3.1 Formula Mass and the Mole Concept

By the end of this section, you will be able to calculate formula mass for covalent and ionic compounds, and explain the relation between mass, moles, and numbers of atoms or molecules.

The atomic theory was an attempt to explain the results of the measurement that allowed him to calculate the relative mass of elements.

Understanding the relationship between the mass of atoms and the chemical formulas of compounds allows us to describe the composition of substances.

The development of the atomic mass unit, the concept of average atomic mass, and the use of chemical formulas to represent the elements were described in an earlier chapter.

The formula mass represents the numbers and types of atoms that make up a single molecule of the substance.

chloroform was once used as a surgical anesthetic and is now used in the production of Teflon.
A single molecule has one carbon atom, one hydrogen atom, and three chlorine atoms.
The average molecule mass is equal to the average atomic mass of the atoms.

The average mass of a chloroform molecule is a sum of the average atomic mass of each of its atoms.

The model shows the structure of chloroform.

A molecule of aspirin has an average mass of 180.15 amu.

The model shows the structure of aspirin.

Advil and Motrin are two popular nonprescription pain medications that contain Ibuprofen.

There are 19 carbon atoms, 18 hydrogen atoms, and 2 oxygen atoms in this compound.

The active ingredient in several popular nonprescription pain medications is acetaminophen.

ion compounds are composed of cations and anions.

The formula mass for an ionic compound is the same as the formula mass for covalent compounds: by summing the average atomic mass of all the atoms in the compound's formula.

Consider the chemical name for common table salt as an example.

The ionic compound composed of Na+ and Cl- is called sodium chloride.

A table salt has an array of salt and salt in it's ratio.

The formula mass is 58.44 amu.

The computation used the average amount of neutral sodium and chlorine atoms, rather than the average amount of sodium cations and chlorine anions.

It's perfectly acceptable to use this approach to calculate the formula mass of an ionic compound.
Even though a sodium cation has a slightly smaller mass than a sodium atom, the difference will be offset by the fact that a chloride anion is more massive.
The mass of an electron is small compared to the mass of a typical atom.
When calculating the mass of an isolated ion, the missing or additional electrons can be ignored, since their contribution to the overall mass is negligible, reflected only in the non significant digits that will be lost when the computed mass is properly rounded.
The few exceptions to this guideline are very light ionized elements.

In the manufacture of paper and in various water purification processes, aluminum sulfate is an ionic compound.

It is helpful to rewrite the formula in the simpler format, Al2S3O12.

A common anti-caking agent is added to food products.

The quantity of each type of atom or ion is what defines the identity of a substance.

Water, H2O, and H2O2 are both composed of hydrogen and oxygen atoms.
The hydrogen peroxide molecule has two oxygen atoms as opposed to the water molecule which only has one.
Today, we possess sophisticated instruments that allow the direct measurement of these defining microscopic traits; however, the same traits were originally derived from the measurement of macroscopic properties using relatively simple tools.

The mole is an amount unit that is similar to other units.

The mole provides a link between a number of atoms and a fundamental property.

This constant is reported with an explicit unit of "per mole," a rounded version being 6.022 x 1023/mol.

1 mole of any element has the same number of atoms as 1 mole of any other element.

Since the individual atoms are different, the mass of 1 mole of different elements is different.

Each sample has 6.022 x 1023 atoms.

From left to right are zinc, carbon, magnesium, and copper.
From left to right, there are 32.1 g sulfur, 28.1 g Silicon, 207 g lead, and 118.7 g tin.

The mole and atomic mass unit are based on the same substance, 12C, so the molar mass of any substance is equivalent to its atomic or formula weight.

The atomic mass of a single 12C atom is 12 amu.
According to the definition of the mole, 12 g of 12C contains 1 mole of 12C atoms.

The composition of substances and solutions are measured relative to 12C.

Each sample contains 1.0 mol of the compound or element.

While atomic mass and molar mass are numerically equivalent, they are vastly different in terms of scale, as shown by the huge difference in the magnitudes of their respective units.

It contains more water than can be seen, even though it is just a tiny fraction of water.
Each person on the planet would get more than 100 billion molecules if the molecules were distributed equally.

The number of people on the planet is less than a single molecule in water.

6.022 x 1023 is a large number, but it can be hard to picture.

After watching this, you can complete the "think" questions that follow.

The mole and formula mass can be used to compute quantities that describe the composition of substances and compounds.

If we know the mass and chemical composition of a substance, we can determine the number of moles and calculate the number of atoms in the sample.
If we know the number of moles of a substance, we can derive the number of atoms or molecules and calculate the substance's mass.

The amount of K in moles is requested after the mass of K is provided.

The atomic mass of K is 39.10 amu, and the molar mass is 39.10 g/mol.

The number of moles would be slightly greater than 0.1mol.

The magnitude of 0.12 mol K is in line with our expectations.

X-ray windows made of beryllium are used for medical purposes.

The mass in grams is derived from the amount of Ar provided.

The result is in line with our expectations.

There are many atoms of Cu in copper wire.

The computed result is on the order of 1022 as expected, because the factor-label method yields the desired cancellation of units.

A prospector is prospecting for gold in a river.

Our bodies are able to synthesise protein.

Glycine has a formula called C2H5O2N.

The molar mass of glycine is required for this calculation, and it is computed in the same way as the molecular mass.

We would expect the computed result to be greater than one-third of a mole because the provided mass of glycine is a bit more than one-third of the molar mass.

The result is in line with our estimate.

The formula C6H8O6 is used for the compound vitamin C. The recommended daily allowance of vitamins C is for children aged 4-7 years.

The compound's mass is calculated to be 176.124 g/mol.

The number of moles is a very small fraction of a mole, so we would expect the corresponding mass to be about one-ten thousandth of the molar mass.

This is in line with the result.

The central nervous system is controlled by the brain.

It sends and receives signals to and from muscles and other internal organs to monitor and control their functions, it processes stimuli detected by sensory organs to guide interactions with the external world, and it houses the complex physiological processes that give rise to our intellect and emotions.
Neuroscience covers all aspects of the structure and function of the central nervous system, including research on the brain.
Over the past few decades, great progress has been made in brain research, and the BRAIN Initiative, a federal initiative, aims to accelerate and capitalize on these advances through the concerted efforts of various industrial, academic, and government agencies.

Different parts of the central nervous system receive and receive electrical and chemical signals from specialized cells.

The OpenStax book is free when one of the cells releases neurotransmitters that diffuse across the small gap between the cells.
When a neuron is stimulated, the neurotransmitters are stored in small structures in the cell wall and break open to release their contents.

Dopamine, C8H11NO2, has been extensively studied.

Dopamine is involved in a wide range of human behaviors.

The number of neurotransmitters released during exocytosis is an important aspect of dopamine signaling.

It is important to know how this number changes with certain controlled stimulations since it is a central factor in determining neurological response and subsequent human thought and action.
It is important to understand the mechanism behind any changes in the number of neurotransmitters released, for example, a change in the number of vesicles in the neuron, or a change in the number of neurotransmitters in each vesicle.

Significant progress has been made recently in measuring the number of dopamine molecule stored in individual vesicles and the amount actually released when the vesicle undergoes exocytosis.

Scientists have determined that the vesicles of a certain type of mouse brain neuron contain an average of 30,000 dopamine molecule per vesicle, using small probes that can detect dopamine in very small amounts.
Depending on the drug used, the average number of dopamine molecule contained in individual vesicles can increase or decrease by up to three-fold.
According to these studies, not all of the dopamine in a given vesicle is released during exocytosis, suggesting that it may be possible to regulate the fraction released using pharmaceutical therapies.