Mole-gram relationship

From this mole-gram relationship come the units of molar mass, grams/mole. For example, the molar mass of silver nitrate (AgN03) is 170 grams/mole. 

In this chapter, you learned how to balance simple chemical equations by inspection. Then you examined the mass/mole/particle relationships. A mole has 6.022 x 1023 particles (Avogadro s number) and the mass of a substance expressed in grams. We can interpret the coefficients in the balanced chemical equation as a mole relationship as well as a particle one. Using these relationships, we can determine how much reactant is needed and how much product can be formed—the stoichiometry of the reaction. The limiting reactant is the one that is consumed completely it determines the amount of product formed. The percent yield gives an indication of the efficiency of the reaction. Mass data allows us to determine the percentage of each element in a compound and the empirical and molecular formulas. 

You make unit conversions everyday when you determine how many quarters are needed to make a dollar or how many feet are in a yard. One unit that is often used in calculations in chemistry is the mole. Chapter 11 shows you equivalent relationships among mole, grams, and the number of representative particles (atoms, molecules, formula units, or ions). For example, one mole of a substance contains 6.02 X 10 representative particles. Try the next example to see how this information can be used in a conversion factor to determine the number of atoms in a sample of manganese. 

Figure 3.4 Summary of the mass-mole-number relationships for compounds. Moles of a compound are related to grams of the compound through the molar mass (jtt in g/mol) and to the number of molecules (or formula units) through Avogadro s number (6.022 XICF molecules/mol). To find the number of molecules (or formula units) in a given mass, or vice versa, convert the information to moles first. With the chemical formula, you can calculate mass-mole-number information about each component element.

Figure 3.8 Summary of the mass-mole-number relationships in a chemical reaction. The amount of one substance in a reaotion is related to that of any other. Quantities are expressed in terms of grams, moles, or number of entities (atoms, molecules, or formula units). Start at any box in the diagram (known) and move to any other box (unknown) by using the information on the arrows as conversion factors. As an example, if you know the mass (in g) of A and want to know the number of molecules of B, the path involves three calculation steps ...

The surface excess per square centimeter F is just n/E, where n is the moles adsorbed per gram and E is the specific surface area. By means of the Gibbs equation (111-80), one can write the relationship... 

Simple mole relationships of this type are readily extended to relate moles of one substance to grams of another or grams of one substance to moles or molecules of another (Example 3.9). 

It is thus seen that heat capacity at constant volume is the rate of change of internal energy with temperature, while heat capacity at constant pressure is the rate of change of enthalpy with temperature. Like internal energy, enthalpy and heat capacity are also extensive properties. The heat capacity values of substances are usually expressed per unit mass or mole. For instance, the specific heat which is the heat capacity per gram of the substance or the molar heat, which is the heat capacity per mole of the substance, are generally considered. The heat capacity of a substance increases with increase in temperature. This variation is usually represented by an empirical relationship such as... 

Background Avogadro s law (Vin2 = V2ni), where moles, n = mw (grams/mole) exPresses the relationship between molar mass, the actual mass and the number of moles of a gas. The molar volume of a gas at STP, VSTP is equal to the volume of the gas measured at STP divided by the number of moles VSTp = pp. Dalton s Law of Partial Pressure (Ptotai = Pi + P2 + P3 +. ..) and the derivation, Pi = pp Ptotai will also be used in this experiment to predict the volume occupied by one mole of hydrogen gas at STP. 

This relationship gives a way of converting from grams to moles to particles and vice versa. If you have any one of the three quantities, you can calculate the other two. For example, the molar mass of iron(III) oxide, Fe203 (rust), is 159.689 g/mol [(2 X 55.846 g/mol for Fe) + (3 X 15.999 g/mol for O)]. Therefore, if we had 50.00 g of iron(III) oxide, we could calculate both the number of moles and the number of particles present. 

Notice that if we had grams and wanted just particles, we still would need to incorporate the mole relationship. 

This balanced equation can be read as 4 iron atoms react with 3 oxygen molecules to produce 2 iron(III) oxide units. However, the coefficients can stand not only for the number of atoms or molecules (microscopic level) but they can also stand for the number of moles of reactants or products. So the equation can also be read as 4 mol of iron react with 3 mol of oxygen to produce 2 mol ofiron(III) oxide. In addition, if we know the number of moles, the number of grams or molecules may be calculated. This is stoichiometry, the calculation of the amount (mass, moles, particles) of one substance in the chemical equation from another. The coefficients in the balanced chemical equation define the mathematical relationship between the reactants and products and allow the conversion from moles of one chemical species in the reaction to another. 

Another useful relationship is one derived from Avogadro s law 1 mol of any gas occupies 22.4 L at STP (standard temperature and pressure of 0°C (273 K) and 1 atm). If you can find the volume at STP, you can then convert it to moles using this relationship and then to grams, if needed. 

The mole (mol) is the amount of a substance that contains the same number of particles as atoms in exactly 12 grams of carbon-12. This number of particles (atoms or molecules or ions) per mole is called Avogadro s number and is numerically equal to 6.022 x 1023 particles. The mole is simply a term that represents a certain number of particles, like a dozen or a pair. That relates moles to the microscopic world, but what about the macroscopic world The mole also represents a certain mass of a chemical substance. That mass is the substance s atomic or molecular mass expressed in grams. In Chapter 5, the Basics chapter, we described the atomic mass of an element in terms of atomic mass units (amu). This was the mass associated with an individual atom. Then we described how one could calculate the mass of a compound by simply adding together the masses, in amu, of the individual elements in the compound. This is still the case, but at the macroscopic level the unit of grams is used to represent the quantity of a mole. Thus, the following relationships apply ... 

In Portland cement studies [14] the reductions in initial and final setting times were determined as a function of the number of gram moles of calcium ion introduced and a straight-line relationship was established as shown in Fig. 5.7. 

The relationship between the moles of a material and grams is explored in much more detail in Chapter 9. 

Just how many molecules are there in a mole Experiments show that one mole of any substance contains 6.022 X 1023 formula units, a value called Avogadro s number (abbreviated NA) after the Italian scientist who first recognized the importance of the mass/number relationship. Avogadro s number of formula units of any substance—that is, one mole—has a mass in grams equal to the molecular or formula mass of the substance. 

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. 

Chemists often need to know the concentration of a solution. Sometimes it is measured in grams per cubic decimetre (gdm-3) but more often concentration is measured in moles per cubic decimetre (mol dm-3). When 1 mole of a substance is dissolved in water and the solution is made up to ldm3 (1000cm3), a 1 molar (1 mol dm-3) solution is produced. Chemists do not always need to make up such large volumes of solution. A simple method of calculating the concentration is by using the relationship ... 

Since the relationship within a chemical formula is a small whole-number relationship of moles of elements to each other, the first step in the solution is to determine the number of grams of each of the elements. This step must isolate the desired element from the compound produced by the burning, which can be performed by multiplying by the fraction of the compound that is the element. 

Stoichiometry is the technical word for the relationships among balanced equations, moles, and grams. Stoichiometry is to chemists what cooking and recipes are to cooks. 

Notice that you cannot use the unit gram here. The coefficients do not refer to weighing but rather to counting. Once again, the mole-molar mass relationship is involved. 

Thermochemical measurements are based on the relationships between heat and temperature. The measurement that relates to the two is heat capacity, defined as the amount of heat that is required to raise the temperature of a substance 1°C. (The amount of substance is sometimes expressed in moles or in grams.) The heat capacity of a mole of a substance is known as the molar heat capacity, while the heat capacity for gram values of a substance are known as specific heat capacities. The specific heat of a substance is the amount of heat required to raise 1 gram of the substance 1°C. The formula that is used to calculate specific heat is Equation 17.4 ... 

In section 5.2, you explored the relationship between the number of atoms or particles and the number of moles in a sample. Now you are ready to relate the number of moles to the mass, in grams. Then you will be able to determine the number of atoms, molecules, or formula units in a sample by finding the mass of the sample. 

How can you use this relationship to relate mass and moles The periodic table tells us the average mass of a single atom in atomic mass units (u). For example, zinc has an average atomic mass of 65.39 u. One mole of an element has a mass expressed in grams numerically equivalent to the element s average atomic mass expressed in atomic mass units. One mole of zinc atoms has a mass of 65.39 g. This relationship allows chemists to use a balance to count atoms. You can use the periodic table to determine the mass of one mole of an element. 

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. 

Thus the mole is defined such that a sample of a natural element with a mass equal to the element s atomic mass expressed in grams contains 1 mole of atoms. This definition also fixes the relationship between the atomic mass unit and the gram. Since 6.022 X 1023 atoms of carbon (each with a mass of 12 amu) have a mass of 12 grams, then... 

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