3.6: Formula Mass and Molar Mass of Compounds (2024)

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Learning Objectives

Calculate formula masses for covalent and ionic compounds
Define the amount unit mole and the related quantity Avogadro’s number
Explain the relation between mass, moles, and numbers of atoms or molecules, and perform calculations deriving these quantities from one another

We can argue that modern chemical science began when scientists started exploring the quantitative as well as the qualitative aspects of chemistry. 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. Understanding the relationship between the masses of atoms and the chemical formulas of compounds allows us to quantitatively describe the composition of substances.

Formula Mass

In an earlier chapter, we described the development of the atomic mass unit, the concept of average atomic masses, and the use of chemical formulas to represent the elemental 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 may be correctly 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 tetrafluoroethylene, the building block for 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 \(\PageIndex{1}\) outlines the calculations used to derive the molecular mass of chloroform, which is 119.37 amu.

3.6: Formula Mass and Molar Mass of Compounds (1)

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 \(\PageIndex{2}\)).

3.6: Formula Mass and Molar Mass of Compounds (2)

Example \(\PageIndex{1}\): Computing Molecular Mass for a Covalent Compound

Ibuprofen, C₁₃H₁₈O₂, is a covalent compound and the active ingredient in several popular nonprescription pain medications, such as Advil and Motrin. What is the molecular mass (amu) 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:

Exercise \(\PageIndex{1}\)

Acetaminophen, C₈H₉NO₂, is a covalent compound and the active ingredient in several popular nonprescription pain medications, such as Tylenol. What is the molecular mass (amu) 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 not correctly be referred to as the “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 \(\PageIndex{3}\)).

3.6: Formula Mass and Molar Mass of Compounds (5)

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. This approach is perfectly acceptable when computing the formula mass of an ionic compound. Even though a sodium cation has a slightly smaller mass than a sodium atom (since it is missing an electron), this difference will be offset by the fact that a chloride anion is slightly more massive than a chloride atom (due to the extra electron). Moreover, the mass of an electron is negligibly small with respect to the mass of a typical atom. Even when calculating the mass of an isolated ion, the missing or additional electrons can generally be ignored, since their contribution to the overall mass is negligible, reflected only in the nonsignificant digits that will be lost when the computed mass is properly rounded. The few exceptions to this guideline are very light ions derived from elements with precisely known atomic masses.

Example \(\PageIndex{2}\): Computing Formula Mass for an Ionic Compound

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:

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Exercise \(\PageIndex{2}\)

Calcium phosphate, \(\ce{Ca3(PO4)2}\), 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

Molar Mass of compounds

The identity of a substance is defined not only by the types of atoms or ions it contains, but by the quantity of each type of atom or ion. For example, water, \(\ce{H2O}\), and hydrogen peroxide, \(\ce{H2O2}\), are alike in that their respective molecules are composed of hydrogen and oxygen atoms. However, because a hydrogen peroxide molecule contains two oxygen atoms, as opposed to the water molecule, which has only one, the two substances exhibit very different properties. 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 (the masses and volumes of bulk quantities of matter) using relatively simple tools (balances and volumetric glassware). This experimental approach required the introduction of a new unit for amount of substances, the mole, which remains indispensable in modern chemical science.

Remember from Chapter 2, the mole is an amount unit similar to familiar units like pair, dozen, gross, etc. It provides a specific measure of the number of atoms or molecules in a bulk sample of matter. The number of entities composing a mole has been experimentally determined to be \(6.02214179 \times 10^{23}\), a fundamental constant named Avogadro’s number (\(N_A\)) or the Avogadro constant in honor of Italian scientist Amedeo Avogadro. This constant is properly reported with an explicit unit of “per mole,” a conveniently rounded version being \(6.022 \times 10^{23}/\ce{mol}\).

Similar to atoms, 1 mole of any compound contains the same number of molecules as 1 mole of any other compund. The masses of 1 mole of different compunds, however, are different, since the masses of the individual molecules are drastically different. The molar mass of a compound is the mass in grams of 1 mole of that substance, a property expressed in units of grams per mole (g/mol)

Because the definitions of both the mole and the formula mass are based on the same reference substance, ¹²C, the molar mass of any compound is numerically equivalent to its formula weight in amu.

Molar Masses of Compounds: https://youtu.be/PhOqgNNv78s

The relationships between formula mass, the mole, and Avogadro’s number can be applied to compute various quantities that describe the composition of compounds. For example, if we know the mass and chemical composition of a compound, we can determine the number of moles and calculate number of molecules in the sample. Likewise, if we know the number of moles of a compound, we can derive the number of molecules and calculate the compound's mass.

Example \(\PageIndex{3}\): Deriving Moles from Grams for a Compound

Our bodies synthesize protein from amino acids. One of these amino acids is glycine, which has the molecular formula C₂H₅O₂N. How many moles of glycine molecules are contained in 28.35 g of glycine?

Solution

We can derive the number of moles of a compound from its mass following the same procedure we used for an element in Example \(\PageIndex{6}\):

The molar mass of glycine is required for this calculation, and it is computed in the same fashion as its molecular mass. One mole of glycine, C₂H₅O₂N, contains 2 moles of carbon, 5 moles of hydrogen, 2 moles of oxygen, and 1 mole of nitrogen:

The provided mass of glycine (~28 g) is a bit more than one-third the molar mass (~75 g/mol), so we would expect the computed result to be a bit greater than one-third of a mole (~0.33 mol). Dividing the compound’s mass by its molar mass yields:

\[\mathrm{28.35\:\cancel{g}\:glycine\left(\dfrac{mol\: glycine}{75.07\:\cancel{g}}\right)=0.378\:mol\: glycine} \nonumber\]

This result is consistent with our rough estimate.

Exercise \(\PageIndex{3}\)

How many moles of sucrose, \(C_{12}H_{22}O_{11}\), are in a 25-g sample of sucrose?

Answer: 0.073 mol

Example \(\PageIndex{4}\): Deriving Grams from Moles for a Compound

Vitamin C is a covalent compound with the molecular formula C₆H₈O₆. The recommended daily dietary allowance of vitamin C for children aged 4–8 years is 1.42 × 10⁻⁴ mol. What is the mass of this allowance in grams?

Solution

As for elements, the mass of a compound can be derived from its molar amount as shown:

The molar mass for this compound is computed to be 176.124 g/mol. The given number of moles is a very small fraction of a mole (~10⁻⁴ or one-ten thousandth); therefore, we would expect the corresponding mass to be about one-ten thousandth of the molar mass (~0.02 g). Performing the calculation, we get:

\[\mathrm{1.42\times10^{-4}\:\cancel{mol}\:vitamin\: C\left(\dfrac{176.124\:g}{\cancel{mol}\:vitamin\: C}\right)=0.0250\:g\: vitamin\: C} \nonumber\]

This is consistent with the anticipated result.

Exercise \(\PageIndex{4}\)

What is the mass of 0.443 mol of hydrazine, \(N_2H_4\)?

Answer: 14.2 g

Example \(\PageIndex{5}\): Deriving the Number of Molecules from the Compound Mass

A packet of an artificial sweetener contains 40.0 mg of saccharin (C₇H₅NO₃S), which has the structural formula:

Given that saccharin has a molar mass of 183.18 g/mol, how many saccharin molecules are in a 40.0-mg (0.0400-g) sample of saccharin? How many carbon atoms are in the same sample?

Solution

The number of molecules in a given mass of compound is computed by first deriving the number of moles, as demonstrated in Example \(\PageIndex{8}\), and then multiplying by Avogadro’s number:

Using the provided mass and molar mass for saccharin yields:

\[\mathrm{0.0400\:\cancel{g}\:\ce{C7H5NO3S}\left(\dfrac{\cancel{mol}\:\ce{C7H5NO3S}}{183.18\:\cancel{g}\:\ce{C7H5NO3S}}\right)\left(\dfrac{6.022\times10^{23}\:\ce{C7H5NO3S}\:molecules}{1\:\cancel{mol}\:\ce{C7H5NO3S}}\right)}\\
=\mathrm{1.31\times10^{20}\:\ce{C7H5NO3S}\:molecules}\]

The compound’s formula shows that each molecule contains seven carbon atoms, and so the number of C atoms in the provided sample is:

\[\mathrm{1.31\times10^{20}\:\ce{C7H5NO3S}\: molecules\left(\dfrac{7\:C\: atoms}{1\:\ce{C7H5NO3S}\: molecule}\right)=9.20\times10^{21}\:C\: atoms} \nonumber\]

Exercise \(\PageIndex{5}\)

How many \(C_4H_{10}\) molecules are contained in 9.213 g of this compound? How many hydrogen atoms?

Answer

\(9.545 \times 10^{22}\; \text{molecules}\; C_4H_{10}\)
\(9.545 \times 10^{23 }\;\text{atoms}\; H\)

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 in atomic mass units. The formula mass of a covalent compound is also called the molecular mass. A convenient amount unit for expressing very large numbers of atoms or molecules is the mole. Experimental measurements have determined the number of entities composing 1 mole of substance to be 6.022 × 10²³, a quantity called Avogadro’s number. The mass in grams of 1 mole of substance is its molar mass. Due to the use of the same reference substance in defining the atomic mass unit and the mole, the formula mass (amu) and molar mass (g/mol) for any substance are numerically equivalent (for example, one H₂O molecule weighs approximately18 amu and 1 mole of H₂O molecules weighs approximately 18 g).

Footnotes

1 Omiatek, Donna M., Amanda J. Bressler, Ann-Sofie Cans, Anne M. Andrews, Michael L. Heien, and Andrew G. Ewing. “The Real Catecholamine Content of Secretory Vesicles in the CNS Revealed by Electrochemical Cytometry.” Scientific Report 3 (2013): 1447, accessed January 14, 2015, doi:10.1038/srep01447.

Glossary

Avogadro’s number (N_A): experimentally determined value of the number of entities comprising 1 mole of substance, equal to 6.022 × 10²³ mol⁻¹

formula mass: sum of the average masses for all atoms represented in a chemical formula; for covalent compounds, this is also the molecular mass

mole: amount of substance containing the same number of atoms, molecules, ions, or other entities as the number of atoms in exactly 12 grams of ¹²C

molar mass: mass in grams of 1 mole of a substance

Contributors and Attributions

Paul Flowers (University of North Carolina - Pembroke),Klaus Theopold (University of Delaware) andRichard Langley (Stephen F. Austin State University) with contributing authors.Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at http://cnx.org/contents/85abf193-2bd...a7ac8df6@9.110).

3.6: Formula Mass and Molar Mass of Compounds (2024)

FAQs

How are formula mass and molar mass of a compound similar? ›

Due to the use of the same reference substance in defining the atomic mass unit and the mole, the formula mass (amu) and molar mass (g/mol) for any substance are numerically equivalent (for example, one H₂O molecule weighs approximately18 amu and 1 mole of H₂O molecules weighs approximately 18 g).

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What is the correct formula to calculate the molar mass of this compound? ›

Multiply the atomic weight (from the periodic table) of each element by the number of atoms of that element present in the compound. 3. Add it all together and put units of grams/mole after the number. For many (but not all) problems, you can simply round the atomic weights and the molar mass to the nearest 0.1 g/mole.

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What is the total formula mass of a compound? ›

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 in atomic mass units. The formula mass of a covalent compound is also called the molecular mass.

What is formula mass with an example? ›

Formula Mass for Ionic Compounds

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. 3).

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How do I find mass formula? ›

The first formula of mass is expressed as, Mass = Density × Volume. This means if we know the density and volume of an object, we can find its mass using this formula of mass. The second formula of mass is expressed as, Mass = Force ÷ Acceleration.

How do you solve for molar mass? ›

To calculate the molar mass of a molecule, we first obtain the atomic weights from the individual elements in a periodic table. We then count the number of atoms and multiply it by the individual atomic masses. Lastly, we add all the atomic masses together to get the molar mass.

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How do you calculate the molar mass of the formula weight for compounds? ›

Answer: Set up a table listing the elements in the compound, the number of atoms of each element, and the atomic weight of each element. Multiply the number of atoms times the atomic weight to get the total mass of each element. Then add the total masses.

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How to calculate the molecular formula? ›

Divide the molar mass of the compound by the empirical formula mass. The result should be a whole number or very close to a whole number. Multiply all the subscripts in the empirical formula by the whole number found in step 2. The result is the molecular formula.

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How do I calculate the molecular mass of a compound? ›

Find the atomic mass for each element using the mass shown in the Periodic Table or Atomic Weight Table. Multiply the subscript (number of atoms) times that element's atomic mass and add the masses of all the elements in the molecule to obtain the molecular mass.

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How to calculate the formula unit mass? ›

The formula unit mass of a substance is the sum of the atomic masses of all atoms in a formula unit of a compound. The term 'formula unit' is used for those substances which are made up of ions. Formula unit mass of NaCl: 1 x Atomic mass of Na + 1 x Atomic mass of Cl = 1 x 23 +1 x 35.5 = 58.5 atomic mass units.

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How do you find the mass number of a compound? ›

The mass number is defined as the total number of protons and neutrons in an atom. It can be calculated by adding the number of neutrons and the number of protons (atomic number) together.

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Are formula mass and molecular mass the same? ›

This is because the formula mass and molecular mass are the same. The main difference is that the formula mass is calculated by adding the masses of atoms present in the simplest formula that can be given for a molecule. In contrast, the molecular mass is calculated using the number of atoms present in a molecule.

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What is the formula for mass and mole calculation? ›

The number of molecules of a substance in one mole is 6.02 × 10²³, this number is known as Avogadro's number. molecular weight×number of moles=mass of substance (in grams). molecular weight × number of moles = mass of substance (in grams) .

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How is formula weight calculated? ›

The formula weight of a substance (element or compound) is the sum of the atomic weights of all the atoms in the chemical formula of the substance. A molecular weight of a substance is the sum of all the atomic weights of all the atoms in a molecule of a molecular substance.

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