Mole/molar concentration/molarity

To convert between molarity and the other mole-based concentration measures, we must relate volume to mass and number of moles. Whereas molar mass lets us convert between mass and moles, we need density to convert... 

The mole fraction concentration scale is generally used for the solvent water, designated by subscript w and having molar mass... 

Solution Convert molarity to mole fraction concentration units ... 

The B term in Equation 3.3 is an entropy correction term for any solutes with a molar volume different from solvent. In a conventional expression, the partial entropy of mixing for an ideal solution can be related to the mole fraction concentration of the species of interest by... 

The mole fraction concentration x is Cwv where C has units of mol/m3 and v is the molar volume of the solution (m3/ mol). Since the solutions are usually dilute, the molar volume is essentially that of water, i.e., approximately 18 x 10 6 m3/mol. It follows that... 

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 more useful way to describe a concentration is molarity. Molarity (M) expresses the number of moles of solute per liter of solution. A 0.1 M NaOH aqueous solution has 0.1 mol of solute (NaOH) in 1 L of water. Because stoichiometric calculations require moles, molarity is more frequently used in calculations. 

Some further nomenclature is now necessary to describe absorption equilibria in ion exchange systems. For a species i, m and C, represent the molal and molar concentrations respectively, whilst A and Xi denote the mole fraction and equivalent ionic fraction of i respectively. Single ion activity coefficients are denoted yj and mean ionic activity coefficients by yj . Whether the latter quantities refer to the molar or molal concentration scales is decided by the choice of units defining concentration. Thermodynamic activities and activity coefficients for the resin phase using the equivalent or mole fraction concentration scale (rational scale) are sometimes defined differently and are discussed in a later section. Finally, the exchanger and external solution phases are differentiated by subscripts r and s respectively. 

Molar volume of the solid solute, volume/mol van der Waal interaction strength of the solute or its chemical class Concentration of the solute in the raffinate exiting stage moles/volume Concentration of the solute in the Feed entering the process, moles/volume Concentration of solute in the raffinate leaving the process, moles/volume Mole fraction of the solute in the solvent... 

The most common mole-based concentration imit is molarity. Molarity, symbolized M, is defined as the number of moles of solute per liter of solution, or... 

This book uses the term concentration to mean the molar density of a component, for example, moles of A per unit volume of the reacting mixture. In the International System of Units (SI) concentration is in moles per cubic meters where the moles are gram moles. Molarity is classically defined as moles per liter of solution and is a similar concentration measurement. Molality is classically defined as moles per kilogram of solvent (not of solution) and is thus not a standard measure of concentration. For gases at low pressure and moderate temperatures, partial pressures are sometimes used instead of concentrations since partial pressures are proportional to concentration for ideal gases. 

In laboratory situations, calculations of this sort are often made with an equation derived by remembering that the number of moles of solute is the same in both the concentrated and dilute solutions and that moles = molarity X liters ... 

Now let us to estimate the equilibrium molarity of the constituent acidic cations in the melt, e.g., the eutectic KCl-LiCl melt (0.4 0.6) contains 8.5 mole of Lfr per 1 kg. Usually the ionic complexes in melts are characterized by the coordination number 4-6. For the solution of O of the 0.1 mole/kg concentration, the maximum possible quantity of fixed LU concentration may be estimated as 0.4-0.6 mole/kg, i.e., efficiently lower than 8.5. In this case the change of actual LF concentration is approximately equal to 5-7% and m,.[5+ in this case may be suggested as constant. Therefore, for each melt the sum in the denominator of [10.4.12] is the constant reflecting its acidic properties. So, pli= -loglj is a measure of melt acidities and may be denoted as the oxobasicity index of the melt. Since the determination of the absolute concentration of free O is practically impossible one should choose the standard melt , for which Ij is conditionally equal to 1 and pl =0. It is reasonable to choose the equimolar mixture KCl-NaCl as the standard melt , since this melt is most frequently investigated. Further, one should choose standard equilibria and formulate the non-ther-modynamic assumptions which usually postulate that the constant of the standard equilibrium calculated using absolute oxide ion eoncentrations remains flie same for all other melts. 

The amounts of CH4, H2O, CO, and in the reformer at equilibrium are listed in Table 3.4. Again, the units for the amounts can also be regarded as number of moles, molarity, volumetric concentration, or partial pressure (standard pressure is 1 bar). 

Detector Sensitivity mass (moles) Sensitivity concentration (molar) Characteristics... 

The concentration scale of a standard chemical potential and an activity coefficient are specified by additional symbols placed as either the subscript or superscript. For example, the mole fraction scale is specified in Equation 1.3. In this equation, if we want to be precise, should be called the standard chemical potential on the mole fraction concentration scale. Equation 1.3 is usually used for solutions of nonelectrolytes, such as 02(aq), and for solvent (water) in electrolyte solutions. Also, this equation can be used for solid solutions such as metal alloys. For electrolyte solutions, molality is commonly used except (1) electrolyte conductivity and (2) electrochemical kinetics, where molarity is commonly used. 

In general, it is always desirable to create a stoichiometric table in terms of moles, or molar flow rates for continuous reactors. You may (or may not) be able to easily convert moles to concentrations, as illustrated below. 

The rate of excess charge deposition in the sprayed fluid is given by the current supplied by the power supply in the circuit. The rate of flow of the sprayed solution is either forced by an external pump or created by the electrospray process. In either case, the molar concentration of excess charge, [Q], is the ratio of the charge and solution flows as given by Eq. (2.1). As mentioned before, a typical value of [Q] for normal electrospray is 10 M. This is a much smaller concentration than the sum of the total ionic species in the solution, so it follows that some of the ions will be the carriers of the excess charge and others will not. Those that are not will be paired with an equivalent number of counterions (anions, in the case of positive ESI). An immediately obvious consequence of this postulate is that [Q is the maximum mole-charge concentration of ions in the solution that can be converted to vapor phase ions. 

In developing this definition, we have used the stoichiometric coefficient, which is the number of moles of species / that reacts or is formed according to the chemical equation. For a constant volume system, we can easily convert this expression from moles to concentration simply by dividing the molar terms in the numerator by the volume. 

Concentrations are independent of temperature if based solely on mass or temperature-independent properties related to mass, specifically, mass percent, molality, mole fraction, and mole percent. Concentrations based on volumes—volume percent and molarity—are temperature dependent. 14-3. HCl is undissociated in C6H6(1), and the concentration of HCl in C6H6(1) should closely follow PHCi(g) above the solution. On the other hand, HCl(g) reacts with H20(l) to produce H30 (aq) and Cl (aq). The relationship between PHCi(g) end the aqueous concentrations of ions is more complex. 14-4. Start with (Pa - Pa)/Pa = Note that ( A - Pa)/Pa = 1 - PJP )-According to Raoult s law, a = xaPai which means that Pa/Pa = Thus, we arrive... 

Experiments on sufficiently dilute solutions of non-electrolytes yield Henry s laM>, that the vapour pressure of a volatile solute, i.e. its partial pressure in a gas mixture in equilibrium with the solution, is directly proportional to its concentration, expressed in any units (molar concentrations, molality, mole fraction, weight fraction, etc.) because in sufficiently dilute solution these are all proportional to each other. 

The quantity e is called the absorption coefficient or extinction coefficient, more completely the molar decadic absorption coefficient it is a characteristic of the substance and the wavelength and to a lesser extent the solvent and temperature. It is coimnon to take path length in centimetres and concentration in moles per... 

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