Molecular Mass Across a Homologous Series

Introduction

Adjacent members of a simple homologous series differ by one CH₂ unit. This creates a regular molar-mass step of about 14 g mol⁻¹ using C ≈ 12 and H ≈ 1. The pattern helps check formulae and calculate mass trends, but does not make all members physically identical.

Core explanation

The alkane sequence methane CH₄, ethane C₂H₆, propane C₃H₈ and butane C₄H₁₀ shows each next formula adding C₁H₂. Their approximate molar masses are 16, 30, 44 and 58 g mol⁻¹ respectively. Each step is 12 + 2(1) = 14 g mol⁻¹. The series shares saturated acyclic single-bond structure and broadly related reactions, but each member has a distinct size.

Alcohols show the same increment under a specified simple saturated monohydric pattern: methanol CH₃OH has approximate molar mass 32 g mol⁻¹; ethanol C₂H₅OH is 46; propan-1-ol C₃H₇OH is 60. The oxygen-containing group remains the same while a CH₂ unit is added to the carbon portion. This does not mean methanol and ethanol have equal hazards or equal boiling points; those are separate questions.

Carboxylic acids similarly progress from methanoic HCOOH (C₁H₂O₂) to ethanoic CH₃COOH (C₂H₄O₂), each step adding CH₂ and about 14 g mol⁻¹. Formula writing may make the step less obvious if one member is written with a structural grouping, so convert both to molecular formulas before subtracting atom counts.

The exact numerical increment depends on atomic masses used. With standard relative atomic masses C about 12.01 and H about 1.008, CH₂ is about 14.03 g mol⁻¹. For most school calculations, 14 g mol⁻¹ is sufficient when the problem supplies rounded values. Do not mix rounded and precise figures without a stated precision rule.

A homologous series needs more than equal mass differences. Unrelated compounds can differ by 14 g mol⁻¹ coincidentally. Members should share a functional group and general structural pattern. Formula comparison is a screening tool, not a complete family classification.

Step-by-step reasoning

1. Confirm that the compounds belong to the same stated family. 2. Write molecular formulas in comparable C/H/heteroatom order. 3. Subtract atom counts for adjacent members. 4. If the difference is CH₂, add approximately 14 g mol⁻¹. 5. Explain property trends separately from the mass arithmetic.

Visual explanation

Write a ladder: CH₄ (16) → C₂H₆ (30) → C₃H₈ (44) → C₄H₁₀ (58), with each arrow labelled +CH₂, +14 g mol⁻¹. A second ladder of alcohols shows oxygen remaining one atom in every member.

Real-world analogy

A necklace gains one identical link at each step, increasing mass regularly while its overall length changes. Homologues gain a CH₂ unit repeatedly, but their increasing size can change boiling and solubility in non-identical ways.

Real-world example

When comparing fuel components, a chemist can use the CH₂ increment to catch a mistaken formula in an alkane list. If an alleged next member adds only H₂ and no carbon, it is not the next simple alkane homologue.

Why?

Why is the mass step the same across different simple series? The added unit is one C and two H each time. The functional group stays constant within a series, so its atom mass contribution cancels when adjacent formulas are subtracted.

Common misconception

“A 14 g mol⁻¹ difference proves two compounds are homologues.” Mass difference alone is insufficient. Check that they share the same functional group and structural pattern and actually differ by CH₂.

Worked example

Ethanol has formula C₂H₆O and propanol has C₃H₈O. Subtracting gives C₁H₂ and no O change. With C = 12 and H = 1, the molar-mass increase is 12 + 2 = 14 g mol⁻¹. Ethanol's rounded 46 becomes propanol's rounded 60 g mol⁻¹. Their alcohol group stays present, though OH position can create isomers within propanol.

Quick check

1. What atom-count unit separates adjacent simple alkane homologues? Answer: CH₂, one carbon and two hydrogens.

Exam focus

Use the atomic masses provided in the question and write units. Check family membership as well as mass difference. A molar-mass step does not directly give a reaction rate or boiling point.

Advanced insight

Branching isomers have the same molecular formula and molar mass but can have different boiling points. Thus homologous mass increments and within-formula isomerism are independent structural ideas that both matter in property comparisons.

Summary

Adjacent members of a simple homologous series add CH₂, increasing molar mass by about 14 g mol⁻¹. This regularity checks formulas and calculations, while actual physical properties also depend on shape and intermolecular forces.

Practice questions

1. What is the approximate molar mass of propane with C = 12 and H = 1? Answer: 3(12) + 8(1) = 44 g mol⁻¹. 2. What is the next alkane formula after C₄H₁₀? Answer: C₅H₁₂, adding CH₂. 3. Does a 14 g mol⁻¹ difference alone prove homology? Answer: No. Shared functional group and structural pattern are also required. 4. What is the approximate mass step from ethanoic to propanoic acid? Answer: About 14 g mol⁻¹, corresponding to CH₂.