6.7: Using Chemical Formulas as Conversion Factors
- Page ID
- 289387
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- 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.
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 \(\PageIndex{1}\).
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.