The empirical formula of a compound represents the simplest whole-number ratio of the elements present. To calculate the empirical formula from the percentages of elements, follow these steps:
First, identify the elements involved and their corresponding symbols from the periodic table. For example, in a compound with 57.47% sodium, 40.01% oxygen, and 2.52% hydrogen, the symbols are Na for sodium, O for oxygen, and H for hydrogen.
Next, convert the percentages into grams by assuming a total mass of 100 grams for the compound. This means that 57.47% sodium translates to 57.47 grams, 40.01% oxygen to 40.01 grams, and 2.52% hydrogen to 2.52 grams.
Then, convert these masses into moles using the atomic masses from the periodic table. The atomic mass of sodium (Na) is approximately 22.99 g/mol, oxygen (O) is about 16.00 g/mol, and hydrogen (H) is roughly 1.008 g/mol. To find the number of moles, divide the mass of each element by its atomic mass:
For sodium: \[\text{Moles of Na} = \frac{57.47 \text{ g}}{22.99 \text{ g/mol}} \approx 2.4998 \text{ moles}\]For oxygen: \[\text{Moles of O} = \frac{40.01 \text{ g}}{16.00 \text{ g/mol}} \approx 2.5006 \text{ moles}\]For hydrogen: \[\text{Moles of H} = \frac{2.52 \text{ g}}{1.008 \text{ g/mol}} \approx 2.5000 \text{ moles}\]
After calculating the moles, divide each mole value by the smallest mole value obtained. In this case, the smallest value is approximately 2.4998 moles of sodium. This results in:
For sodium: \[\frac{2.4998}{2.4998} = 1\]For oxygen: \[\frac{2.5006}{2.4998} \approx 1.0003 \approx 1\]For hydrogen: \[\frac{2.5000}{2.4998} \approx 1.0008 \approx 1\]
Since all values are close to whole numbers, the empirical formula can be directly written as NaOH. If any of the resulting values were not whole numbers or were close to 0.1 or 0.9, rounding would be appropriate. If the values were not easily rounded, you would multiply all ratios by the same factor to achieve whole numbers. For instance, if you had a value of 1.5 for oxygen, you would multiply all ratios by 2 to get 2 sodium, 3 oxygen, and 2 hydrogen, resulting in a different empirical formula.
In summary, the empirical formula derived from the given percentages is NaOH, representing the simplest ratio of sodium, oxygen, and hydrogen in the compound.