What benefits does reviewing a solution procedure provide? Problem

Develop an approximate solution for the following calculation of the volume in cubic feet:

2.6. The Mole and Molecular Weight

What is a mole? For our purposes we will say that a mole is a certain amount of material

corresponding to a specified number of molecules, atoms, electrons, or other specified types of particles.

In the SI system a mole (which we will call a gram mole to avoid confusing units) is composed of 6.022 × 1023 (Avogadro’s number) molecules. However, for convenience in calculations and for clarity, we will make use of other specifications for moles such as the pound mole (lb mol, composed of 6.022 × 1023 × 453.6) molecules, the kg mol (kilomole, kmol, composed of 1000

moles), and so on. You will find that such nonconforming (to SI) definitions of the amount of material will help avoid excess details in many calculations. What would a metric ton mole of molecules consist of?

One important calculation at which you should become skilled is to convert the number of moles to mass and the mass to moles. To do this you make use of the molecular weight—the mass per mole:

Based on this definition of molecular weight:

Therefore, from the definition of the molecular weight, you can calculate the mass knowing the number of moles or the number of moles knowing the mass. For historical reasons, the terms atomic weight and molecular weight are usually used instead of the more accurate terms atomic mass and molecular mass. Does using weight for mass make any difference?

If a bucket holds 2.00 lb of NaOH:

a. How many pound moles of NaOH does it contain? b. How many gram moles of NaOH does it contain?

Solution

You can convert pounds to pound moles, and then convert the values to the SI system of units. Look up the molecular weight of NaOH, or calculate it from the atomic weights. (It is 40.0.) Note that the molecular weight is used as a conversion factor in this calculation:

a.

b1.

Check your answer by converting the 2.00 lb of NaOH to the SI system first and completing the conversion to gram moles:

b2.

Example 2.10. Use of Molecular Weights to Convert Moles to Mass How many pounds of NaOH are in 7.50 g mol of NaOH?

Solution

This problem involves converting gram moles to pounds. From Example 2.9, the MW of NaOH is 40.0:

Note the conversion between pound moles and gram moles was to proceed from SI to the AE system of units. Could you first convert 7.50 g mol of NaOH to grams of NaOH, and then use the conversion of 454g = 1 lb to get pounds of NaOH? Of course.

Values of the molecular weights (relative molar masses) are built up from the values of atomic weights based on a scale of the relative masses of the elements. The atomic weight of an element is the mass of an atom based on the scale that assigns a mass of exactly 12 to the carbon isotope 12C. The value 12 is selected in this case because an atom of carbon 12 contains 6 protons and 6 neutrons for a total molecular weight of 12.

Appendix B lists the atomic weights of the elements. On this scale of atomic weights, hydrogen is 1.008, carbon is 12.01, and so on. (In most of our calculations we shall round these off to 1 and 12, respectively, for convenience). The atomic weights of these and other elements are not whole

numbers because elements can appear in nature as a mixture of different isotopes. As an example, approximately 0.8% of hydrogen is deuterium (a hydrogen atom with one proton and one neutron); thus the atomic weight is 1.008 instead of 1.000.

A compound is composed of more than one atom, and the molecular weight of the compound is nothing more than the sum of the weights of atoms of which it is composed. Thus H₂O consists of 2 hydrogen atoms and 1 oxygen atom, and the molecular weight of water is (2)(1.008) + 16.000 = 18.016, or approximately 18.02.

You can compute average molecular weights for mixtures of constant composition even though they are not chemically bonded if their compositions are known accurately. Example 2.11 shows how to calculate the fictitious quantity called the average molecular weight of air. Of course, for a material such as fuel oil or coal whose composition may not be exactly known, you cannot determine an exact molecular weight, although you might estimate an approximate average molecular weight, which is good enough for most engineering calculations.

Example 2.11. Average Molecular Weight of Air

Calculate the average molecular weight of air, assuming that air is 21% O₂ and 79% N₂. Solution

Because the composition of air is given in mole percent, a basis of 1 g mol is chosen. The MW of the N₂ is not actually 28.0 but 28.2 because the value of the MW of the pseudo 79% N₂ is actually a combination of 78.084% N₂ and 0.934% Ar. The masses of the O₂ and pseudo N₂ are

Therefore, the total mass of 1 g mol of air is equal to 29.0 g, which is called the average molecular weight of air. (Because we chose 1 g mol of air as the basis, the total mass calculated directly provides the average molecular weight of 29.0.)

Example 2.12. Calculation of Average Molecular Weight

Since the discovery of superconductivity almost 100 years ago, scientists and engineers have speculated about how it can be used to improve the use of energy. Until recently most applications were not economically viable because the niobium alloys used had to be cooled below 23 K by liquid He. However, in 1987 superconductivity in Y-Ba-Cu-O material was achieved at 90 K, a situation that permits the use of inexpensive liquid N₂ cooling.

What is the molecular weight of the cell of a superconductor material shown in Figure E2.12? (The figure represents one cell of a larger structure.)

Figure E2.12

Solution

First look up the atomic weights of the elements from the table in Appendix B. Assume that one cell is a molecule. By counting the atoms you can find:

The molecular weight of the cell is 1972.3 atomic masses/1 molecule or 1972.3 g/g mol. Check your calculations and check your answer to ensure that it is reasonable.

Mole fraction is simply the number of moles of a particular substance in a mixture or solution divided by the total number of moles present in the mixture or solution. This definition holds for gases, liquids, and solids. Similarly, the mass (weight) fraction is nothing more than the mass (weight) of the substance divided by the total mass (weight) of all of the substances present in the mixture or solution. Although mass fraction is the correct term, by custom ordinary engineering usage frequently employs the term weight fraction. These concepts can be expressed as

Mole percent and weight percent are the respective fractions times 100. Be sure to learn how to convert from mass fraction to mole fraction and vice versa without thinking, because you will have to do so quite often. Unless otherwise specified, when a percentage or fraction is given for a gas, it is assumed that it refers to a mole percentage or a mole fraction. When a percentage or fraction is given for a liquid or a solid, it is assumed that it refers to a weight percentage or a weight fraction.

Example 2.13. Conversion between Mass (Weight) Fraction and Mole Fraction

mass (weight) fraction and mole fraction of each component in the drain cleaner? Solution

You are given the masses so it is easy to calculate the mass fractions. From these values you can then calculate the desired mole fractions.

A convenient way to carry out the calculations in such conversion problems is to form a table as shown below. Become skilled at doing so, because this type of problem and its inverse—that is, conversion of mole fraction to mass (weight) fraction—will occur more frequently than you would like. List the components, their masses, and their molecular weights in columns.

Basis: 10.0 kg of total solution

Self-Assessment Test

Questions

1. Indicate whether the following statements are true or false: