4.1: The Mole

Last updated
Save as PDF

Page ID: 213285

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

Learning Objectives

Define mole.

In the previous chapters of this text, the quantitative, or numerical, and qualitative, or chemical-based, concepts have been handled separately. However, in order to achieve a true understanding of chemistry, these aspects must be integrated with one another.

The Mole

Many of the measurements that were discussed in Chapter 1 are not easily related to one another and cannot be easily applied to chemical quantities. As a result, chemists established a new unit, the mole, as the standard to which amounts of chemicals could be equated. The mole, which is abbreviated mol, can be directly linked to many chemical quantities, including

the number of chemical particles that are present in a substance,
the amount of an element that is present within a compound or molecule,
the mass of an element, compound, or molecule,
the relative amounts of chemicals or energy involved in a chemical reaction,
the volume of a gas under standard conditions, and
the volume of a solution.

Equality Patterns

Each of the relationships indicated above can be represented using equality patterns. As stated in Chapter 1, equalities have equal signs, but they do not contain variables. The measured equalities and prefix modifier equalities that were developed in Section 1.6 were relatively simple, as each contained a number and a single unit on both sides of an equal sign. Furthermore, these equalities related specific quantities that could not be varied in any way. For example, consider the statement that relates weeks and days: There are always seven days in one week. Alternatively, this information can be written as a measured equality: 1 week (wk) = 7 days (d). In order to accurately represent the relationship between weeks and days, neither the numbers nor the units within this measured equality can be altered.

However, the molar, or mole-based, quantities that will be discussed in the current chapter, as well as in future chapters, are designed to be related to chemical measurements. Therefore, in order to most accurately represent a molar relationship, the identity of the chemical that is being considered must be included within the equality that is developed. As a result, an equality pattern that includes a properly-formatted, chemically-correct chemical formula must be generated. Equality patterns can be distinguished from measured equalities and prefix modifier equalities in two ways. First, an equality pattern will contain one number and two units on both sides of an equal sign. Additionally, certain units and/or numbers within an equality pattern will change, based on the identity of the chemical that is being measured. Each of the molar relationships indicated above will have its own unique equality pattern, as will be discussed in greater detail when these quantities are further defined in the following sections and chapters of this text.

Once an equality pattern has been developed, the information that it contains can be represented in a conversion factor, which can then be used to change one unit of measurement into another. Recall that a conversion factor is a fraction in which both the numerator and the denominator contain numbers and units. To create a conversion factor from an equality, the quantity on one side of the equal sign is written in the numerator of a fraction, and the other quantity is written in the denominator. Finally, a second conversion factor could be developed by interchanging where each quantity is written, relative to the fraction bar.

Indicator Words

Calculations that involve the mole are among the most difficult encountered by students in a general chemistry survey course, as these relationships involve unfamiliar numbers and units that are often presented within the context of a word problem. Therefore, correctly identifying which molar quantity is relevant in a particular context is highly challenging. Fortunately, chemists have chosen specific indicator words or indicator phrases to correspond with each of the molar relationships that are listed above. Recall that an indicator word or indicator phrase is a word or a phrase that has a deeper meaning or application. These key words, which will be specified when the above-mentioned molar quantities are further discussed, are intended to identify which relationship and, therefore, which equality pattern, must be applied to solve the problem at-hand.