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 correct answer is (b) \(1.568 \times 10^{4} \text{ U}\).

Step 1: Understanding the Given Mass Percentage

The problem states that selenium (Se) makes up 0.5% of the enzyme's mass. This means if the total enzyme mass is \( x \), then the mass of Se in the enzyme is \( 0.005x \).

Step 2: Using the Atomic Mass of Selenium

We are given the atomic mass of selenium as \( 78.4 \text{ U} \). This means that in the enzyme, the mass of Se represented by this 0.5% has to equal the atomic mass times the number of Se atoms. However, since the problem specifies the minimum molecular mass, we assume there is at least one atom of Se.

Step 3: Setting Up the Equation

Since we assume one selenium atom is present, we have \(0.5\%\) of the total mass \(x\) is \(78.4 \text{ U}\): \(0.005x = 78.4\).

Step 4: Solving for Total Molecular Mass

Solving \(0.005x = 78.4\), divide both sides by \(0.005\) to find \(x\): \[x = \frac{78.4}{0.005} = 15680 \text{ U}\]

Step 5: Identifying the Correct Option

The calculated minimum molecular mass of \(15680\text{ U}\) corresponds to the option \((b) \ 1.568 \times 10^{4} \text{ U}\).

Key Concepts

Peroxidase Anhydrase

Peroxidase anhydrase is an enzyme that contains selenium as a part of its molecular structure. Enzymes are biological catalysts that accelerate chemical reactions in cells. Peroxidase anhydrase is particularly notable for its unique composition, including the incorporation of selenium, an essential trace element in some biological systems. In this exercise, understanding peroxidase anhydrase requires recognizing the role of selenium in its composition. Knowing this helps in calculating the molecular mass and understanding the amount of selenium relative to the entire mass of the enzyme. The enzyme harnesses selenium to participate effectively in catalyzing a specific set of reactions, underlining the importance of its accurate molecular configuration.

Percentage Composition

The percentage composition is a way of expressing the proportion of each element within a compound. It indicates how much of the total mass of a molecule is due to a particular element. In our exercise, we know that selenium constitutes 0.5% of the total mass of a peroxidase anhydrase enzyme.

• To find the percentage composition, you calculate the mass of the element in the compound divided by the total mass of the compound, multiplied by 100.
• In problems like this, understanding percentage composition allows you to determine what fraction of the whole is accounted for by one element, which in turn helps in solving for unknowns like total molecular mass.

This figure provides a concise way to express the distribution of mass throughout the compound, pivotal for chemical calculations and understanding molecular structures.

Atomic Mass of Selenium

The atomic mass of selenium is given as 78.4 U. Atomic mass is the mass of an atom expressed in atomic mass units (U), and it reflects the average mass of atoms of an element, factoring in the relative abundance of isotopes. In the exercise, the atomic mass of selenium is crucial for setting up the calculation for determining the enzyme's minimum molecular mass.

• Knowing the atomic mass allows us to determine how much selenium contributes to the total weight.
• Because selenium is 0.5% of the peroxidase anhydrase enzyme, setting up the proportion between its atomic contribution and the whole helps derive the minimum molecular mass.

Understanding atomic mass is a foundational aspect of chemistry, essential for ascribing specific weights to atoms in calculations.

Minimum Molecular Mass

The minimum molecular mass is the smallest possible mass for a molecule given a set of constraints. It can be determined when you know the specific contribution of an element within a molecule. In this context, you calculate the minimum molecular mass using the information that selenium composes 0.5% of the enzyme.
The steps involved:

• Assume at least one atom of selenium is present, given that selenium is part of the composition.
• Use the equation 0.005x = 78.4 to set up the relationship between the percentage composition and atomic mass.
• Solving this equation, dividing 78.4 by 0.005, provides the minimum molecular mass of the enzyme: 15680 U.

This minimum mass is a theoretical lower limit, noting that the enzyme might have higher configurations in practical scenarios.