Molar concentrations

The majority of the chemical reactions discussed in this chapter take place in solution. This is because the reaction between two solid reactants often proceeds very slowly or not at all. In a solid, the molecules or ions in a crystal tend to occupy approximately fixed positions, so that the chance of two molecules or ions coming together to react is small. In liquid solutions, reactant molecules are free to move throughout the liquid therefore, reaction is much faster. When you run reactions in liquid solutions, it is convenient to dispense the amounts of reactants by measuring out volumes of reactant solutions. In the next two sections, we will discuss calculations involved in making up solutions, and in Section 4.10 we will describe stoichiometric calculations involving such solutions. 

When we dissolve a substance in a liquid, we call the substance the solute and the liquid the solvent. Consider ammonia solutions. Anunonia gas dissolves readily in water, and aqueous ammonia solutions are often used in the laboratory. In such solutions, ammonia gas is the solute and water is the solvent. 

The general term concentration refers to the quantity of solute in a standard qiran-tity of solution. Qualitatively, we say that a solution is dilute when the solute concentration is low and concentrated when the solute concentration is high. UsiraUy these terms are used in a comparative sense and do not refer to a specific concentration. We say that one solution is more dilute, or less concentrated, than another. However, for commercially available solutions, the term concentrated refers to the maximum, or near maximum, concentration available. For example, concentrated aqueous ammonia contains about 28% NH3 by mass. 

In this example, we expressed the concentration quantitatively by giving the mass percentage of solute—that is, the mass of solute in 100 g of solution. However, we need a unit of concentration that is convenient for dispensing reactants in solution, such as one that specifies moles of solute per solution volume. 

Molar concentration, or molarity (Af), is defined as the moles of solute dissolved in one liter (cubic decimeter) of solution. 

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Cfeed = molar concentration of FEED in the reactor di, 0-2 = constants (order of reaction) for primary and secondary reactions... 

Cmea = molar concentration of monoethanolamine Cdea = molar concentration of diethanolamine... 

The equation is more conventionally written expressing the variable n/V as the inverse of the molar volume, l/v, although nJVis just the molar concentration c, and one could equally well write the equation as... 

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 agreement is excellent up to a 1 molar concentration. The excess energies for 1-1, 2-1, 2-2 and 3-1 charge types calculated from the MS and HNC approximations are shown in figure A2.3.13. The Monte Carlo... 

In isothermal conditions this can also be written in terms o the molar concentration c, since p = c RT. Thus we obtain... 

Find the partial molal volume of ZnCl2 in these solutions at 0.5, 1.0, 1.5 and 2.0 molar concentrations. 

Nitration in the presence of strong acids or Lewis acids Solutions of dinitrogen pentoxide in sulphuric acid nitrate 1,3-dimethyl-benzene-4,6-disulphonic acid twice as fast as a solution of the same molar concentration of nitric acid. This is consistent with Raman spectroscopic and cryoscopic data, which establish the following ionisation ... 

Radical source Molar concentration Temperature (°C) 2 5 Reactivitv... 

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. 

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. ... 

The concentration of lead in an industrial waste stream is 0.28 ppm. What is its molar concentration ... 

Calculate the molar concentration of NaCl, to the correct number of significant figures, if 1.917 g of NaCl is placed in a beaker and dissolved in 50 mF of water measured with a graduated cylinder. This solution is quantitatively transferred to a 250-mF volumetric flask and diluted to volume. Calculate the concentration of this second solution to the correct number of significant figures. 

To determine the concentration of ethanol in cognac a 5.00-mF sample of cognac is diluted to 0.500 F. Analysis of the diluted cognac gives an ethanol concentration of 0.0844 M. What is the molar concentration of ethanol in the undiluted cognac ... 

As equilibrium is established, two IO3- ions are produced for each ion of Pb. If we assume that the molar concentration of Pb at equilibrium is x then the molar concentration of IO3- is 2x. To help keep track of these relationships, we can use the following table. 

Wou may recall that this is the difference between a formal concentration and a molar concentration. 

True thermodynamic constants use a species activity in place of its molar concentration a). 

Note that the unit for ionic strength is molarity, but that the molar ionic strength need not match the molar concentration of the electrolyte. For a 1 1 electrolyte, such as NaCl, ionic strength and molar concentration are identical. The ionic strength of a 2 1 electrolyte, such as Na2S04, is three times larger than the electrolyte s molar concentration. 

The true thermodynamic equilibrium constant is a function of activity rather than concentration. The activity of a species, a, is defined as the product of its molar concentration, [A], and a solution-dependent activity coefficient, Ya. 

A quantitative solution to an equilibrium problem may give an answer that does not agree with the value measured experimentally. This result occurs when the equilibrium constant based on concentrations is matrix-dependent. The true, thermodynamic equilibrium constant is based on the activities, a, of the reactants and products. A species activity is related to its molar concentration by an activity coefficient, where a = Yi[ ] Activity coefficients often can be calculated, making possible a more rigorous treatment of equilibria. 

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