Calculations Involving Molarity

The ideal gas equation and the molecular view of gases lead to several useful applications. We have already described how to cany out calculations involving P-V-n-T relationships. In this section, we examine the use of the gas equation to determine molar masses, gas density, and rates of gas movement. 

In mass balance calculations involving chemical and biochemical systems, it is sometimes more convenient to use the molar units, such as kilomoles, rather than simple mass units, such as the kilograms. 

Calculations involving equivalents, milliequivalents, normalities, and volumes of solutions are made in just the same way as those involving molarities of solutions. The unique and useful feature about the use of equivalents is that, for any chemical reaction, when reactant A has just exactly consumed reactant B, we can say... 

Stoichiometric calculations involving solutions of specified molar concentration are usually quite simple since the number of moles of a reactant or product is simply volume x molar concentration. 

Sometimes, the calculation involves a monoprotic acid and a dihydroxy base or another set of conditions in which the relationship is not 1 1. We have to keep track of the various concentrations so that the molarities do not get mixed up. However, stoichiometric calculations involving solutions of specified normalities are even simpler. By the definition of equivalent mass in Chapter 12, two solutions will react exactly with each other if... 

Table 16-1 compiles some data for S°, the molar entropy, and AGp the free energy of formation from the elements. All values in Table 16-1 are presented at 25°C and at standard states. Notice that the units of entropy and free energy are stated per mole, mol-1. This means that the moles used to balance a chemical reaction are included by the multiplication of the coefficient (mol in balanced equation) and the value from the table so that unit mol cancels. This is also the way in which we handled calculations involving AH values. 

Because virtually all stoichiometric calculations involve moles (abbreviated mol) of material, molarity is probably the most common concentration unit in chemistry. If we dissolved 1.0 mol of glucose in enough water to give a total volume of 1.0 L, we would obtain a 1.0 molar solution of glucose. Molarity is abbreviated with a capital M. Notice that, because molarity has units of moles per liter, molar concentrations are conversion factors between moles of material and liters of solution. 

Notice that the numerator in molality calculations is the same as the numerator in molarity calculations, but that the denominators are different. For molality, the denominator differs in two respects It is in kilograms rather than liters and it involves solvent rather than solution. For the preparation of molal solutions, a volumetric flask is not needed. This is a preparation based only on weight. Molality is expressed in moles/kilo-gram. 

You can use what you now know about the mole to carry out calculations involving molar mass and the Avogadro constant. One mole of any compound or element contains 6.02 x 1023 particles. The compound or element has a mass, in grams, that is determined from the periodic table. 

Vapor-pressure lowering calculations involve mole fraction freezing-point depression and boiling-point elevation calculations use molality and osmotic pressure is calculated with molarity. 

To save time and space in the laboratory, routinely used solutions are often purchased or prepared in concentrated form (these are called stock solutions). In a process called dilution, water is then added to achieve the molarity desired for a particular solution. For example, the common acids are purchased as concentrated solutions and diluted as needed. A typical dilution calculation involves determining how much water must be added to an amount of stock solution to achieve a solution of the desired concentration. The key to doing these calculations is to remember that since only water is added in the dilution, all of the solute in the final dilute solution must come from the concentrated stock solution. That is,... 

An equation of state relates the molar quantity and volume of a gas to temperature and pressure. The simplest and most widely used of these relationships is the ideal gas equation of state (the familiar PV = nRT), which, while approximate, is adequate for many engineering calculations involving gases at low pressures. However, some gases deviate from ideal behavior at nearly all conditions and all gases deviate substantially at certain conditions (notably at high pressures and/or low temperatures). In such cases it is necessary to use more complex equations of state for PVT calculations. 

Box 6.1 Useful procedures for calculations involving molar concentrations... 

When reactants are liquids, they are almost always measured by volume. So, to do calculations involving liquids, you add two more steps to the sequence of mass-mass problems—the conversions of volume to mass and of mass to volume. Five conversion factors—two densities, two molar masses, and a mole ratio—are needed for this type of calculation, as shown in Skills Toolkit 4. 

There are ways other than density to include volume in stoichiometry problems. For example, if a substance in the problem is a gas at standard temperature and pressure (STP), use the molar volume of a gas to change directly between volume of the gas and moles. The molar volume of a gas is 22.41 L/mol for any gas at STP. Also, if a substance in the problem is in aqueous solution, then use the concentration of the solution to convert the volume of the solution to the moles of the substance dissolved. This procedure is especially useful when you perform calculations involving the reaction between an acid and a base. Of course, even in these problems, the basic process remains the same change to moles, use the mole ratio, and change to the desired units. 

Why must conditions of temperature and pressure be stated to do calculations involving molar volume ... 

Slightly more difficult examples of molarity problems involve an extra calculation. Remember You need to know the number of moles of solute in order to calculate the molarity of a solution. Sometimes you will start with the mass of the solute and you will need to determine the number of moles of solute that you are starting with by using a formula that you studied in Chapter 7 ... 

Most of the uses of UV spectrometry in the field of amino acids, peptides and proteins are entirely routine. The measurements and interpretations are simple and can be useful for determining solution concentrations of proteins, expressed in mol 1 1, on the basis of knowledge of the overall amino-acid composition of the particular protein (Chapter 4). They depend on calculations involving the determination of the absorbance at A near 280 nm, using the value of the molar absorptivity (e) for constituent non-transparent amino acids in the calculation. 

This is slightly above typical room temperature. Notice that these thermodynamic standard conditions are not the same as the standard temperature and pressure (STP) that we used in gas calculations involving standard molar volume (Chapter 12). 

In all calculations involving the ideal solution model, we assume that we know the molar Gibbs free energy of each of the pure species as a function of temperature and pressure. Mathematically, this means that know the form of the functions (T, p). Physically, this means that we know everything about the thermodynamics of the pure species. 

By definition, the atomic mass of the carbon-12 atom is exactly 12.00 amu. One mole of carbon-12 atoms has a mass of exactly 12.00 g, and that 12.00 g mass contains exactly 6.022 x 1023 carbon-12 atoms. This statement sets the benchmark for all chemical calculations involving the mole. One mole of any element is an amount of that element equal to its atomic mass in grams (its molar mass), and that mass contains 6.022 x 1023 atoms of that element. Using atomic masses, you can apply these relationships to the elements hydrogen and nitrogen. 

The heat associated with chemical and physical changes, AH, and the sign of AH are discussed in Chapter 7. Calculations involving molar heats of fusion and vaporization are done in the following examples. 

Stoichiometry concerns calculations based on balanced chemical equations, a topic that was presented in Chapter 8. Remember that the coefficients in the balanced equations indicate the number of moles of each reactant and product. Because many reactions take place in solution, and because the molarity of solutions relates to moles of solute and volumes, it is possible to extend stoichiometric calculations to reactions involving solutions of reactants and products. The calculations involving balanced equations are the same as those done in Chapter 8, but with the additional need to do some molarity calculations. Let s get our feet wet by working a couple of problems involving solutions in chemical reactions. 

Partial molar quantities play an important role in the study of non-ideal mixtures but we have to use them to only a limited extent in elementary thermodynamics. They can usually be replaced by the corresponding molar quantities. Thus, in simple calculations involving perfect gases or ideal solutions, Vi can be replaced by the volume of one mole of pure i in the appropriate physical state. 

Titrate the other two samples in the same manner as the first and calculate the molarity of the HCl from the weights of Na2C03 taken, remembering that each carbonate has reacted with two protons. Use the mean of the three determinations for calculations involving the unknown. 

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