Problem 51 - Chemistry Matter and Change

Question

The average molecular mass of an amino acid is 110 \(\mathrm{g} / \mathrm{mol}\) . Calculate the approximate number of amino acids in a protein that has a molecular mass of \(36,500 \mathrm{g} / \mathrm{mol}\) .

Step-by-Step Solution

Answer

The protein contains approximately 332 amino acids.

Step 1: Understand the Problem

We need to determine how many amino acids (each with an average mass of 110 g/mol) make up a protein with a molecular mass of 36,500 g/mol. This will help us understand the size of the protein in terms of its amino acid composition.

Step 2: Set Up the Calculation

We can find the number of amino acids in the protein by dividing the total molecular mass of the protein by the average molecular mass of a single amino acid. This gives us the formula: \[\text{Number of Amino Acids} = \frac{\text{Molecular Mass of Protein}}{\text{Average Molecular Mass of Amino Acid}}\]

Step 3: Perform the Calculation

Substitute the given values into the formula. Molecular mass of the protein is 36,500 g/mol and the average molecular mass of an amino acid is 110 g/mol: \[\text{Number of Amino Acids} = \frac{36,500}{110} \approx 331.82\] Since the number of amino acids must be a whole number, round 331.82 to 332.

Key Concepts

Amino Acids

Amino acids are the building blocks of proteins and play a crucial role in biology. They are organic compounds that contain both amino and carboxyl functional groups. There are twenty standard amino acids that are used by cells to build proteins. Each amino acid has a specific side chain, or R-group, which determines its characteristics and role within proteins.

• Amino acids combine through peptide bonds to form polypeptide chains, which then fold into proteins.
• These compounds are vital for cellular processes, including enzyme activity, signaling, and structural functions.
• Amino acids have an average molecular mass of 110 g/mol, making it easier to estimate protein sizes in terms of amino acid numbers.

Amino acids can also form non-protein functions in the body, such as acting as neurotransmitters or hormones.

Molecular Mass Calculation

Calculating molecular mass is an essential skill in protein chemistry. It helps determine how many individual components, like amino acids, make up larger structures, like proteins.

• The molecular mass of a compound is the sum of the atomic masses of all atoms in its molecule.
• For proteins, the molecular mass is often measured in g/mol, useful for biochemical calculations.
• To determine the number of amino acids in a protein, divide the protein's total molecular mass by the molecular mass of an average amino acid (110 g/mol).

This calculation gives a quick estimate of the number of amino acids, which is essential in understanding protein structures and their biochemical functions.

Protein Structure

Proteins have a complex and vital structure that is determined by their amino acid sequence. The structure of proteins is typically described in four levels of organization:

• Primary Structure: The sequence of amino acids in a polypeptide chain. This sequence dictates the protein’s final shape and function.
• Secondary Structure: Local folded structures, such as alpha-helices and beta-sheets, stabilized by hydrogen bonds.
• Tertiary Structure: The overall three-dimensional shape of the protein, formed by interactions between the side chains of the amino acids.
• Quaternary Structure: Some proteins consist of multiple polypeptide chains or subunits. These structures describe how these subunits are oriented and interact in a multi-subunit complex.

The precise folding and structure are crucial for the protein's function. Small changes in the amino acid sequence can lead to significant changes in the protein's structure and function, affecting its biological activity.