Problem 46 - Chemistry The Science in Context

Question

The molecular formula for glycine is \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{NO}_{2} .\) What is the molecular formula of the linear peptide formed when ten glycine molecules are linked together in peptide bonds?

Step-by-Step Solution

Answer

Answer: The molecular formula for the linear peptide formed when ten glycine molecules are linked together in peptide bonds is C20H32N10O11.

Step 1: Understand the Components of a Glycine Molecule

A glycine molecule has the molecular formula \(\mathrm{C}_2\mathrm{H}_5\mathrm{NO}_2\), which means it contains 2 carbon atoms, 5 hydrogen atoms, 1 nitrogen atom, and 2 oxygen atoms.

Step 2: Calculate Total Number of Atoms in Ten Glycine Molecules

In order to find the molecular formula of ten glycine molecules combined (without forming peptide bonds), we simply multiply each atom count by 10: Carbon: \(2\times10=20\) Hydrogen: \(5\times10=50\) Nitrogen: \(1\times10=10\) Oxygen: \(2\times10=20\) So, ten glycine molecules combined have the molecular formula \(\mathrm{C}_{20}\mathrm{H}_{50}\mathrm{N}_{10}\mathrm{O}_{20}\).

Step 3: Account for Water Molecules Lost During Peptide Bond Formation

When two glycine molecules form a peptide bond, one water molecule is lost from the reacting amino and carboxyl groups. Since there are 10 glycine molecules, 9 peptide bonds are formed and therefore 9 water molecules are lost. The molecular formula of water is \(\mathrm{H}_{2}\mathrm{O}\), so 9 water molecules have a total molecular formula of \(\mathrm{H}_{18}\mathrm{O}_{9}\).

Step 4: Subtract Lost Water Molecules from Combined Glycine Molecules

Now we subtract the atoms in the lost water molecules from the total atoms in the combined glycine molecules: Carbon: \(20-0=20\) Hydrogen: \(50-18=32\) Nitrogen: \(10-0=10\) Oxygen: \(20-9=11\)

Step 5: Write the Molecular Formula for the Linear Peptide

The molecular formula for the linear peptide formed when ten glycine molecules are linked together in peptide bonds is \(\mathrm{C}_{20}\mathrm{H}_{32}\mathrm{N}_{10}\mathrm{O}_{11}\).

Key Concepts

Glycine

Glycine is a simple yet foundational building block in the world of biochemistry. As the smallest amino acid, glycine is unique in its simplicity. Its molecular formula is given by \( \mathrm{C}_2\mathrm{H}_5\mathrm{NO}_2 \). This means that each glycine molecule consists of:

• 2 carbon atoms
• 5 hydrogen atoms
• 1 nitrogen atom
• 2 oxygen atoms

Despite its simple structure, glycine plays numerous roles in biological processes. It serves as a constituent of proteins and is vital for the health of neurons and other cells. Furthermore, its starkly simple side chain, a single hydrogen atom, differentiates it from all other amino acids by offering it flexibility in proteins like collagen.

Molecular Formula

The molecular formula of a compound tells us the kind and number of each type of atom present. For glycine, the molecular formula \( \mathrm{C}_2\mathrm{H}_5\mathrm{NO}_2 \) indicates its basic composition. This can help in decoding the specific roles each atom plays in glycine's structure.

• Carbon (\( \mathrm{C} \)) atoms become the backbone in organic compounds.
• Hydrogen (\( \mathrm{H} \)) provides saturation to molecules.
• Nitrogen (\( \mathrm{N} \)) and oxygen (\( \mathrm{O} \)) are essential for forming the amino and carboxyl groups respectively.

Understanding these atoms helps one grasp how glycine can link up with itself and other amino acids to form larger molecules like peptides, which are crucial for biological function. Each part of the molecular formula is crucial for its biological role, and losses or gains during bonding, such as loss of water in peptide bond formation, alter the stoichiometry and molecular formula of the compounds formed.

Amino Acids

Amino acids are the building blocks of proteins and play a vital role in biochemistry. There are 20 standard amino acids, and each features a central carbon atom bonded to a hydrogen atom, a carboxyl group (\( -\mathrm{COOH} \)), an amino group (\( -\mathrm{NH}_2 \)), and a unique side chain. Glycine is particularly simple among amino acids, having a side chain that is just a hydrogen atom.

• Central Carbon: Connects to all functional groups.
• Amino Group: Consists of one nitrogen and binds with carboxyl groups to form peptide bonds.
• Carboxyl Group: Important for reactivity and peptide bond formation.
• Side Chain: Determines characteristics and interactions (hydrophobic, hydrophilic, etc.).

This configuration allows amino acids to form diverse proteins through peptide bonds, each with distinct functions and properties tailored by the sequence and composition of amino acids involved. The unique properties of glycine, such as its lack of a bulky side chain, enable it to fit into flexible regions of proteins.

Peptide Bonds

Peptide bonds are the chemical linkages between amino acids that form proteins. These bonds form during a dehydration synthesis reaction, where the amino group of one amino acid reacts with the carboxyl group of another, releasing a molecule of water (\( \mathrm{H}_2\mathrm{O} \)).Steps in Peptide Formation:

• An amino group \(( \mathrm{-NH}_2 )\) of one amino acid reacts with a carboxyl group \(( \mathrm{-COOH} )\) of another.
• A water molecule is removed. From these, each bond formation results in the loss of one \( \mathrm{H}_2\mathrm{O} \).
• The resulting bond is a peptide linkage (\( -\mathrm{CONH}- \)) connecting the amino acids.

When combining multiple glycine molecules, as in the exercise, forming peptide bonds results in a change in total molecular composition. Specifically, if ten glycine molecules form a linear peptide by linking via nine peptide bonds, nine water molecules are lost during the process (\( \mathrm{H}_{18}\mathrm{O}_9 \)). The resulting molecular formula reflects this loss and the formation of new peptide bonds, altering hydrogen and oxygen counts within the peptide chain.