Molarity expressing concentration

The concentration of a solntion is the amount of solute present in a given amount of soln-tion. Molarity expresses concentration as the number of moles of solute in 1 liter of solution. 

Both molarity and formality express concentration as moles of solute per liter of solution. There is, however, a subtle difference between molarity and formality. Molarity is the concentration of a particular chemical species in solution. Formality, on the other hand, is a substance s total concentration in solution without regard to its specific chemical form. There is no difference between a substance s molarity and formality if it dissolves without dissociating into ions. The molar concentration of a solution of glucose, for example, is the same as its formality. 

The relative amount of a constituent in a sample is expressed as its concentration. There are many ways to express concentration, the most common of which are molarity, weight percent, volume percent, weight-to-volume percent, parts per million, and parts per billion. Concentrations also can be expressed using p-functions. 

For expressing concentrations of reagents, the molar system is universally applicable, i.e. the number of moles of solute present in 1 L of solution. Concentrations may also be expressed in terms of normality if no ambiguity is likely to arise (see Appendix 17). 

The concentration c, in equation 4.1-3, the rate law, is usually expressed as a molar volumetric concentration, equation 2.2-7, for any fluid, gas or liquid. For a substance in a gas phase, however, concentration may be expressed alternatively as partial pressure, defined by... 

Equation (88) is the expression used commonly for solutions of synthetic polymers, but, where the nature of adsorption and binding is of critical interest, alternative forms exist. These differ mainly in the modes of expressing concentration (e.g. activity, molality, molarity, mass/unit volume). Interrelations among the units and expressions have been presented very clearly by Timasheff and Townend15. ... 

In this expression, K is the thermodynamic equilibrium constant, which can be multiplied by Na/p (with Na equal to Avogadro s number) to obtain the commonly used equilibrium constants based on the molar bulk concentration reference state. It is important to note that the exponential term in the right-hand side of Equations 2.20 and 2.21 is an activity coefficient term. This term depends on the interaction field n z), which is nonlocal and therefore it couples with all the interactions and chemical equilibria in all regions of the film. 

Molarity a way to express concentration of a solution, moles of solute per liter of solution... 

You can use the dilution equation with any units of concentration, provided you use the Scime units throughout the calculation. Because molarity is such a common way to express concentration, the dilution equation is sometimes expressed in the following way, where Mj and refer to the initial and final molarity, respectively ... 

There are numerous ways of expressing concentration in diffusion problems, the most important for our purposes being mass density, molar density, mass fraction, and mole fraction. The chemical engineer and the chemist are familiar with the relationships between these quantities. Table I is given for the sake of summarizing the notation used here. 

At this point let us address the problem of expressing abundance of compounds in a bulk phase. In environmental chemistry, the most common way to express concentrations is not by mole fraction, but by the number of molecules per unit volume, for example, as moles per liter of solution (mol L, M). This molar concentration scale is sometimes not optimal (volumes are, for example, dependent on Tandp, whereas masses are not hence, the use of concentration data normalized per kilogram of seawater is often seen in the oceanographic literature). However, the molar scale is widely used. We can convert mole fractions to molar concentrations by ... 

The solid-state hexamers (2)—(4) at first appeared to dissolve intact in benzene (94). Cryoscopic rmm measurements over a range of concentrations (0.03-0.09 M, molarity expressed relative to the empirical formula mass) implied n values of 5.9-6.1. Furthermore, their room-temperature 7Li NMR spectra in c/8-toluene each consisted of broad singlets within the narrow chemical shift (6) range of + 0.6 to -0.2 ppm (relative to external phenyllithium in the same solvent). However, variations in temperature and concentration affected the 7Li NMR spectra of (2) and, in particular, of (4) (95). Figure 18a shows these spectra for three d8-toluene solutions of (4) at -100°C. The most concentrated solution has a dominant signal at 8 -+0.7, though five or six other signals (indicated by asterisks) are apparent. On dilution,... 

In daily life, it s often sufficient to describe a solution as either dilute or concentrated. In scientific work, though, it s usually necessary to know the exact concentration of a solution—that is, to know the exact amount of solute dissolved in a given amount of solvent. There are many ways of expressing concentration, each of which has its own advantages and disadvantages. We ll look briefly at four of the most common methods molarity, mole fraction, mass percent, and molality. 

The most common way of expressing concentration in a chemistry laboratory is to use molarity. As discussed previously in Section 3.7, a solution s molarity is given by the number of moles of solute per liter of solution (mol /L, abbreviated M). If,... 

Note that the solute concentration is given in molarity when calculating osmotic pressure rather than in molality. Because osmotic-pressure measurements are made at the specific temperature given in the equation n = MKT, it s not necessary to express concentration in a temperature-independent unit such as molality. 

Rather than write hydronium ion concentrations in molarity, it s more convenient to express them on a logarithmic scale known as the pH scale. The term pH is derived from the French puissance d hydrogene ("power of hydrogen") and refers to the power of 10 (the exponent) used to express the molar H30+ concentration. The pH of a solution is defined as the negative base-10 logarithm (log) of the molar hydronium ion concentration ... 

Chemists often express concentrations in moles per liter, or molarity, M. Molarity is given by the relationship... 

Approaches for calculating activity coefficients will be discussed later in this chapter. Three important concepts are introduced here. The first is that in dilute solutions the activity coefficient approaches 1 as the concentration of all electrolytes approaches zero. The second is that the activity coefficient must be calculated on the same scale (e.g., molality, molarity, etc.) as that used to express concentration. The third is that activity in the gas phase is expressed as fugacity. Because the fugacity coefficient for CO2 is greater than 0.999 under all but the most extreme conditions for sediment geochemistry (e.g., deep subsurface), the partial pressure of CO2 (Pc02 may reasonably used in the place of fugacity. 

The equilibrium constant A-of a reaction is dimensionless but we can express concentration in different units. For a gaseous mixture, in addition to the molar fraction xt, two other concentration units may be used One is the partial pressure pt = xtp, which is proportional to the molar fraction xt and the total pressure p and the other is the molar concentration (molarity) ct = nt/V, which is inversely proportional to the volume Vof the gaseous mixture. In terms of these concentration units the equilibrium constant of a gas reaction is expressed in three different formulas shown, respectively, in Eq. 6.10 ... 

You have learned about several different ways in which chemists express concentration mass/volume, mass/mass, and volume/volume percent parts per million and parts per billion and molar concentration. The Concept Organizer above summarizes what you have learned in this chapter so far. 

This is a way of expressing concentration. One molar (1m) concentration contains the mass one mole in grams dissolved in 11 (1 dm3) of solution. 

The most common way of expressing concentration in chemistry is molarity. Molarity is the ratio of moles of solute to total liters of solution ... 

Several methods are used to express concentrations in water and wastewater and it is appropriate to present some of them here. They are molarity, molality, mole fraction, mass concentration, equivalents concentration, and normality. 

Equivalent concentration and normality. This method of expressing concentrations is analogous to molar concentrations, with the solute expressed in terms of equivalents. One problem that is often encountered is the conversion of a molar concentration to equivalent concentration. Let [C] be the molar concentration of any substance, where the symbol [ ] is read as the concentration of. Convert this to equivalent concentration. 

Activity is given in the same units as concentration—molarity, mole fraction, and so forth. In (2-9) the concentration C usually is expressed either in moles per liter of solution (molarity M) or in moles per kilogram of solvent (molality m). In dilute aqueous solutions the molarity and molality are nearly equal in nonaqueous solutions molarity is usually larger than molality, since the density of the solvent is usually less than unity. Analytical chemists ordinarily find it more convenient to express concentration in molarity, even though it varies slightly with temperature. The analytical concentration is represented by the symbol C, to indicate the moles of solute added per liter of solution. Analytical concentration should be distinguished from the equilibrium concentration, which is indicated by enclosure in square brackets. 

There are a number of instances when it is much more convenient to work in terms of the number of moles (iV, N-g) or molar flow rates (Fj, Fg, etc.) rather than conversion. Membrane reactors and multiple reactions taking place in the gas phase are two such cases where molar flow rates rather than conversion are preferred. In Section 3.4 we de.scribed how we can express concentrations in terms of the molar flow rates of the reacting species rather than conversion, We will develop our algorithm using concentrations (liquids) and molar flow rates (gas) as our dependent variables. The main difference is that when conversion is used as our variable to relate one species concentration to that of another species concentration, we needed to write a mole balance on only one species, our basis of calculation. When molar flow rates and concentrations are used as our variables, we must write a mole balance on each species and then relate the mole balances to one another through the relative rates of reaction for... 

Any activity can be written as the product of a concentration and activity coefficient. Here we usually express concentration in terms of mol liter" of solution (molarity, M). Concentration may also be expressed in terms of mol kg" of solvent (molality, M). The molal scale gives concentrations that are independent of temperature and pressure and is used in precise physicochemical calculations. The difference between molarity and molality is small in dilute solutions, especially in comparison to the uncertainties involved in determining... 

Depending on the units used to express concentration we can have either a molal activity coefficient, a molar activity coefficient, /(., or, if mole fractions are used, a rational activity coefficient, y. ... 

Although quahtative descriptions of concentration can be useful, solutions are more often described quantitatively. Some commonly used quantitative descriptions are percent by either mass or volume, molarity, and molality. These descriptions express concentration as a ratio of measured amounts of solute and solvent or solution. Table 15-3 lists each ratio s description. 

The use of g cm-3 to express concentration in equation (1), though common in polarimetry, is unusual concentration is more commonly expressed in mol dm-3. A molar rotation [M] is known, but is used less frequently. 

---