The molecular and empirical formulas are the same when the molecular formula represents the simplest whole-number ratio of atoms in a compound; in other words, when the subscripts in the molecular formula cannot be further reduced to the lowest whole number ratio.
Understanding Molecular and Empirical Formulas
To understand why they can be the same, let's quickly define each:
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Molecular Formula: This formula shows the exact number of each type of atom in a molecule. For example, the molecular formula for glucose is C6H12O6.
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Empirical Formula: This formula shows the simplest whole-number ratio of atoms in a compound. To find it, you reduce the subscripts in the molecular formula to the smallest possible whole numbers.
The Key to Identical Formulas
The molecular and empirical formulas are identical when the subscripts in the molecular formula are already in their simplest whole-number ratio. This means the subscripts have no common divisor other than 1.
Examples
Here are some examples illustrating when the molecular and empirical formulas are the same:
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Water (H2O): The ratio of hydrogen to oxygen is 2:1. This is already the simplest whole-number ratio. Therefore, both the molecular and empirical formula are H2O.
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Ammonia (NH3): The ratio of nitrogen to hydrogen is 1:3. This is the simplest ratio, making the molecular and empirical formulas both NH3.
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Methane (CH4): The ratio of carbon to hydrogen is 1:4. As with the above examples, the simplest ratio of carbon to hydrogen is already represented; therefore, both the molecular and empirical formulas are CH4.
Examples Where They Differ
To solidify the concept, consider examples where the formulas differ:
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Hydrogen Peroxide: The molecular formula is H2O2. The ratio 2:2 can be simplified to 1:1. The empirical formula is thus HO.
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Glucose: As mentioned earlier, the molecular formula is C6H12O6. This simplifies to a ratio of 1:2:1. Therefore, the empirical formula is CH2O.
In Summary
The molecular formula and empirical formula are identical when the molecular formula already represents the simplest whole-number ratio of elements in the compound, meaning the subscripts in the molecular formula cannot be reduced any further.
