6.7: Using Chemical Formulas as Conversion Factors

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⚙️ Learning Objectives

Use chemical formulas as conversion factors.

Figure \(\PageIndex{1}\) shows that 2 hydrogen atoms and 1 oxygen atom are required to make one water molecule, 4 hydrogen atoms and 2 oxygen atoms for two water molecules, and 6 hydrogen atoms and 3 oxygen atoms for three water molecules. To make any number of water molecules, the ratio is always the same: 2 hydrogen atoms to 1 oxygen atom.

Figure \(\PageIndex{1}\): The ratio of hydrogen atoms to oxygen atoms used to make water molecules, H₂O is always 2:1, regardless of the number of water molecules.

By using formulas to indicate how many atoms of each element we have in a substance, we can relate the number of molecules to the number of atoms of each element. The possible relationships for 1 mole of water are shown in last column of Table \(\PageIndex{1}\).

Table \(\PageIndex{1}\): Molecular Relationships for Water
1 molecule H₂O has:	1 dozen H₂O molecules has:	1 mol H₂O has:	Mole Relationships
2 H atoms	2 dozen H atoms	2 mol H	\(\dfrac{2\:\mathrm m\mathrm o\mathrm l\:\mathrm H}{1\:\mathrm m\mathrm o\mathrm l\:{\mathrm H}_2\mathrm O}\) or \(\dfrac{1\:\mathrm m\mathrm o\mathrm l\:{\mathrm H}_2\mathrm O}{2\:\mathrm m\mathrm o\mathrm l\:\mathrm H}\)
1 O atom	1 dozen O atoms	1 mol O	\(\dfrac{1\:\mathrm m\mathrm o\mathrm l\:\mathrm O}{1\:\mathrm m\mathrm o\mathrm l\:{\mathrm H}_2\mathrm O}\) or \(\dfrac{1\:\mathrm m\mathrm o\mathrm l\:{\mathrm H}_2\mathrm O}{1\:\mathrm m\mathrm o\mathrm l\:\mathrm O}\)

Therefore, with 30.2 mol H₂O, there would be:

\(30.2\;\cancel{\mathrm{mol}\;{\mathrm H}_2\mathrm O}\times\dfrac{2\;\mathrm{mol}\;\mathrm H}{1\;\cancel{\mathrm{mol}\;{\mathrm H}_2\mathrm O}}=\boxed{\;60.4\;\mathrm{mol}\;\mathrm H}\)

\(30.2\;\cancel{\mathrm{mol}\;{\mathrm H}_2\mathrm O}\times\dfrac{1\;\mathrm{mol}\;\mathrm O}{1\;\cancel{\mathrm{mol}\;{\mathrm H}_2\mathrm O}}=\;\boxed{30.2\;\mathrm{mol}\;\mathrm O}\)

The following example illustrates how we can use the relationships in Table \(\PageIndex{1}\) as conversion factors.

✅ Example \(\PageIndex{1}\): Ethanol

How many moles of hydrogen atoms are present in 2.5 mol of ethanol (C₂H₆O)?

Solution

Steps for Problem Solving
Identify the "given" information and what the problem is asking you to "find."	Given: 2.5 mol C₂H₆O Find: mol H atoms
List known relationships.	1 mol C₂H₆O = 6 mol H
Prepare a concept map and use the proper conversion factor.	\({\color[rgb]{0.8, 0.0, 0.0}\boxed{\;\mathrm{mol}\;{\mathrm C}_2{\mathrm H}_6\mathrm O\;}}\xrightarrow[{1\;\mathrm{mol}\;{\mathrm C}_2{\mathrm H}_6\mathrm O}]{6\;\mathrm{mol}\;\mathrm H}{\color[rgb]{0.0, 0.0, 1.0}\boxed{\;\;\;\;\mathrm{mol}\;\mathrm H\;\;\;\;}}\)
Calculate the answer.	\(2.5\:\cancel{\mathrm{mol}\:{\mathrm C}_2{\mathrm H}_6\mathrm O}\times\dfrac{6\:\mathrm{mol}\:\mathrm H}{1\:\cancel{\mathrm{mol}\:{\mathrm C}_2{\mathrm H}_6\mathrm O}}=\boxed{15\:\mathrm{mol}\:\mathrm H}\)
Think about your result.	There 6 H atoms per C₂H₆O molecule, so the final answer should be 6 times as large.

✏️ Exercise \(\PageIndex{1}\)

How many moles of sodium, sulfur, and oxygen atoms are in a sample containing 6.75 mol of Na₂SO₄, sodium sulfate?

Answer: 13.5 mol Na atoms, 6.75 mol S atoms, and 27.0 mol O atoms

Summary

In any given formula, the ratio of the number of moles of molecules (or formula units) to the number of moles of atoms can be used as a conversion factor.

This page is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Lance S. Lund (Anoka-Ramsey Community College), Anonymous, Marisa Alviar-Agnew, and Henry Agnew.