Expressing Concentration in Terms of Molarity

A typical solution consists of a smaller amount of one substance, the solute, dissolved in a larger amount of another substance, the solvent When a solution forms, the solute s individual chemical entities become evenly dispersed throughout the available volume and surrounded by solvent molecules. The concentration of a solution is usually expressed as the amount of solute dissolved in a given amount of solution. Concentration is an intensive quantity (like density or temperature) and thus independent of the volume of solution a 50-L tank of a given solution has the same concentration (solute amount/solution amount) as a 50-mL beaker of the solution. Molarity (M) expresses the concentration in units of moles of solute per liter of solution  

Problem Glycine (H2NCH2COOH) is the simplest amino acid. What is the molarity of an aqueous solution that contains 0.715 mol of glycine in 495 mL  

Plan The molarity is the number of moles of solute in each liter of solution. We are given the number of moles (0.715 mol) and the volume (495 mL), so we divide moles by volume and convert the volume to liters to find the molarity (see the roadmap). 

Check A quick look at the math shows about 0.7 mol of glycine in about 0.5 L of solution, so the concentration should be about 1.4 mol/L, or 1.4 M. 

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In Chapter 3, you used molarity to convert liters of solution into moles of dissolved solute. Expressing concentration in terms of molarity may have drawbacks, however. Because volume is affected by temperature, so is molarity. A solution expands when heated, so a unit volume of hot solution contains slightly less solute than a unit volume of cold solution. This can be a source of error in very precise... 

Express concentration in terms of molarity, molality, mole fraction, and parts by mass or by volume and be able to interconvert these terms ( 13.4) (SPs 13.3-13.5) (EPs 13.37-13.58)... 

It is most common to express rates in terms of molar concentrations of species, even for gas-phase reactions. The usual units of a reaction rate are mol L s-1. 

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... 

Now to express the concentrations in terms of molar flew rates we recall that for liqnids... 

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... 

Under what circumstances might it be easier to express solution concentrations in terms of molarity in terms of parts per million ... 

The results are expressed either in terms of molar concentration (millimoles per liter) or mass concentration (milligrams per deciliter). The following equation is used to convert mmol/dL to mg/dL ... 

These units are more convenient for low concentrations because they avoid using the very low numbers that would be involved if the concentrations were to be expressed in mol dm water pollutants are often given in ppm units. Also, we may use these units to describe trace concentrations of metals when we are not sure of the exact nature of the species involved. For example, drinking water may be found to have a total aluminium content at a concentration of 3 ppm. The nature and concentration of the different aluminium compounds present in a sample of drinking water is dependent on pH and can be a very complex problem to solve the ions AP, AlOH " and Al(OH)2 are but a few species that may be found. Without exact knowledge of the species present, calculations of molar concentration cannot be made, but it is always possible to express concentration in terms of the total mass of metal present. 

Since mass is a more practical property to measure than moles, flowrates are often given as mass flowrates rather than molar flowrates. When this occurs, it is convenient to express concentrations in terms of mass fractions defined similarly to mole fractions. 

Note that we have assumed constant density in the system in order to arrive at an expression directly in terms of molar concentration. This has been done for simplicity, although it is more correct to begin with moles and then convert to concentration or mass tractions if need be. 

Strategy Use Table 3.3 to express activities in terms of molar concentrations or pressures. Then use eqn 4.6 to write an expression for the reaction quotient Q. In reactions involving gases and solutes, the expression for Q will contain pressures and molar concentrations. 

Other conventions for treating equiUbrium exist and, in fact, a rigorous thermodynamic treatment differs in important ways. Eor reactions in the gas phase, partial pressures of components are related to molar concentrations, and an equilibrium constant i, expressed directiy in terms of pressures, is convenient. If the ideal gas law appHes, the partial pressure is related to the molar concentration by a factor of RT, the gas constant times temperature, raised to the power of the reaction coefficients. 

Processes involving chemical reactions must be approached differently. It is best to express the compositions of flow streams entering the process or unit operation in terms of molar concentrations. Balances are developed in terms of the largest components that remain unchanged by the reactions. 

As a result standard solutions are now commonly expressed in terms of molar concentrations or molarity (AT). Such standard solutions are specified in terms of the number of moles of solute dissolved in 1 litre of solution for any solution,... 

We have seen that the value of an equilibrium constant tells us whether we can expect a high or low concentration of product at equilibrium. The constant also allows us to predict the spontaneous direction of reaction in a reaction mixture of any composition. In the following three sections, we see how to express the equilibrium constant in terms of molar concentrations of gases as well as partial pressures and how to predict the equilibrium composition of a reaction mixture, given the value of the equilibrium constant for the reaction. Such information is critical to the success of many industrial processes and is fundamental to the discussion of acids and bases in the following chapters. 

For thermodynamic calculations, gas-phase equilibria are expressed in terms of K but, for practical calculations, they may be expressed in terms of molar concentrations by using Eq. 12. 

If the reaction involves gas-phase species and the rate law is expressed in terms of molar concentrations, then instead of K use Kc. 

In complex systems, fA is not a unique parameter for following the course of a reaction, unlike in simple systems. For both kinetics and reactor considerations (Chapter 18), this means that rate laws and design equations cannot be uniquely expressed in terms of /A, and are usually written in terms of molar concentrations, or molar flow rates or extents of reaction. Nevertheless, fA may still be used to characterize the overall reaction extent with respect to reactant A. 

For a constant-density system, several simplifications result. First, regardless of the type of reactor, the fractional conversion of limiting reactant, say fA, can be expressed in terms of molar concentration, cA ... 

P has a very suggestive form in relation to Figure 8.26. For a large concentration of acceptors, the second term in the denominator can be made considerably smaller than 1 (i.e., Xt is proportional to acceptor concentration [A]), and P will be independent of concentration. On the other hand, for a small concentration of acceptors, the second term in the denominator can be made considerably larger than 1, and P will fall off linearly as the concentration is reduced. The scale factor in all of this is Q. With Q large, the transition from concentration independence to linear concentration dependence will be at low acceptor concentrations. P falls to 5 when the second term in the denominator of Eq. (8.27) is equal to 1, and so a critical concentration of acceptors [A], /2 can be defined to characterize the falloff. Expressing Xt in terms of molecular parameters (x, = em[A] ln(10)/, where n is the particle refractive index, em is the molar decadic extinction coefficient, [A] is the concentration of acceptors, and k is 2n/X) yields... 

The equilibrium expression is usually expressed in terms of molar concentrations. Thus, the subscript c is usually used instead of eq in the equilibrium constant. 

Absorbance is proportional to concentration and path length (the Beer-Lambert Law). The intensity of absorption is usually expressed in terms of molar absorbance or the molar extinction coefficient (a) given by ... 

For mass transfer in the gas phase, the molar flux of a particular component N (in kmolm s ) is related to the concentration difference in the gas phase AC, expressed in terms of molar concentration (kmol m ), by... 

The amount of a substance dissolved in a given amount of solvent is the concentration of the solute, which can be expressed in terms of molarity or molality. If you know the molarity of a solution, you can determine the exact volume of the solution that contains a desired amount of the solute. An advantage of using solutions is that measuring volumes is easier than doing weighings to obtain a desired amount of a compound. 

Every reversible reaction has an equilibrium expression in which K, the equilibrium constant, is defined in terms of molar concentrations (mol/L) as indicated by the square brackets ... 

The (able below contains solubility and density data lor the salts Na SQ4 and MgS()4. Express their solubilities in terms of molar concentrations, molalities and mole fractions. Calculate the contractions in volume that occur when the solutions are made from the solid salts and the solvent. Comment on the results in terms of the ell ect of ionic charges. The concentrations have been cho-.cn to be comparable. 

Carotenoids in solution obey the Beer-Lambert law, where absorbance (A) equals concentration multiplied by extinction coefficient (A/%), where the extinction coefficient (A1%) is defined as the absorbance of a 1% (10 g/liter) solution of carotenoid, in a defined solvent, in a 1-cm path-length cuvette, at a specific wavelength (X). This information can be used to quantify the concentration of a pure (standard) carotenoid (see Basic Protocol 1), or to estimate the total carotenoid concentration in a mixture or extract of carotenoids in a sample (see Basic Protocol 2). The extinction coefficient may also be expressed in terms of molar-ity. 

First, we express Kc in terms of the volume of the system. The molar concentration of each gas is the amount, n, of that gas divided by the volume, V, of the reaction vessel ... 

An idealized water, derived from the attack of C02-bearing water on a typical felsic rock to produce only kaolinite, should have the following characteristics, expressed in terms of molar concentrations ... 

Write the balanced equation for the dissolution reaction, and define x as the number of moles per liter of AgCl that dissolves. Then, express the equilibrium concentrations in terms of x and substitute them into the appropriate equilibrium equation. Solving for x gives the molar solubility. 

However, for most reactions in solution, a less rigorously defined practical equilibrium constant, derived from Equation 3.9 and expressed in terms of molar concentrations of species at equilibrium, may be sufficient, and we note that, defined in Equation 3.10, Kc is not dimensionless, but has units (unless [vx + Vy + ] = [va + + ]) ... 

Concentrations of reagents and titrants in wet analysis are commonly expressed in terms of molarity (M) or normality (N). One mole (molecular or formula weight expressed in grams) of a substance dissolved in 1 L of its aqueous solution produces 1 M. 

The overall reaction rate has a temperature dependence governed by the specific reaction rate k(T) and a concentration dependence that is expressed in terms of several concentration-based properties depending on the suitability for the particular reaction type mole or mass concentration, component vapor partial pressure, component activity, and mole or mass fraction. For example, if the dependence is expressed in terms of molar concentrations for components A(Ca) and B(Cb), the overall reaction rate can be written as... 

We can express the forward reaction rate in terms of molar concentrations of reactants Ca and Cb that are dependent on the reaction orders a and /3... 

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