Problem 51 - Chemistry Matter and Change

Question

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

Step-by-Step Solution

Answer

The approximate number of amino acids in a protein with a molecular mass of 36,500 g/mol can be calculated using the formula: Number of amino acids = (Molecular mass of the protein) / (Average molecular mass of an amino acid). Plugging in the values, we get Number of amino acids ≈ (36,500 g/mol) / (110 g/mol) ≈ 332. Therefore, there are approximately 332 amino acids in the protein.

Step 1: Identify the given values

The problem gives us the following information: - The average molecular mass of an amino acid is 110 g/mol. - The molecular mass of the protein is 36,500 g/mol.

Step 2: Set up the formula to calculate the number of amino acids

To determine the approximate number of amino acids in the protein, we will use the following formula: Number of amino acids = (Molecular mass of the protein) / (Average molecular mass of an amino acid)

Step 3: Plug the values into the formula

Now, we will plug the given values into the formula: Number of amino acids = (36,500 g/mol) / (110 g/mol)

Step 4: Calculate the number of amino acids

Divide the molecular mass of the protein by the average molecular mass of an amino acid to calculate the number of amino acids: Number of amino acids ≈ 36,500 / 110

Step 5: Simplification

Simplify the division to get the approximate number of amino acids in the protein: Number of amino acids ≈ 332 This means there are approximately 332 amino acids in the protein with a molecular mass of 36,500 g/mol.

Key Concepts

Average Molecular Mass of Amino Acids

The concept of molecular mass is crucial for understanding amino acids and proteins. Amino acids, the building blocks of proteins, each have their own molecular mass. This value represents the sum of the atomic masses of all the atoms in an amino acid molecule. The average molecular mass of amino acids is approximately 110 g/mol. This value is an approximation, as different amino acids have varying atomic structures and thus different molecular masses.
However, using an average value of 110 g/mol helps simplify calculations when determining the number of amino acids in larger molecules like proteins. Proteins are long chains of amino acids linked together to perform a wide array of functions in the body. Knowing the average molecular mass helps to make educated estimations about protein structure and size. It is important to remember that this is an average, and individual cases might slightly differ. Still, it provides a solid foundation for calculations in molecular biology.

Calculate Number of Amino Acids

Determining the number of amino acids in a protein involves understanding the relationship between the molecular mass of the protein and the average molecular mass of a single amino acid. In this case, the protein's molecular mass is 36,500 g/mol. By using the formula to calculate the number of amino acids, you can easily find the approximate quantity of amino acids within the protein:

• Number of amino acids = (Molecular mass of the protein) / (Average molecular mass of an amino acid)

This approach stems from essentially dividing the total mass of the protein by the mass of a single amino acid's average. It enables scientists and students alike to estimate the complexity and length of proteins, facilitating a better understanding of their structure and function. Since the molecular mass values are averages, results are approximate but generally reliable for academic and practical purposes.

Molecular Mass Division

The dividing step is fundamental in calculating the number of amino acids in a protein. In our example, we have the protein's molecular mass as 36,500 g/mol and the average molecular mass of an amino acid as 110 g/mol. By utilizing division in this context, we determine how many of these average-sized amino acids could make up the protein.

Perform the division by taking:

• Number of amino acids = 36,500 g/mol / 110 g/mol

By simplifying this division, you will find that the result is approximately 332 amino acids. This means that theoretically, 332 average amino acids are needed to form a protein with a molecular mass of 36,500 g/mol.
Overall, the division process is not just a mathematical operation; it's an essential analytical tool in biochemistry, allowing us to explore the quantitative aspects of large biomolecules like proteins. This simple calculation can provide insights into the protein's structural and functional attributes.