Molarity amount-mass-number relationships

Figure 3.9 Summary of amount-mass-number relationships in solution. The amount (mol) of a substance in solution is related to the volume (L) of solution through the molarity (M mol/L). As always, convert the given quantity to amount (mol) first.

Amount-Mass-Number Conversions Involving Compounds Only one new step is needed to solve amount-mass-number problems involving compounds we need the chemical formula to find the molar mass and the amount of each element in the compound. The relationships are shown in Figure 3.3, and Sample Problems 3.4 and 3.5 apply them. 

Figure 3.3 Summary of the mass-mole-number relationships for elements. The amount (mol) of an element is related to its mass (g) through the molar mass (jU in g/mol) and to its number of atoms through Avogadro s number (6.022x10 atoms/mol). For elements that occur as molecules, Avogadro s number gives molecules per mole.

For work in the laboratory, it s necessary to weigh reactants rather than just know numbers of moles. Thus, it s necessary to convert between numbers of moles and numbers of grams by using molar mass as the conversion factor. The molar mass of any substance is the amount in grams numerically equal to the substance s molecular or formula mass. Carrying out chemical calculations using these relationships is called stoichiometry. 

You can get the same kind of information from a balanced chemical equation. In Chapter 4, you learned how to classify chemical reactions and balance the chemical equations that describe them. In Chapters 5 and 6, you learned how chemists relate the number of particles in a substance to the amount of the substance in moles and grams. In this section, you will use your knowledge to interpret the information in a chemical equation, in terms of particles, moles, and mass. Try the following Express Lab to explore the molar relationships between products and reactants. 

This simply shows that there is a physical relationship between different quantities that one can measure in a gas system, so that gas pressure can be expressed as a function of gas volume, temperature and number of moles, n. In general, some relationships come from the specific properties of a material and some follow from physical laws that are independent of the material (such as the laws of thermodynamics). There are two different kinds of thermodynamic variables intensive variables (those that do not depend on the size and amount of the system, like temperature, pressure, density, electrostatic potential, electric field, magnetic field and molar properties) and extensive variables (those that scale linearly with the size and amount of the system, like mass, volume, number of molecules, internal energy, enthalpy and entropy). Extensive variables are additive whereas intensive variables are not. 

Molarity can be thought of as a conversion factor used to convert between volume of solution and amount (mol) of solute, from which we then find the mass or the number of entities of solute. Figure 3.10 (on the next page) shows this new stoichiometric relationship, and Sample Problem 3.13 applies it. 

On a microscopic basis, one mole of a substance represents Avogadro s number (6.022 x 10 ) of indi-vidual units (atoms or molecules) of the substance. On a macroscopic basis, one mole of a substance represents the amount of substance present when the molar mass of the substance in grams is taken. Chemists have chosen these definitions so that a simple relationship will exist between measurable amounts of sub-... 

The choice of method depends primarily on the information required, and secondarily on the field of study, the amount of substance available, the time required, and, when necessary, on the effort required to purify the samples. Determinations are generally made at various concentrations. Then the apparent molar mass is calculated with the aid of an ideal theoretical relationship—that is, a relationship that only applies strictly at infinite dilution. This apparent molar mass must then be extrapolated to zero concentration to obtain the true molar mass. Apparent and true molar masses may differ considerably. Coil-shaped macromolecules of number-average molar mass of 10 g/ mol can, for example, have an apparent number-average molar mass in good solvents of 555 000 g/mol at a concentration of 0.01 g/ ml and 110 000 g/mol only, on the other hand, when the concentration is 0.1 g/ml. 

We remember from Chapter 5 that the coefficients in equations such as Equation 7.3 allow the relative number of moles of pure reactants and products involved in the reaction to be determined. These relationships coupled with the mole definition in terms of masses then yield factors that can be used to solve stoichiometric problems involving the reactants and products. Similar calculations can be done for reactions that take place between the solutes of solutions if the amount of solute contained in a specific quantity of the reacting solutions is known. Such relationships are known as solution concentrations. Solution concentrations may be expressed in a variety of units, but only two, molarity and percentage, will be discussed at this time. 

STRATEGIZE Since the reaction occurs under standard temperature and pressure, you can convert directly from the volume (in L) of hydrogen gas to the amount in moles. Then use the stoichiometric relationship from the balanced eqnation to find the number of moles of water formed. Finally, use the molar mass of water to obtain the mass of water formed. 

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