Problem 80 - Chemistry: An Atoms-Focused Approach

Question

Cytochrome \(\mathrm{c}\) is an enzyme involved in oxidationreduction reactions and is an intermediate in apoptosis, a controlled form of killing cells in response to infection or DNA damage. An elemental analysis of cytochrome c determined that it is \(0.43 \%\) iron and \(1.48 \%\) sulfur by mass. What is the minimum molecular weight of cytochrome c, and what is the minimum number of sulfur atoms per molecule?

Step-by-Step Solution

Answer

Answer: The minimum molecular weight of cytochrome c is 248.26 g/mol, and the minimum number of sulfur atoms per molecule is 6.

Step 1: Calculate moles of iron and sulfur in the molecule

Knowing the percent composition of iron and sulfur in the cytochrome c molecule, we can calculate the moles of each element by assuming 100 grams of the compound. For iron: Mass of iron = 0.43 grams Molar mass of iron (Fe) = 55.84 g/mol Moles of iron (Fe) = 0.43 / 55.84 = 7.70×10^{-3} For sulfur: Mass of sulfur = 1.48 grams Molar mass of sulfur (S) = 32.07 g/mol Moles of sulfur (S) = 1.48 / 32.07 = 4.61×10^{-2}

Step 2: Find the mole ratio of iron and sulfur

To find the mole ratio of iron and sulfur in the compound, we divide the moles of each element by the smallest number of moles. In this case, it is the moles of iron (Fe). Mole ratio of iron (Fe): 7.70×10^{-3} / 7.70×10^{-3} = 1 Mole ratio of sulfur (S): 4.61×10^{-2} / 7.70×10^{-3} ≈ 6

Step 3: Calculate minimum molecular weight

To calculate the minimum molecular weight of the cytochrome c molecule, we need to take into account the number of iron and sulfur atoms present in the molecule. Minimum molecular weight of cytochrome c = Molar mass of iron × Mole ratio of iron + Molar mass of sulfur × Mole ratio of sulfur Minimum molecular weight of cytochrome c = (55.84 × 1) + (32.07 × 6) = 55.84 + 192.42 = 248.26 g/mol

Step 4: Determine the minimum number of sulfur atoms per molecule

Since we found the mole ratio of sulfur (S) to be 6, that means there are 6 sulfur atoms per molecule in cytochrome c. Hence, the minimum molecular weight of cytochrome c is 248.26 g/mol, and the minimum number of sulfur atoms per molecule is 6.

Key Concepts

Molecular Weight Calculation

Molecular weight calculation is a fundamental process in chemistry. It helps in understanding the size and mass of a molecule. To calculate it, you need to know the molar masses of the constituent atoms and their mole ratio in the molecule.
In the case of cytochrome c, the minimum molecular weight is determined by considering both iron and sulfur, as given in the elemental analysis. By multiplying the molar mass of each element by its respective proportion, we add them together to find the total molecular weight.
For cytochrome c, this involved multiplying the molar mass of iron, 55.84 g/mol, by its ratio of 1. The sulfur molar mass, 32.07 g/mol, was multiplied by its ratio of 6. Summing these gives us the molecular weight of 248.26 g/mol.
This calculated weight is crucial for further chemical calculations and applications, including determining how much of the molecule interacts in biochemical reactions.

Mole Ratio

Understanding the mole ratio is key to predicting how molecules interact. This ratio shows the relative quantities of each atom in the compound.
To find the mole ratio, divide the moles of each element by the smallest number of moles in the set. For cytochrome c, assuming 100 grams, the moles of iron (Fe) were calculated as approximately 0.0077 moles. For sulfur, it was approximately 0.0461 moles.

• Mole ratio of iron: Calculate by dividing 0.0077 by 0.0077, equaling 1.
• Mole ratio of sulfur: Divide 0.0461 by 0.0077 to derive approximately 6.

These calculations revealed that for every one iron atom, there are six sulfur atoms.
Identifying mole ratios helps in chemical equations, allowing precise calculations of reactants and products.

Oxidation-Reduction Reactions

Oxidation-reduction (redox) reactions play a crucial role in chemistry, involving the transfer of electrons between molecules.
This transfer changes the oxidation state of the molecules, often producing energy critical for biological processes. In cytochrome c, redox reactions are key to cellular respiration within mitochondria, helping convert nutrients into energy.
The molecule itself exists in oxidized and reduced forms, dynamically shifting electrons to carry out its functions. Understanding these reactions is essential for grasping how cytochrome c functions as an enzyme, aiding electron transport chains in cells.

Apoptosis

Apoptosis is a controlled process of programmed cell death that is essential for maintaining health.
Cytochrome c acts as an intermediary in this process. Upon certain cellular signals, it is released from mitochondria into the cytoplasm. This triggers a cascade ultimately leading to apoptosis.
This biological regulation is crucial in preventing diseases. It removes cells that are no longer needed, damaged, or potentially harmful.

• Defects in apoptosis can result in uncontrolled cell growth, leading to cancer.
• Excessive apoptosis can lead to degenerative diseases, like Alzheimer’s.

Studying cytochrome c in relation to apoptosis provides insight into how cells maintain balance within an organism.

Minimum Molecular Weight

The minimum molecular weight of a compound signifies the smallest weight required to maintain its chemical structure with all essential components present.
For cytochrome c, determining this involves identifying the least mass, considering the number of each essential atom. Through elemental analysis and mole ratio calculations, it was shown that the minimum molecular weight is 248.26 g/mol.
This concept is significant because it aids in predicting the molecule's behavior in reactions. It ensures that all key functional groups within the molecule are accounted for, which is critical in biochemical processes.
Grasping the idea of minimum molecular weight helps in constructing models that depict accurate structures, crucial for chemical engineering and pharmaceuticals.