To determine the empirical formula from percent composition, you'll follow a straightforward, step-by-step process of converting percentages to grams, grams to moles, and then finding the simplest whole-number ratio of those moles.
Steps to Find the Empirical Formula
Here's a detailed breakdown of the process:
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Assume a 100g Sample and Convert Percentages to Grams: Pretend you have 100 grams of the compound. This makes the percentage directly equal to the mass in grams for each element. For instance, if a compound is 40% carbon, you assume you have 40 grams of carbon.
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Convert Grams to Moles: Use the molar mass of each element to convert the mass in grams to moles. The molar mass can be found on the periodic table. The formula is:
Moles = Grams / Molar Mass
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Determine the Simplest Mole Ratio: Divide the number of moles of each element by the smallest number of moles calculated in the previous step. This will give you a preliminary mole ratio.
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Convert to Whole Numbers (If Necessary): If the mole ratios are close to whole numbers (e.g., 1.1, 2.9), round them to the nearest whole number. If any ratio is not a whole number (e.g., 1.5, 2.33, 3.25, etc.), you'll need to multiply all the ratios by a common factor to get whole numbers. Here are some common multipliers:
- .5 (multiply by 2)
- .33 or .67 (multiply by 3)
- .25 or .75 (multiply by 4)
- .2 (multiply by 5)
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Write the Empirical Formula: Use the whole-number mole ratios as subscripts for each element in the empirical formula.
Example
Let's say a compound contains 40.0% Carbon (C), 6.7% Hydrogen (H), and 53.3% Oxygen (O).
| Element | Percentage | Mass (g) | Molar Mass (g/mol) | Moles | Mole Ratio |
|---|---|---|---|---|---|
| C | 40.0 | 40.0 | 12.01 | 3.33 | 1 |
| H | 6.7 | 6.7 | 1.01 | 6.63 | 2 |
| O | 53.3 | 53.3 | 16.00 | 3.33 | 1 |
- Step 1: We assume a 100g sample, so the percentages become grams.
- Step 2: We calculate the moles of each element (Grams / Molar Mass).
- Step 3: We divide each mole value by the smallest mole value (3.33).
The empirical formula is therefore CH2O.
By following these steps, you can accurately determine the empirical formula of a compound from its percent composition. Remember that the empirical formula represents the simplest whole-number ratio of elements in the compound.
