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 \(1.568 \times 10^{4} \mathrm{U}\), so the answer is (b).

Step 1: Understanding the Mass Percentage

The percentage by mass of selenium in the enzyme is given as 0.5%. This means that for every 100 units of the enzyme mass, 0.5 units are selenium.

Step 2: Setting Up the Formula for Minimum Molecular Mass

We need to assess if selenium meets the 0.5% mass condition when compared to its atomic mass. The formula for percentage mass is \( \text{(mass of component)} / \text{(total molecular mass)} \times 100\% \).

Step 3: Calculating Using the Atomic Mass of Selenium

The atomic mass of selenium is given as 78.4 U. So, \( \frac{78.4}{M} \times 100 = 0.5 \), where \( M \) is the molecular mass of the enzyme.

Step 4: Solving for the Minimum Molecular Mass

Rearrange the equation \( \frac{78.4}{M} \times 100 = 0.5 \) to find \( M \). This becomes \( M = \frac{78.4 \times 100}{0.5} = 15680 \mathrm{U} \).

Step 5: Selecting the Closest Option

We calculated the molecular mass as \( 15680 \mathrm{U} \), which can also be written as \( 1.568 \times 10^{4} \mathrm{U} \). Comparing the options, option (b) matches our result.

Key Concepts

Understanding Percentage Composition

Percentage composition is a convenient way of expressing the proportion of each element within a compound. It's calculated as the mass of a specific element divided by the total molecular mass of the compound, multiplied by 100 to express it as a percentage. This concept is particularly useful when dealing with compounds like enzymes, which can have complex structures.

In real-world applications, knowing the percentage composition enables scientists to determine how much of a substance is needed when combined with others. It also helps in the analytical determination of a compound’s formula. When you have the percentage mass of an element, it is positioned as a key indicator of its influence in the substance’s properties.

• To find the percentage composition: Calculate the total molecular mass of the compound.
• Divide the mass of the individual element by this total molecular mass.
• Multiply by 100 to obtain a percentage.

Understanding this principle allows you to decipher complex chemical formulas and make sense of other molecular property calculations.

The Role of Atomic Mass in Calculations

Atomic mass is fundamental in calculating molecular properties because it represents the mass of an atom at the atomic scale. It's essential for determining how much space they take and is measured in atomic mass units (amu), u, or Daltons (Da). Understanding atomic mass aids in grasping the basic building block of matter.

In calculations involving compounds, atomic mass provides the base unit that helps add or subtract values when finding molecular mass. For selenium in the example of a peroxidase anhydrase enzyme, knowing that its atomic mass is 78.4 u tells you what proportion of any molecular formula or mass it will occupy. This enables you to:

• Determine the total molecular weight of compounds.
• Convert between mass and moles in stoichiometry.
• Identify molecular structure proportions for reacting elements.

In some instances, like with high-precision drugs or enzymes, atomic mass ensures that calculations are as accurate as possible, affecting the effectiveness and safety of these compounds.

Enzymes in Chemistry and Their Significance

Enzymes are biological catalysts that speed up chemical reactions in biological systems. They're crucial in processes like metabolism and digestion. In chemistry, enzymes offer insights into how substances interact at a molecular and sometimes even atomic level.

Understanding the enzyme's composition, including elements like selenium, allows chemists to decipher its functionality and efficacy within biological processes. Enzymes are often named after the reaction they catalyze - for example, peroxidase denotes breaking down peroxide substrates, critical in defending against oxidative damage.

• Enzymes lower activation energy, enabling reactions to occur faster.
• They are specific, meaning each works with specific substrates, ensuring accuracy in biological systems.
• Enzyme-substrate interactions often involve non-covalent bonding, allowing versatility in chemical reactions.

By studying the percentage composition and atomic mass within enzyme structures, scientists can predict and manipulate reactions, enhancing the development of pharmaceuticals, agricultural products, and diagnostics, making enzymes indispensable in both chemistry and biology.