the formation of dimer complex is more under in vivo conditions. However, in certain cases of cancer the metal ion concentration goes down to micro molar range. Under these unusual conditions, complex I is formed. Recently we have shown that mithramycin forms only dimer complex with Zn +, another metal ion playing an important role as cofactor in many enzymes and DNA binding proteins like transcription factors. 

As we have already seen, the mole is the mass unit in the SI system. The molar concentrations of components in geochemical systems assume different significances as a function of the adopted reference unit ... 

The process of hydration of an ion refers to the conversion of one mole of the gaseous ions under standard conditions at a pressure of I bar to the hydrated ions at a molar concentration of 1 mol dm-3. The process may be divided into two parts. These are the compression of the one mole of gaseous ions into a volume of 1 dm3 followed by the interaction of the ions with water to produce the hydrated ions. Assuming ideal gas behaviour, the compression of one mole of a gas at standard pressure and at 298.15 K into a volume of I dm3 requires the expenditure of enthalpy given by RT ln(24.79/l. 0) = +7.96 kJ mol -. The quoted values of ionic hydration enthalpies include a contribution from the compression of the gaseous ions and the enthalpy changes associated with the hydration process are given by the equation ... 

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