You can calculate the molecular formula directly if you know the percentage composition of each element in the compound and the compound's molar mass, bypassing the need to first calculate the empirical formula.
Here's a step-by-step breakdown of the process:
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Determine the Percentage Composition: Obtain the percentage by mass of each element present in the compound. This information is usually provided.
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Assume a 100g Sample: For ease of calculation, assume you have a 100g sample of the compound. This means the percentage of each element directly translates to its mass in grams.
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Convert Mass to Moles: Divide the mass (in grams) of each element by its respective molar mass (found on the periodic table). This gives you the number of moles of each element in the assumed 100g sample.
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Calculate Moles per Mole of Compound: Divide the moles of each element by the molar mass of the entire compound. This result indicates the number of moles of each element present in one mole of the compound.
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Round to Whole Numbers (or Multiply if Necessary): Ideally, the values obtained in step 4 should be close to whole numbers. Round them to the nearest whole number. If they are not close to whole numbers (e.g., you have a value like 1.5 or 2.33), you may need to multiply all the values by a common factor to get them to whole numbers. For example, if you have a ratio of 1:1.5, multiplying by 2 would give you a ratio of 2:3.
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Write the Molecular Formula: Use the whole number ratios obtained in step 5 as the subscripts for each element in the molecular formula.
Example:
Let's say a compound is found to contain 40.0% Carbon, 6.7% Hydrogen, and 53.3% Oxygen by mass. The molar mass of the compound is 180 g/mol.
| Element | % Composition | Mass in 100g (g) | Molar Mass (g/mol) | Moles in 100g Sample | Moles per Mole of Compound (Divided by 180 g/mol) | Round to Whole Number |
|---|---|---|---|---|---|---|
| Carbon | 40.0% | 40.0 | 12.01 | 3.33 | 3.33/180 = 0.0185 | 6 |
| Hydrogen | 6.7% | 6.7 | 1.01 | 6.63 | 6.63/180 = 0.0368 | 12 |
| Oxygen | 53.3% | 53.3 | 16.00 | 3.33 | 3.33/180 = 0.0185 | 6 |
Therefore, the molecular formula is C6H12O6.
In summary: The key to calculating the molecular formula directly is to use the percentage composition and the molar mass of the entire compound to find the exact number of moles of each element present in one mole of the compound. This avoids the intermediate step of finding the simplest whole-number ratio (empirical formula).
