Question

Cytochrome \(c\) is an enzyme found in the cells of all aerobic organisms. Elemental analysis of cytochrome \(c\) shows that it contains \(0.43 \%\) iron. What is the minimum molecular weight of this enzyme?

Short answer

The minimum molecular weight of cytochrome \( c \) is approximately 12988 g/mol.

Step-by-step solution

Define the Problem

We need to find the minimum molecular weight of cytochrome \( c \) given that it contains \( 0.43\% \) iron.

Understand the Percentage

A 0.43% means that in every 100 grams of cytochrome \( c \), there are 0.43 grams of iron.

Calculate Iron Weight Fraction

The weight fraction is \( \frac{0.43}{100} = 0.0043 \).

Set Up the Equation

Let \( M \) be the molecular weight of cytochrome \( c \). The iron content would be \( 0.0043 \times M \), and this is equal to the molar mass of one iron atom, which is 55.85 g/mol.

Solve for the Molecular Weight

Set up the equation from the weight fraction: \( 0.0043M = 55.85 \). Solving for \( M \), we get \( M = \frac{55.85}{0.0043} \).

Calculate the Molecular Weight

\( M = \frac{55.85}{0.0043} \approx 12988 \). Thus, the minimum molecular weight of cytochrome \( c \) is approximately 12988 g/mol.

Key concepts

Elemental Analysis

Elemental analysis is a process often used in chemistry to identify the elemental composition of a compound. It helps us understand the amount or percentage of each element within a substance. For example, in the case of cytochrome \( c \), the elemental analysis reveals that iron constitutes \( 0.43\% \) of its total weight.
To break this down:

• Elemental analysis provides data on the different elements present in a compound.
• For compounds like enzymes, knowing these percentages is crucial for further calculations, such as determining molecular weight.
• In cytochrome \( c \), knowing the specific percentage of iron allows us to use it as a basis for calculating its molecular weight considering the precise role iron plays in its functionality.

Elemental analysis can thus function as a bridge between qualitative insights and quantitative calculations in the context of biochemical studies.

Iron Content in Proteins

Proteins can contain various elements, and iron is a vital one, especially in enzymes like cytochrome \( c \). Iron's presence and percentage in a protein are not just numerical values; they indicate the role iron plays in the protein's structure and biological function.
Here’s why understanding iron content is important:

• Iron is crucial for the protein's role in electron transport in cells, a critical function for aerobic organisms.
• The iron content aids in calculating the protein's molecular weight. In the case of cytochrome \( c \), the calculation begins from knowing that iron constitutes \( 0.43\% \) of the protein, allowing us to deduce the rest.
• Knowing the exact iron content helps in designing pharmaceutical agents that might interact with such proteins or in understanding diseases related to iron metabolism.

The understanding of iron content hence provides insights into both the protein’s function and the chemical calculations needed for research or application.

Aerobic Organisms Enzyme

Cytochrome \( c \) is an essential enzyme found in all aerobic organisms, meaning those that depend on oxygen for survival. Its primary role involves the transfer of electrons during the process of cellular respiration, which is fundamental for generating energy in cells.
Key facts about such enzymes include:

• They play a critical role in the electron transport chain, a series of reactions in mitochondria.
• Without enzymes like cytochrome \( c \), aerobic organisms would face challenges in efficiently utilizing oxygen to produce energy.
• The presence of iron in cytochrome \( c \) is directly related to its function in catalyzing electron transfers.

Understanding the role of these enzymes thus provides a snapshot of a broader biological process that supports life through the effective use of oxygen for energy conversion.