Molarity, Moles, and Volume

If we know any two of the three quantities in Equation 4.32, we can calculate the third. For example, if we know the molarity of an HNO3 solution to be 0.200 M, which means 0.200 mol of HNO3 per liter of solution, we can calculate the number of moles of solute in a given volume, say 2.0 L. Molarity therefore is a conversion factor between volume of solution and moles of solute  

To illustrate the conversion of moles to volume, let s calculate the volume of 0.30 M HNO3 solution required to supply 2.0 mol of HNO3  

In this case we must use the reciprocal of molarity in the conversion Liters = moles x 1/M = i oiSs X liters/iaote. 

How many grams of Na2S04 are required to make 0.350 L of0.500 M Na2S04  

Analyze We are given the volume of the solution (0.350 L), its concentration (0.500 Af), and the identity of the solute Na2S04 and asked to calculate the number of grams of the solute in the solution. 

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One mole of NaOH has a mass of 40.0 g. If this quantity of NaOH is dissolved in enough water to make exactly 1.00 L of solution, the solution is a 1 M solution. If 20.0 g of NaOH, which is 0.500 mol, is dissolved in enough water to make 1.00 L of solution, a 0.500 M NaOH solution is produced. This relationship between molarity, moles, and volume may be expressed in the following ways. 

The chemicai formuia identifies the ions that are present in the finai soiution. The formula also tells us how many moles of each ion are present in one moie of the sait. Use mass, molar mass, and volume to calculate molarity. 

FIGURE 3.5 A flow diagram summarizing the use of molarity as a conversion factor between moles and volume in stoichiometry calculations. 

You have already encountered problems involving moles, molecules, and molar masses earlier in this book. There is still one other relationship that needs to be connected with the mole and that is molar volume. Once you make a connection between moles and volume, mass, and molecules you will be able to solve problems easily. One very helpful mnemonic device to use is the Mole-Go-Round. Some think of this method as a way of cheating the system, but because the SAT II exam does not require you to show work, the Mole-Go-Round is a perfectly acceptable method for achieving better results. 

Molarity, the most common measure of concentration used by chemists, is introduced in Section 11.1 and nsed to solve problems involving numbers of moles and volumes. The concentrations of individual ions in aqueous solutions of ionic snbstances are discnssed in Section 11.2. The technique of titration, nsed to determine experimentally the nnknown concentrations of solutions or unknown nnmbers of moles of a snbstance, is presented in Section 11.3. 

As we observed in Section 6.2, the properties of a process material are either e.xtensive (proportional to the quantity of the material) or intensive (independent of the quantity ). Nfass. number of moles, and volume (or mass flow rate, molar flow rate, and volumetric flow rate for a continuous stream), and kinetic energy, potential energy, and internal energy (or the rates of transport of these quantities by a continuous stream) are extensive properties, while temperature, pressure, and density are intensive. 

Concentrations will be expressed as mole fraction of a component or species /, x = nj/E nj as molality, mole per mass of solvent, mol kg or molarity, mole per volume of solution. The concentration scale will depend on the properties of the solutes (i.e., ionic, polar, nonpolar, etc.). Pressure, p, and the gas phase partial pressure of species i, / , will be expressed in bars (approximately equal to atmospheres). 

Thus the formation of an ideal dilute solution is in general accompanied by a contraction or expansion. But despite this volume change, and despite the thermal effects, the mean molar enthalpy and volume both vary linearly with mole fraction, in accordance with (20.23), within the range of ideal behaviour. 

Table 1.2. 1 (a) Concentration units encountered in oceanography Equivalents, eq, is equal to moles x absolute value of the charge of the species. Units indicated as seawater units are those preferred in oceanography. Molality, molarity, normality and volume ratio all have a long history of use in classical chemistry because of their convenience for laboratory preparations. ... 

Variation in solvent density corresponds to changing the amount of CO2 in a reactor of constant volume, and hence the chemical potential and the mole fraction of a solute can be varied at constant molar (mole per volume) concentration. Obviously, such changes may have a strong impact on chemical equilibria and reaction rates, which in turn determine yields and selectivities of synthetic processes [11]. In addition, a number of solvent properties of the fluid phase are directly related or change in parallel with the density. Accordingly, such properties can be tuned in SCCO2. Variation of the so-called solvent power is the most obvious application and discussed in more detail below. 

You are given the volume, pressure, and temperature of a gas sample. The mole and volume ratios of gaseous reactants and products are given by the coefficients in the balanced chemical equation. Volume can be converted to moles and thus related to mass by using molar mass and the ideal gas law. 

From the moles and volume of KOH, we calculate the molarity of the KOH solution. 

Because 2 mol NaOH 1 mol H2SO4, we need twice as much NaOH to react completely with a H2SO4 solution of the same molar concentration and volume as a monoprotic acid like HCl. On the other hand, we would need twice the amount of HCl to neutralize a Ba(OH)2 solution compared to a NaOH solution having the same concentration and volume because 1 mole of Ba(OH)2 yields 2 moles of OH ions ... 

The great majority of solutions, however, are those which approach ideality only when one of the species, the solvent, is in great excess and the remainder, the solutes, are very dilute. In such cases Hi and Vi can be interpreted as hi and Vi respectively only in the case of the solvent, whose mole fraction approaches unity whilst the solution remains ideal. As regards the solutes, the partial molar enthalpy and volume are constant, in the region of ideality, but are not equal to the enthalpy and volume respectively per mole of the pure solutes in their normal states.f Moreover, the magnitude of these partial molar quantities is strongly dependent on the nature of the solvent, exactly as in the case of/ef and discussed previously. Suppose, for example,... 

Then add a second part to the solution map indicating how moles and volume can be used to determine molarity. 

You now have both moles and volume, the numerator and the denominator in the defining equation for molarity. Plug them into the equation and do whatever else you must do. Then calculate the answer. 

Plan the problem. Molarity is used as a Per expression to convert between moles and volume in milliliters. 

PURE calculates pure liquid standard-state fugacities at zero pressure, pure-component saturated liquid molar volume (cm /mole), and pure-component liquid standard-state fugacities at system pressure. Pure-component hypothetical liquid reference fugacities are calculated for noncondensable components. Liquid molar volumes for noncondensable components are taken as zero. 

Substituting the molarity and volume of titrant for moles, and rearranging gives... 

The systems of interest in chemical technology are usually comprised of fluids not appreciably influenced by surface, gravitational, electrical, or magnetic effects. For such homogeneous fluids, molar or specific volume, V, is observed to be a function of temperature, T, pressure, P, and composition. This observation leads to the basic postulate that macroscopic properties of homogeneous PPIT systems at internal equiUbrium can be expressed as functions of temperature, pressure, and composition only. Thus the internal energy and the entropy are functions of temperature, pressure, and composition. These molar or unit mass properties, represented by the symbols U, and S, are independent of system size and are intensive. Total system properties, J and S do depend on system size and are extensive. Thus, if the system contains n moles of fluid, = nAf, where Af is a molar property. Temperature... 

The process to reach a quantitative solution to the problem requires working with moles. Thus, we need the relationship linking moles to molarity and volume n — M V We must use the equation In two ways ... 

First, we must identify the chemistry. This is an acid-base titration in which hydrogen phthalate anions (the acid) react with OH (the base). We use the molar equality of acid and base at the stoichiometric point together with the equations that link moles with mass and volume. 

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