Question

Cytochrome \(\mathrm{C}\) is a molecule with an iron-porphyrin head connected to a protein tail. Analysis shows the molecule is \(0.45\) percent iron by weight. Calculate the molecular weight of cytochrome \(\mathrm{C}\).

Short answer

The molecular weight of cytochrome C is approximately 12410 g/mol.

Step-by-step solution

Convert the percentage of iron to a decimal value

To convert the percentage to a decimal value, simply divide the percentage value by 100. So, we have: 0.45% = 0.45/100 = 0.0045 This means that there is 0.0045 parts of iron by weight in cytochrome C.

Find the molar mass of iron

The molar mass of iron, denoted as Fe, can be found on the periodic table. The molar mass of iron is approximately M(Fe) = 55.845 g/mol

Set up an equation relating the weight of iron to the total molecular weight

Let the molecular weight of cytochrome C be denoted as M(CytC). The equation relating the weight of iron to the total molecular weight is: 0.0045 * M(CytC) = M(Fe)

Solve the equation for the molecular weight of cytochrome C

Plugging in the molar mass of iron found in step 2: 0.0045 * M(CytC) = 55.845 g/mol Now, we can solve for the molecular weight of cytochrome C: M(CytC) = M(Fe) / 0.0045 M(CytC) = 55.845 g/mol / 0.0045 M(CytC) ≈ 12410 g/mol The molecular weight of cytochrome C is approximately 12410 g/mol.

Key concepts

Understanding Cytochrome C

Cytochrome C is an essential molecule found in the mitochondria of cells. It plays a crucial role in the electron transport chain, which is a series of chemical reactions that help generate energy in the form of ATP. This molecule has two primary components: an iron-porphyrin head and a protein tail. The iron-porphyrin complex is responsible for the electron transfer process, while the protein tail aids in attaching the molecule within the mitochondrial membrane.
Cytochrome C's function in cellular respiration makes it vital for energy production, underpinning many metabolic processes. This molecule is also interesting for its role in apoptosis, or programmed cell death, thus making it a focal point in studies related to diseases such as cancer.

Iron Percentage in Molecular Structure

The iron percentage in a molecule like cytochrome C is a measure of how much of the molecule's mass is made up of iron. This is typically expressed as a percentage by weight. In the given problem, cytochrome C is said to be 0.45% iron by weight.
When you hear '0.45% iron,' it means that out of every 100 grams of cytochrome C, 0.45 grams is iron.
Understanding the iron content is crucial because iron's presence and amount can significantly impact the molecule's properties and functionality, particularly in its role in electron transport.

Calculating Molar Mass

Molar mass is essentially the weight of one mole of a given substance, usually measured in grams per mole (g/mol). It is calculated by summing the atomic masses of all atoms in a molecule.
For elemental iron, the molar mass is approximately 55.845 g/mol, as stated in the periodic table. Molar masses are essential for converting moles to grams or vice versa, particularly in chemical reactions and stoichiometry.

• To find the molecular weight of a compound, multiply the molar mass of its component parts by their frequency in a single molecule, summing the total.
• For cytochrome C, we use the equation derived in the original solution to apply these principles.

Importance of Chemical Analysis

Chemical analysis involves determining the constituents or composition of a substance.
In the context of cytochrome C, chemical analysis helps determine not only the percentage of iron but also its molecular weight and other crucial parameters. Methods like spectrometry can precisely measure the proportions of various compounds in a sample.
For students learning about chemical analysis, it's important to understand that these procedures help scientists and researchers to delve deeper into the properties and functions of various molecules.

• It provides insights into the elements a molecule is comprised of and in what ratios.
• It aids in understanding how these molecular characteristics influence overall chemical behavior.

By exploring the molecular composition, chemical analysis can solve mysteries about complex biological processes and assist in the design of pharmaceuticals and new materials.