Glycine has the molecular formula C2H5O2N. If ten glycines are linked linearly by peptide (condensation) reactions to form an oligomer, what is the correct overall molecular formula?

Introduction:
Forming peptide bonds between amino acids is a condensation process that eliminates water. Accounting correctly for the number of water molecules lost is essential for deriving the empirical formula of a peptide from its monomer building blocks.

Given Data / Assumptions:

• Monomer formula for glycine: C2H5O2N.
• Ten glycines linked linearly create nine peptide bonds.
• Each peptide bond formation eliminates one H2O.

Concept / Approach:
The total formula is the sum of monomers minus the water molecules removed during condensation. For n residues in a linear chain, there are n − 1 peptide bonds and thus n − 1 waters lost.

Step-by-Step Solution:

Verification / Alternative check:
General formula check: for n glycines, overall becomes C(2n) H(5n − 2(n − 1)) O(2n − (n − 1)) N(n) which simplifies to C(2n) H(3n + 2) O(n + 1) N(n). For n = 10, this yields C20H32O11N10, confirming the calculation.

Why Other Options Are Wrong:

• C20H50O20N10: ignores water loss entirely.
• C20H40O10N10 and C20H42O12N10: remove the wrong number of hydrogens and oxygens.
• C20H68O29N10: chemically implausible for a condensation product.

Common Pitfalls:
Forgetting that the number of waters lost equals n − 1 for a linear chain, or mistakenly subtracting one water per residue.

Final Answer:
C20H32O11N10