A compound is $40 \%$ carbon, $6.7 \%$ hydrogen, and $53.3 \%$ oxygen. What is the empirical formula?
A. $CH _2 O _2$
B. $CH _2 O$
C. $C _2 H _4 O$
D. $C _2 H _4 O _2$
Answer (2)
Assume 100g of the compound, so we have 40g of C, 6.7g of H, and 53.3g of O.
Convert the mass of each element to moles using their molar masses: n C = 12.01 40 ≈ 3.33 , n H = 1.008 6.7 ≈ 6.65 , n O = 16.00 53.3 ≈ 3.33 .
Divide each mole value by the smallest mole value (3.33) to get the simplest ratio: C:1, H:2, O:1.
The empirical formula is C H 2 O .
Explanation
Problem Analysis We are given the percentage composition of a compound: 40% carbon, 6.7% hydrogen, and 53.3% oxygen. Our goal is to determine the empirical formula of this compound, which represents the simplest whole-number ratio of atoms in the compound.
Converting Percentages to Grams Assume we have 100g of the compound. This simplifies the percentages to grams: 40g of carbon, 6.7g of hydrogen, and 53.3g of oxygen.
Calculating Moles To convert the mass of each element to moles, we divide by its molar mass. The molar masses are approximately: Carbon (C) = 12.01 g/mol, Hydrogen (H) = 1.008 g/mol, Oxygen (O) = 16.00 g/mol.
Moles of Carbon: n C = 12.01 g/mol 40 g = 3.33 mol Moles of Hydrogen: n H = 1.008 g/mol 6.7 g = 6.65 mol Moles of Oxygen: n O = 16.00 g/mol 53.3 g = 3.33 mol
Finding the Simplest Ratio Now, we divide each mole value by the smallest mole value (3.33 mol) to find the simplest ratio:
Ratio of Carbon: 3.33 mol 3.33 mol = 1 Ratio of Hydrogen: 3.33 mol 6.65 mol = 1.99 \tapprox 2 Ratio of Oxygen: 3.33 mol 3.33 mol = 1
Determining the Empirical Formula The simplest whole number ratio of C:H:O is 1:2:1. Therefore, the empirical formula is C H 2 O .
Examples
Understanding empirical formulas is crucial in various fields. For instance, in nutrition, knowing the empirical formula of glucose ( C H 2 O ) helps us understand its basic composition and how it provides energy. Similarly, in environmental science, determining the empirical formula of pollutants aids in identifying their sources and developing effective mitigation strategies. This concept is also fundamental in pharmaceuticals, where the precise composition of drugs determines their efficacy and safety.
The empirical formula of the compound, which is 40% carbon, 6.7% hydrogen, and 53.3% oxygen, is determined to be CH₂O, corresponding to option B. This was found by converting mass percentages to moles and finding the simplest whole-number ratio. The ratios for each atom yield 1 carbon, 2 hydrogens, and 1 oxygen.
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