Problem 136 - A Complete Resource Book in Chemistry for JEE Main

Question

Percentage of Se in peroxidase anhydrous enzyme is \(0.5 \%\) by weight (at. wt \(=78.4\) ) then minimum molecular weight of peroxidase anhydrous enzymes is (a) \(1.568 \times 10^{3}\) (b) \(1.568 \times 10^{4}\) (c) \(25.68\) (d) \(4.316 \times 10^{4}\)

Step-by-Step Solution

Answer

The minimum molecular weight is \( 1.568 \times 10^{4} \).

Step 1: Understanding the Problem

We are tasked with finding the minimum molecular weight of peroxidase anhydrous enzymes given that selenium (Se) constitutes 0.5% by weight. The atomic weight of Se is given as 78.4.

Step 2: Calculating Selenium Contribution

Since selenium constitutes 0.5% of the enzyme's weight, we start by converting this percentage to a fraction: \(0.5\% = \frac{0.5}{100} = 0.005\). This means 0.5% of the enzyme's molecular weight is the weight of selenium.

Step 3: Setting Up the Molecular Weight Equation

Let the molecular weight of the enzyme be \( M \). According to the problem, \(0.005 \times M\) represents the weight of selenium in the enzyme. Thus, we set up the equation: \(0.005 \times M = 78.4\), which allows us to calculate for \( M \).

Step 4: Solving for Molecular Weight

We solve for \( M \) by dividing the atomic weight of selenium by its proportion in the enzyme:\[M = \frac{78.4}{0.005}\]Carrying out the division results in a molecular weight, \( M \).

Step 5: Calculating the Final Answer

Calculating the division gives:\[M = 78.4 \div 0.005 = 15680\]Thus, the minimum molecular weight of the anhydrous enzyme is \( 1.568 \times 10^{4} \), corresponding to option (b).

Key Concepts

Percentage Composition

Understanding percentage composition is crucial in chemistry, especially when analyzing compounds. This concept shows us what fraction of a compound's total mass comes from each individual element. For a compound like peroxidase anhydrous enzyme, knowing the percentage of selenium (Se) helps us determine the minimum molecular weight of the entire compound.
To find the percentage composition by mass:

• Take the mass of a specific element in a compound.
• Divide it by the total mass of the compound.
• Multiply by 100 to convert the fraction into a percentage.

In our example, selenium makes up 0.5% of the enzyme's total weight. By converting 0.5% into a decimal (0.005), we gain clarity on how much selenium contributes to the whole compound’s mass. With this information, it becomes easier to set up equations or solve problems related to the compound's overall structure.

Atomic Weight

Atomic weight is a key factor in calculating molecular properties. It represents the average mass of atoms of an element, measured in atomic mass units (amu). Knowing the atomic weight of elements like selenium, which is 78.4 amu, allows us to perform various calculations about compounds containing these elements.
Every element's atomic weight is the sum of its isotopes, taking into account their natural abundance on Earth. Using atomic weight is essential when calculating molecular masses, as it allows us to convert between the number of atoms and their collective mass.
For example, when looking at the percentage of selenium in the enzyme, we use its atomic weight to find how much this element contributes to the compound's total weight. The formula is: \[ \M = \frac{{\text{Atomic Weight of Se}}}{\text{Fraction of Se in the compound}}\] Plugging in known values helps solve for the molecular weight of the entire enzyme.

Chemical Stoichiometry

Chemical stoichiometry involves calculations based on the quantities of reactants and products in chemical reactions. It is also immensely valuable when dealing with problems about composition and molecular weights.
This branch of chemistry helps predict the outcomes of reactions by understanding the relationships among molar masses and compounds. In our example, stoichiometry helps us create a relationship between selenium's proportion and the enzyme's total molecular weight.

• Identify percentages and atomic/molecular weights.
• Set up equations reflecting these relationships.
• Solve equations to find unknowns like the molecular weight.

Applying stoichiometric principles ensures precise mole-to-mass calculations and allows us to understand chemical compositions better. By bridging atomic weights and percentage compositions, stoichiometry provides a solid framework for calculating overall molecular structures.