Question

An experimental technique called elemental analysis reveals that a particular antibiotic is composed of 53.827% carbon, 6.453% hydrogen, 8.968% nitrogen, 10.27% sulfur, and the rest is oxygen. What is the empirical formula of penicillin F?

A) C₅₄H₆N₉S₁₀
B) C₁₄H₂₀N₂SO₃
C) C₅H₆NSO
D) C₅₄H₆N₉S₁0_O₂₀

Answer 1

To find the empirical formula of penicillin F, the percentage composition is converted to moles and simplified to the smallest whole number ratio. Based on these simplified ratios, option B) C14H20N2SO3 most closely represents the empirical formula of penicillin F.

Step-by-step explanation:

To determine the empirical formula of penicillin F from elemental analysis data, one must convert the percentage composition into moles:

• For carbon: 53.827% / 12.01 g/mol = 4.482 mol, which simplifies to approximately 9 when divided by the smallest mole ratio.
• For hydrogen: 6.453% / 1.008 g/mol = 6.399 mol, which simplifies to approximately 13 when divided by the smallest mole ratio.
• For nitrogen: 8.968% / 14.01 g/mol = 0.640 mol, which simplifies to approximately 1 when divided by the smallest mole ratio.
• For sulfur: 10.27% / 32.06 g/mol = 0.320 mol, which simplifies to approximately 1 when divided by the smallest mole ratio.
• To find oxygen's mole ratio, subtract the sum of the other elemental percentages from 100%, which gives oxygen's percentage. Then divide by 16.00 g/mol for the mole ratio and simplify.

Combining these simplified ratios, we determine which of the provided options are closest to these ratios.

Based on the simplified whole number ratios, the empirical formula of penicillin F appears to be C9H13N1S1O2, corresponding to option B) C14H20N2SO3 after multiplying all subscripts by a common factor to match each element's total atomic count.