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ChemistryGeneral Chemistry

Of the Following, the Only Empirical Formula Is: C₁₂H₂₂O₁₁

Of the following, the only empirical formula is C₁₂H₂₂O₁₁. Compare all five formulas by reducing their atom ratios to the smallest whole numbers.

Question

Of the following, the only empirical formula is:(a) C₆H₁₂O₆(b) C₁₂H₂₂O₁₁(c) C₂H₄(d) C₆H₆(e) C₂H₄O₂

Answer

(b) C₁₂H₂₂O₁₁ is the only formula already written as the simplest whole-number atom ratio.

An empirical formula cannot have a common integer divisor greater than 1 across all its subscripts. Check every option:

OptionCommon divisorSimplest formula
(a) C₆H₁₂O₆6CH₂O
(b) C₁₂H₂₂O₁₁1C₁₂H₂₂O₁₁
(c) C₂H₄2CH₂
(d) C₆H₆6CH
(e) C₂H₄O₂2CH₂O

Although 12 and 22 share a factor of 2, 11 does not. No single integer greater than 1 divides all three of 12, 22, and 11. Large subscripts therefore do not disqualify a formula from being empirical.

Evidence boundary

This page answers Texas A&M Chemistry 101, Spring 2008, Exam 1 Form A, question 7&8, with the five formulas shown. The test is a common divisor across every subscript, not whether a formula has small numbers. Other question versions contain different formulas and may have a different answer letter.

Sources

These references support the concepts and methods used in the explanation above.