An organic compound contains 69% carbon, 15.3% hydrogen and 30.7% oxygen. Calculate the the empirical formula [C=12, H = 1, O = 16]

To find the empirical formula of this organic compound, we need to determine the simplest whole-number ratio of the atoms present. We follow these steps:

1. Analyze the composition

• Carbon (C): 69%
• Hydrogen (H): 15.3%
• Oxygen (O): 30.7%

2. Calculate the number of moles

Assume we have 100g of the compound. This means we have 69g of C, 15.3g of H, and 30.7g of O. We divide the mass of each element by its relative atomic mass:

• Moles of C: $\frac{69}{12} = 5.75$
• Moles of H: $\frac{15.3}{1} = 15.3$
• Moles of O: $\frac{30.7}{16} = 1.91875 \approx 1.92$

3. Find the simplest ratio

Divide each mole value by the smallest value obtained (which is 1.92):

• Ratio of C: $\frac{5.75}{1.92} \approx 2.99 \approx 3$
• Ratio of H: $\frac{15.3}{1.92} \approx 7.96 \approx 8$
• Ratio of O: $\frac{1.92}{1.92} = 1$

4. Determine the Empirical Formula

Based on the ratios calculated, we have 3 atoms of Carbon, 8 atoms of Hydrogen, and 1 atom of Oxygen.

The empirical formula is C$_3$H$_8$O.

Note on the calculation: While the math leads us to C$_3$H$_8$O, it is important to note that in chemistry, the sum of percentages must equal 100%. Here, $69 + 15.3 + 30.7 = 115$. This suggests a slight error in the question's provided percentages. However, by using the ratio method, we identify the most consistent empirical formula provided in the options.

Exam Tip: When calculating empirical formulas, if your division results in a decimal like 0.5, multiply all ratios by 2 to get a whole number. If you get 0.33, multiply by 3. Always round to the nearest whole number only if the decimal is very close (e.g., 2.99 to 3).