Step 1: Understanding the Question:
The question asks for the exact difference in molar mass (expressed in $\mathrm{g\ mol}^{-1}$) between any two consecutive, neighboring members within a standard organic homologous series.
Step 2: Key Formula or Approach:
A homologous series is a family of structural organic compounds that share the same functional group and general chemical formula. Consecutive members in a homologous series always structurally differ from one another by a single repeating methylene structural unit, which is a $-\mathrm{CH_2}-$ group.
Step 3: Detailed Explanation:
To find the mass difference, we simply calculate the molar mass of the differentiating methylene ($-\mathrm{CH_2}-$) unit:
Atomic mass of a Carbon ($\mathrm{C}$) atom = $12\ \mathrm{g\ mol}^{-1}$
Atomic mass of a Hydrogen ($\mathrm{H}$) atom = $1\ \mathrm{g\ mol}^{-1}$
Summing these atomic masses together for the single carbon and two hydrogen atoms:
$$\text{Molar mass of } -\mathrm{CH_2}- = 12 + (2 \times 1) = 14\ \mathrm{g\ mol}^{-1}$$
For instance, in the alkane series, methane ($\mathrm{CH_4}$, $16\ \mathrm{g/mol}$) and ethane ($\mathrm{C_2H_6}$, $30\ \mathrm{g/mol}$) differ by exactly $14\ \mathrm{g\ mol}^{-1}$. This constant shift applies globally across all true homologous families.
Step 4: Final Answer:
The regular difference in mass between consecutive members is 14, matching option (A).