Using Molarity in Calculations

We can use the molarity of a solution as a conversion factor between moles of the solute and liters of the solution. For example, a 0.500 M NaCl solution contains 0.500 mol NaCl for every liter of solution. 

This conversion factor converts from liters of solution to moles of NaCl. If you want to go the other way, simply invert the conversion factor. 

For example, to determine how many grams of sucrose (Ci2Ff220n) are contained in 1.72 L of 0.758 M sucrose solution, begin by sorting the information in the problem statement. 

We strategize by drawing a solution map that begins with L solution and shows the conversion to moles of sucrose using the molarity, and then the conversion to mass of sucrose using the molar mass. 

In this example, we used molarity to convert from a given amount of solution to the amoimt of solute in that solution. In tire example that follows, we use molarity to convert from a given amount of solute to the amount of solution containing that solute. 

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Next, let s see how we can use molarity to calculate moles. How many moles of ammonium ions are in 0.100 L of a 0.20 M ammonium sulfate solution ... 

Solution Two solution methods will be used. The first method is better for those who are good at unit manipulations and less skilled at memorizing formulas. HCI contains one acid equivalent and NaOH contains one base equivalent, so we may use molarity in all our calculations. 

Describe the procedure for preparing a solution of a certain molarity. Use molarity in stoichiometric calculations. 

Formal molal-scale values are approximated here by molar-scale values calculated by using molarities in place of molalities, m, in the Debye-Hiickel relationship, 0.5 z w. 

Molar mass is useful for chemical calculations because it provides a connection between a quantity that is easy to measure (mass) and one that is conceptually important (moles). Another readily measured quantity is volume. When we work with aqueous solutions, we often use volume in calculations rather than mass. It should not be surprising, therefore, that we would want to define quantities that will help us relate a volume measurement to the number of moles. 

Commercially available concentrated hydrochloric acid is 37.0% w/w HCl. Its density is 1.18 g/mL. Using this information calculate (a) the molarity of concentrated HCl, and (b) the mass and volume (in milliliters) of solution containing 0.315 mol of HCl. 

Parachor is the name (199) of a temperature-independent parameter to be used in calculating physical properties. Parachor is a function of Hquid density, vapor density, and surface tension, and can be estimated from stmctural information. Critical constants for about 100 organic substances have been correlated to a set of equations involving parachors and molar refraction (200). 

Only a small amount of potassium iodate is needed so that the error in weighing 0.14-0.15 g may be appreciable. In this case it is better to weigh out accurately 4.28 g of the salt (if a slightly different weight is used, the exact molarity is calculated), dissolve it in water, and make up to 1 L in a graduated flask. Twenty-five millilitres of this solution are treated with excess of pure potassium iodide (I g of the solid or 10 mL of 10 per cent solution), followed by 3 mL of IM sulphuric acid, and the liberated iodine is titrated as detailed above. 

STRATEGY First, the limiting reactant must be identified (Toolbox M.l). This limiting reactant determines the theoretical yield of the reaction, and so we use it to calculate the theoretical amount of product by Method 2 in Toolbox L.l. The percentage yield is the ratio of the mass produced to the theoretical mass times 100. Molar masses are j calculated using the information in the periodic table inside the front cover of this i book. 

Step 2 Use this molarity to calculate the amount of solute, Solute (in moles), in the stated volume, V (in liters), of solution ... 

The data in Example 1.2 are in moles of the given component per mole of mixed feed. These are obviously calculated values. Check their consistency by using them to calculate the feed composition given that the feed contained only para-xylene and chlorine. Is your result consistent with the stated molar composition of 40% xylene and 60% chlorine ... 

The gas stored in the tank is not at standard pressure, so apply Equation to calculate its molar entropy. As the gas leaves the tank, it expands and its entropy increases. The final pressure is not standard pressure, so again use Equation to calculate its molar entropy at the final pressure. Then calculate the entropy change for the expansion, taking the difference in molar entropies between initial and final conditions and multiplying by the number of moles undergoing the expansion. 

If we assume that al and a.2 are the results of two distinct sets of products, then it is imperative to first separate the contribution of each in terms of mass or molar production before determining the al value. This is because the total product spectrum for Cl to CIO (typically used for the calculation of al) will be a combination of the two product spectra and will give an erroneous al value. Since we are interested in not only the paraffin and olefin production but also the oxygenates, we use molar production. A typical molar production of a standard LTFT run is shown in Figure 10.3. 

In the multimedia models used in this series of volumes, an air-water partition coefficient KAW or Henry s law constant (H) is required and is calculated from the ratio of the pure substance vapor pressure and aqueous solubility. This method is widely used for hydrophobic chemicals but is inappropriate for water-miscible chemicals for which no solubility can be measured. Examples are the lower alcohols, acids, amines and ketones. There are reported calculated or pseudo-solubilities that have been derived from QSPR correlations with molecular descriptors for alcohols, aldehydes and amines (by Leahy 1986 Kamlet et al. 1987, 1988 and Nirmalakhandan and Speece 1988a,b). The obvious option is to input the H or KAW directly. If the chemical s activity coefficient y in water is known, then H can be estimated as vwyP[>where vw is the molar volume of water and Pf is the liquid vapor pressure. Since H can be regarded as P[IC[, where Cjs is the solubility, it is apparent that (l/vwy) is a pseudo-solubility. Correlations and measurements of y are available in the physical-chemical literature. For example, if y is 5.0, the pseudo-solubility is 11100 mol/m3 since the molar volume of water vw is 18 x 10-6 m3/mol or 18 cm3/mol. Chemicals with y less than about 20 are usually miscible in water. If the liquid vapor pressure in this case is 1000 Pa, H will be 1000/11100 or 0.090 Pa m3/mol and KAW will be H/RT or 3.6 x 10 5 at 25°C. Alternatively, if H or KAW is known, C[ can be calculated. It is possible to apply existing models to hydrophilic chemicals if this pseudo-solubility is calculated from the activity coefficient or from a known H (i.e., Cjs, P[/H or P[ or KAW RT). This approach is used here. In the fugacity model illustrations all pseudo-solubilities are so designated and should not be regarded as real, experimentally accessible quantities. 

Worked Example 3.11 The wood mentioned in our title question is a complicated mixture of organic chemicals so, for simplicity, we update the scene. Rather than prehistoric men sitting around a fire, we consider the calorific value of methane in a modem central-heating system. Calculate the value of A Hc for methane at 25 °C using molar enthalpies of formation AH. ... 

The freezing point depression and boiling point elevation techniques are useful in calculating the molar mass of a solute or its van t Hoff factor. In these cases, you will begin with the answer (the freezing point depression or the boiling point elevation), and follow the same steps as above in reverse order. 

Solubilities are calculated from a variety of sources compiled by the author. The mean ionic diameter is calculated by Eq. (6.13) using molar volumes in CRC Handbook of Chemistry and Physics. The value of a for OCPp is calculated from the crystallographic data on OCP in Brown et al. (1962). 

Using the molar mass, calculate the moles of all weighed samples. The moles of substances are converted to molarities by dividing by the volume (in liters) of the solution. Molarities may also be determined from pipet or buret readings using the dilution equation. (If a buret is used, one of the volumes is calculated from the difference between the initial and final readings.) The dilution equation may be needed to calculate the concentration of each reactant immediately after all the solutions are mixed. 

It is possible to measure the absorbance of a sample of a known compound at its absorption maximum and to calculate the actual concentration of the compound in the sample using a known value for the molar absorption coefficient (often obtainable from published spectral tables). In Figure 2.2 the absorption spectrum of ADP shows an absorbance of 0.22 at 258 nm. The quoted value for the molar absorption coefficient of ADP at this wavelength is 1.54 X 104 1 mol-1 cm-1 and hence the concentration of ADP in the sample used can be calculated from the Beer-Lambert equation ... 

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