Question

Cytochrome \(c\) is an important 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 \( 12988.37 \text{ g/mol} \).

Step-by-step solution

Identify the mass percentage formula

To find the minimum molecular weight of cytochrome \( c \), we use the formula for mass percentage: \[ \text{Mass percentage} = \frac{\text{Mass of element in one mole}}{\text{Molecular weight}} \times 100 \% \].

Set up the equation

We know the mass percentage of iron is \(0.43\%\). Let \( M \) be the molecular weight of cytochrome \( c \). The equation becomes: \[ 0.43 = \frac{55.85}{M} \times 100 \]. Here, \(55.85\, \text{g/mol}\) represents the atomic mass of iron.

Rearrange to solve for \( M\)

Rearrange the equation to isolate \( M \): \[ M = \frac{55.85 \times 100}{0.43} \]. Perform the arithmetic to solve for \( M \).

Calculate the minimum molecular weight

Compute the value: \[ M = \frac{5585}{0.43} \approx 12988.37 \]. Therefore, the minimum molecular weight of cytochrome \( c \) is approximately \( 12988.37 \text{ g/mol} \).

Key concepts

Elemental Analysis

Elemental analysis is a crucial process in identifying the composition of a chemical substance by determining the proportions of its constituent elements. For instance, in the case of cytochrome \( c \), the elemental analysis indicates the presence of iron as one of its components. Knowing the exact percentage of iron is key for further calculations. Measurement in terms of mass percentage allows scientists to determine how much of the substance is composed of specific elements.
This process involves breaking down a complex molecule into its constituent elements and measuring each element's contribution to the overall molecular weight. Elemental analysis is particularly valuable in biochemistry, where understanding the composition of proteins, like cytochrome \( c \), can reveal insights into their function and biological significance.

Mass Percentage Formula

The mass percentage formula is an essential tool used when analyzing the composition of a compound. It helps in relating the mass of an element to the entire molecular weight. The formula is given by:

• Mass percentage = \( \frac{\text{Mass of element in one mole}}{\text{Molecular weight}} \times 100 \% \)

This formula expresses the fraction of the mass contributed by a specific element as a percentage.
In practice, when we say cytochrome \( c \) contains \(0.43\%\) iron, it means that out of the total molecular weight of cytochrome \( c \), \(0.43\%\) is due to iron. Understanding how to employ this formula is crucial for determining the minimum molecular weight, as it directly relates the known atomic masses of elements to the unknown molecular weight, facilitating the calculation process.

Atomic Mass of Iron

The atomic mass of iron is a critical value used in various chemical calculations. For iron, this value is approximately \( 55.85 \text{ g/mol} \). This atomic mass is derived from the isotopic composition of iron found naturally, considering the abundance and atomic masses of each isotope.
Knowing the atomic mass of iron allows scientists to calculate its contribution to the total molecular weight of compounds like cytochrome \( c \). This is clearly demonstrated in calculations where the mass percentage of iron in a compound is known, and using this value helps solve for the minimum molecular weight of the compound. Being familiar with atomic masses is foundational in chemistry, enabling precise and accurate analyses.

Aerobic Organisms

Aerobic organisms are life forms that depend on oxygen to survive. They utilize oxygen in cellular respiration to convert energy stored in nutrients into a form usable by the cell: ATP. This process is highly efficient and enables complex living beings, including humans, animals, and plants, to thrive in oxygen-rich environments.
Within these organisms, enzymes like cytochrome \( c \) play a vital role. Cytochrome \( c \), found in the mitochondria, is crucial in the electron transport chain during respiration, helping to transfer electrons and promote ATP synthesis. Without such enzymes, aerobic organisms couldn't maintain their energy demands or sustain various biochemical processes essential for life.

Enzyme Chemistry

Enzyme chemistry revolves around understanding the structure, function, and kinetics of enzymes, which are proteins facilitating biochemical reactions. Enzymes like cytochrome \( c \) are of particular interest due to their role in vital processes like cellular respiration in aerobic organisms.
Cytochrome \( c \) is an electron carrier, transferring electrons between complexes in the electron transport chain. The presence of iron in its structure is crucial as it participates directly in electron transfer, showcasing the interplay between its elemental composition and function. The study of enzyme chemistry not only aids in comprehending biological processes but also provides insights into developing medical therapies and industrial applications where enzymes can catalyze specific reactions.