Problem 84 - A Complete Resource Book in Chemistry for JEE Main

Question

In the enzyme peroxidase anhydrase the percentage of selenium (Se) by mass is \(0.5 \%\). If atomic mass of Se is \(78.4 \mathrm{U}\), then minimum molecular mass of peroxidase anhydrase enzyme is (a) \(1.568 \times 10^{3} \mathrm{U}\) (b) \(1.568 \times 10^{4} \mathrm{U}\) (c) \(1.568 \mathrm{U}\) (d) \(2.136 \times 10^{4} \mathrm{U}\)

Step-by-Step Solution

Answer

The minimum molecular mass is \(1.568 \times 10^{4} \mathrm{U}\) (option b).

Step 1: Define Mass Percentage Formula

To find the minimum molecular mass, you need to use the mass percentage formula: \( \text{Mass Percentage} = \frac{\text{Mass of Element in one Molecule}}{\text{Molecular Mass of Compound}} \times 100 \% \). Here, the mass percentage is given as \(0.5\%\).

Step 2: Set Up Equation Using Given Values

Substitute the known values into the formula: \(0.5 = \frac{78.4}{M} \times 100\). Here, \(78.4\) is the atomic mass of selenium (Se) and \(M\) is the molecular mass of the enzyme.

Step 3: Solve for Molecular Mass (M)

Rearrange the equation to solve for \(M\): \[ M = \frac{78.4 \times 100}{0.5} \]. Calculate \(M\) to find the minimum molecular mass.

Step 4: Calculate the Value of M

Perform the calculation: \( M = \frac{78.4 \times 100}{0.5} = 15680 \). Thus, the minimum molecular mass of peroxidase anhydrase enzyme is \(15680 \mathrm{U}\).

Key Concepts

Understanding the Mass Percentage Formula

The mass percentage formula is a crucial tool when you want to describe the composition of a chemical compound. It's used to express the concentration of an element in a compound, providing insight into how much of the compound's mass is due to one specific element. When working with the mass percentage formula, you calculate it as follows:

• Mass Percentage = \( \frac{\text{Mass of Element in one Molecule}}{\text{Molecular Mass of Compound}} \times 100 \% \)

For example, if you know the mass of selenium in a molecule and the molecular mass of the compound, you can figure out what percentage of the compound's mass is made up by selenium.
This formula allows chemists to predict properties and behaviors of compounds by knowing their compositions, crucial for applications in biochemistry and other fields.

Calculating Minimum Molecular Mass

To determine the minimum molecular mass, particularly in biochemical compounds like enzymes, we need to comprehend how to manipulate the mass percentage formula. The challenge is to find the smallest possible molecular mass of a compound given a particular mass percentage of an element. The calculation uses the given mass percentage and known atomic mass of the element.
For example, in the peroxidase anhydrase enzyme, the mass percentage of selenium is given as \(0.5\%\), and the atomic mass of selenium (Se) is \(78.4\, \mathrm{U}\). By rearranging the mass percentage formula, you solve for the molecular mass \(M\):

• Substitute given values into the equation: \(0.5 = \frac{78.4}{M} \times 100\)
• Rearrange: \[ M = \frac{78.4 \times 100}{0.5} \]
• Calculate \(M\) to find the minimum molecular mass: \(15680 \, \mathrm{U}\).

This understanding provides the minimal measurement for the enzyme's molecular structure and is vital for applications in molecular biology and enzymology.

The Role of Selenium in Enzymes

Selenium is a trace element that's essential in the nutrition of humans and other animals. Within enzymes, selenium is a critical component due to its influential role in catalytic functions. Many enzymes rely on selenium because it acts as a cofactor, facilitating crucial biochemical reactions.
Enzymes such as peroxidase and glutathione peroxidase contain selenium. These play pivotal roles in protecting organisms by breaking down harmful peroxides. The presence of selenium within these enzymes makes them more effective and is essential for maintaining health.

• Selenium aids in shield against oxidative damage.
• It's integral to the activity of antioxidant enzymes.
• Deficiencies in selenium can lead to weakened immune function and other health issues.

Understanding how selenium operates within enzymes justifies its importance in biochemistry and health science, showcasing why its mass percentage in compounds can be critical for determining enzyme effectiveness.