15 5.1 Formula Mass
Learning Objectives
By the end of this section, you will be able to:
- Calculate formula masses for covalent and ionic compounds
Advancements in chemistry have come from advancements in measurement. The quantitative side of chemistry was integral to the development of early chemical theories. For example, Dalton’s atomic theory was an attempt to explain the results of measurements that allowed him to calculate the relative masses of elements combined in various compounds. Quantitative chemistry continues to be critically important to practicing scientists of all types.
The use of careful measurements helped Dalton uncover links between macroscopic phenomena and the microscopic world of atoms. That link continues to help chemists work today. Understanding the relationship between the masses of atoms and the chemical formulas of compounds allows us to quantitatively describe the composition of substances. It allows us to move between the points of Johnstone’s Triangle, from making macroscopic observations to microscopic and symbolic explanations.
Formula Mass
In an earlier chapter, we described the development of the atomic mass unit and the use of chemical formulas to represent the makeup of substances. These ideas can be extended to calculate the formula mass of a substance by summing the average atomic masses of all the atoms represented in the substance’s formula.
Formula Mass for Covalent Substances
For covalent substances, the formula represents the numbers and types of atoms composing a single molecule of the substance; therefore, the formula mass is sometimes referred to as a molecular mass.
Consider chloroform (CHCl3), a covalent compound once used as a surgical anesthetic and now primarily used in the production of the “anti-stick” polymer, Teflon. The molecular formula of chloroform indicates that a single molecule contains one carbon atom, one hydrogen atom, and three chlorine atoms. The average molecular mass of a chloroform molecule is therefore equal to the sum of the average atomic masses of these atoms. Figure 1 outlines the calculations used to derive the molecular mass of chloroform, which is 119.377 amu.
| 1 C mass | = 12.011 amu |
| 1 H masses | = 1.00794 amu |
| 3 Cl masses = 3 x 35.4527 amu | = 106.3581 |
Total |
= 119.377 amu = the molecular mass of CHCl3 |
Likewise, the molecular mass of an aspirin molecule, C9H8O4, is the sum of the atomic masses of nine carbon atoms, eight hydrogen atoms, and four oxygen atoms, which amounts to 180.15 amu (Figure 2).
| 9 C mass = 9 x 12.011 amu | = 108.099 amu |
| 8 H masses = 8 x 1.00794 amu | = 8.06352 amu |
| 4 O masses = 4 x 15.9994 amu | = 63.9976 amu |
Total |
= 180.160 amu = the molecular mass of C9H8O4 |
Example 1
Ibuprofen, C13H18O2, is a popular non-steroidal anti-inflammatory compound (NSAID). What is the formula mass for this compound?
Solution
Molecules of this compound are comprised of 13 carbon atoms, 18 hydrogen atoms, and 2 oxygen atoms. Following the approach described above, the average molecular mass for this compound is therefore:
| 13 C mass = 13 x 12.011 amu | = 156.143 amu |
| 18 H masses = 18 x 1.00794 amu | = 18.14292 amu |
| 2 O masses = 2 x 15.9994 amu | = 31.9988 amu |
Total |
= 206.285 amu = the molecular mass of C13H18O2 |
Test Yourself
Acetaminophen, C8H9NO2, is the active ingredient in Tylenol. What is the molecular mass for this compound?
Answer
151.16 amu
Formula Mass for Ionic Compounds
Ionic compounds are composed of discrete cations and anions combined in ratios to yield electrically neutral bulk matter. The formula mass for an ionic compound is calculated in the same way as the formula mass for covalent compounds: by summing the average atomic masses of all the atoms in the compound’s formula. Keep in mind, however, that the formula for an ionic compound does not represent the composition of a discrete molecule, so it may should not be described as a molecular mass.
As an example, consider sodium chloride, NaCl, the chemical name for common table salt. Sodium chloride is an ionic compound composed of sodium cations, Na+, and chloride anions, Cl−, combined in a 1:1 ratio. The formula mass for this compound is computed as 58.44 amu (Figure 3).
| 1 Na mass | = 22.9898 amu |
| 1 Cl masses | = 35.4527 amu |
Total |
= 58.4425 amu = the molecular mass of NaCl |
Note that the average masses of neutral sodium and chlorine atoms were used in this computation, rather than the masses for sodium cations and chlorine anions. When calculating the mass of an ion, the missing or additional electrons can generally be ignored since their contribution to the overall mass is negligible.
Example 2
Aluminum sulfate, Al2(SO4)3, is an ionic compound that is used in the manufacture of paper and in various water purification processes. What is the formula mass (amu) of this compound?
Solution
The formula for this compound indicates it contains Al3+ and SO42− ions combined in a 2:3 ratio. For purposes of computing a formula mass, it is helpful to rewrite the formula in the simpler format, Al2S3O12. Following the approach outlined above, the formula mass for this compound is calculated as follows:
| 2 Al mass = 2 x 26.9815 amu | = 53.9630 amu |
| 3 S masses = 3 x 32.066 amu | = 96.198 amu |
| 12 O masses = 12 x 15.9994 amu | = 191.9928 amu |
Total |
= 342.154 amu = the molecular mass of Al2S3O12 |
Test Yourself
Calcium phosphate, Ca3(PO4)2, is an ionic compound and a common anti-caking agent added to food products. What is the formula mass (amu) of calcium phosphate?
Answer
310.18 amu
Chemistry Is Everywhere: Sulfur Hexafluoride
On March 20, 1995, the Japanese terrorist group Aum Shinrikyo (Sanskrit for “Supreme Truth”) released some sarin gas in the Tokyo subway system; twelve people were killed, and thousands were injured. Sarin (molecular formula C4H10FPO2) is a nerve toxin that was first synthesized in 1938 (Figure 4). It is regarded as one of the most deadly toxins known, estimated to be about 500 times more potent than cyanide. Scientists and engineers who study the spread of chemical weapons such as sarin (yes, there are such scientists) would like to have a less dangerous chemical, indeed one that is nontoxic, so they are not at risk themselves.
Sulfur hexafluoride is used as a model compound for sarin. SF6 (Figure 5) has a similar molecular mass (about 146 amu) as sarin (about 140 amu), so it has similar physical properties in the vapour phase. Sulfur hexafluoride is also very easy to accurately detect, even at low levels, and it is not a normal part of the atmosphere, so there is little potential for contamination from natural sources. Consequently, SF6 is also used as an aerial tracer for ventilation systems in buildings. It is nontoxic and very chemically inert, so workers do not have to take special precautions other than watching for asphyxiation.
Sulfur hexafluoride also has another interesting use: a spark suppressant in high-voltage electrical equipment. High-pressure SF6 gas is used in place of older oils that may have contaminants that are environmentally unfriendly (part (c) in the accompanying figure).
Key Concepts and Summary
The formula mass of a substance is the sum of the average atomic masses of each atom represented in the chemical formula and is expressed with atomic mass units.
Review-Reflect, Extend
Review-Reflect
b) What is the molecular mass of oxygen in its elemental form (meaning in the form it naturally occurs in)?
2. Determine the molecular mass of each substance.
a) F2 b) CO c) CO2
3. Calculate the molecular or formula mass of each of the following:
a) P4 b) H2O c) Ca(NO3)2 d) CH3CO2H (acetic acid)
e) C12H22O11 (sucrose, cane sugar)
4. Determine the molecular mass of the following compounds:
a)
b)
c)
Extend
- Consider the common fruits, limes and oranges; If the ratio of the mass of a lime to the mass of an orange is about 1:3, then what is the ratio of the masses of: a) a bag of 8 limes compared to a bag of 8 oranges? A crate of 400 limes compared to a crate of 400 oranges? Use these ratios to figure out, if an average lime is 112 grams, how much each of these containers of fruit would weigh. Is there more than one way to solve the problem?
- Mass Spectrometry was introduced in an earlier chapter as a way to measure the mass of individual atoms. Review this method and think about how mass spectrometry could be used to get formula mass of a compound such as acetaminophen (shown in Example 1). How would the data be different than the data one would get from use of the atomic masses off the periodic table?
Answers to Review-Reflect
1. a) 15.999 amu b) The elemental for of oxygen is O2. Its moleculass mass is 31.998 amu.
2. a) 37.997 amu b) 28.010 amu c) 44.010 amu
3. a) 123.895 amu b) 18.015 amu c) 164.088 amu d) 60.052 amu e) 342.300 amu
4. a) 56.108 amu b) 54.092 amu c) 199.9977 amu
Glossary
formula mass: sum of the average masses for all atoms represented in a chemical formula; for covalent compounds, this is also the molecular mass
