Question

Myoglobin stores oxygen for metabolic processes in muscle. Chemical analysis shows that it contains 0.34 percent Fe by mass. What is the molar mass of myoglobin? (There is one Fe atom per molecule.)

Short answer

The molar mass of myoglobin is approximately 16,426.47 g/mol.

Step-by-step solution

Understand the Given Information

The problem states that myoglobin contains 0.34% Fe by mass and that there is one Fe atom per myoglobin molecule.

Determine the Mass of Iron Per Mole of Myoglobin

The atomic mass of Fe (iron) is approximately 55.85 g/mol. Since there is one atom of Fe per molecule of myoglobin, the mass of Fe in a mole of myoglobin is 55.85 g.

Express the Mass Percentage as a Fraction

The mass percentage is given as 0.34%, which means that 0.34 grams of iron is present in 100 grams of myoglobin. Thus, the fraction of the mass of Fe to the mass of myoglobin is 0.34/100.

Calculate the Molar Mass of Myoglobin

Using the mass of iron per mole of myoglobin (55.85 g) and knowing that this represents 0.34% of the total molar mass (M) of myoglobin, we use the proportion \( \frac{55.85}{M} = \frac{0.34}{100} \). Solving for \( M \) gives: \( M = \frac{55.85 \times 100}{0.34} = 16426.47 \) g/mol.

Key concepts

Myoglobin

Myoglobin is a protein essential for oxygen storage in muscle cells. It is particularly abundant in muscle tissues that require a rapid supply of oxygen. Myoglobin binds oxygen molecules for release during intense activity. The molecule consists of a protein chain and a heme group that contains a central iron atom. This iron (Fe) is crucial for oxygen binding, which facilitates the transport and storage of oxygen in the muscle cells. The presence of one iron atom per myoglobin molecule is a key aspect in molar mass calculations.

Iron (Fe) Content

Iron is a vital element within the myoglobin molecule. It is responsible for the actual binding of oxygen due to its presence in the heme group. Knowing the iron content in myoglobin, as given in the problem, allows us to determine other molecular properties of myoglobin itself. The exercise reveals that iron constitutes 0.34% of the mass of myoglobin. This percentage helps establish the relationship between the mass of iron in a single molecule and the total mass of the myoglobin. Also, knowing that there is one iron atom per myoglobin molecule is instrumental when calculating other values.

Percentage by Mass

The percentage by mass expresses how much of a particular element or compound is present in a mixture or compound. This percentage is calculated by taking the mass of the individual component and dividing it by the total mass of the compound, then multiplying by 100 to express it as a percentage. In the context of myoglobin, the percentage by mass is 0.34%, meaning that in every 100 grams of myoglobin, 0.34 grams are iron. This percentage is essential for linking the atomic mass of iron to the entire molecule of myoglobin and plays a critical role in determining the molar mass of the compound.

Molecular Weight Determination

Molecular weight determination involves calculating the total mass of a molecule by summing the atomic masses of all the atoms present in it. For myoglobin, this involves considering the unique iron atomic mass along with the percentages provided. Calculating the molar mass requires using a proportion, where the expression involves equating the percentage of iron by mass to the ratio of iron's mass to the total molar mass. The calculation is completed by multiplying and solving the resulting proportion. As per the given exercise, this methodology leads to a total molecular weight of 16426.47 g/mol for myoglobin. Accurate determination of molecular weight is crucial for understanding biochemical processes and the behavior of macromolecules like myoglobin.