Problem 95 - Chemistry The Molecular Science

Question

Nitrogen fixation in the root nodules of peas and other legumes occurs with a reaction involving a molybdenumcontaining enzyme named nitrogenase. This enzyme contains two Mo atoms per molecule and is \(0.0872 \%\) Mo by mass. Calculate the molar mass of the enzyme.

Step-by-Step Solution

Answer

The molar mass of the enzyme is approximately \( 220,004.59 \, \text{g/mol} \).

Step 1: Determine the Mass Contribution of Molybdenum

Since molybdenum makes up \(0.0872\%\) of the enzyme by mass, we can express the mass contribution of molybdenum in terms of the enzyme's total mass. Let \( M_{enzyme} \) be the molar mass of the enzyme. Then, the mass of molybdenum in the enzyme can be expressed as \( 0.000872 \times M_{enzyme} \).

Step 2: Calculate Moles of Molybdenum

The enzyme contains two Mo atoms, so the moles of Mo present can be calculated by considering the molar mass of Mo, which is \( 95.95 \, \text{g/mol} \). If the total mass of Mo is \( 0.000872 \times M_{enzyme} \), then the moles of Mo in one mole of the enzyme is \( \frac{0.000872 \times M_{enzyme}}{95.95} \).

Step 3: Solve for Molar Mass of Enzyme

Since there are 2 mol of Mo per mol of enzyme, equate the moles calculated in Step 2 to 2 and solve for \( M_{enzyme} \): \( \frac{0.000872 \times M_{enzyme}}{95.95} = 2 \). Rearrange and solve for \( M_{enzyme} \): \( M_{enzyme} = \frac{2 \times 95.95}{0.000872} \).

Step 4: Calculate Numeric Value

Compute \( M_{enzyme} \) using the formula derived in Step 3: \( M_{enzyme} = \frac{2 \times 95.95}{0.000872} = 220004.59 \, \text{g/mol} \).

Key Concepts

Molybdenum enzyme

Nitrogen fixation is an essential biological process involving special enzymes. Among these is the molybdenum enzyme, known specifically as nitrogenase. This enzyme plays a critical role in enabling legumes to naturally enrich soil with nitrogen. Molybdenum is a vital component of nitrogenase, aiding in breaking down the strong triple bond of gaseous nitrogen ( N_2 ) into compounds that plants can absorb.

A molybdenum enzyme is characterized by the presence of molybdenum (Mo) atoms in its structure. In the case of nitrogenase, it contains exactly two molybdenum atoms for each enzyme molecule. This metal acts as a catalyst, facilitating essential biochemical reactions. Understanding the structural role of molybdenum helps us appreciate its importance in agricultural practices and environmental balance.

• Molybdenum acts as a catalyst.
• Particularly crucial in nitrogen fixation for legumes.

Molar mass calculation

Calculating the molar mass of complex molecules, like enzymes, can initially seem challenging, but it's a valuable skill in chemistry. Molar mass is essentially the mass of one mole of a given substance and is expressed in grams per mole (g/mol). In the context of nitrogenase, the challenge was to find the molar mass of the entire enzyme molecule knowing only the percentage of molybdenum by mass.

Here's how you solve it:

• Identify the percentage by mass of a specific component, here molybdenum, in the larger molecule.
• Calculate the contribution of molybdenum mass, using its percentage and the unknown molar mass of the enzyme, expressed as 0.000872 times the enzyme's molar mass.
• Compute how many moles of the component fit in the enzyme, considering both the element's own molar mass (95.95 g/mol for molybdenum) and its atomic presence in the molecule.
• Solve for the molar mass of the enzyme using these moles figures to find: \(M_{enzyme} = \frac{2 \times 95.95}{0.000872} = 220004.59 \text{ g/mol}\).

By mastering molar mass calculations, you gain a deeper understanding of substances and their chemical composition.

Legumes

Legumes, such as peas, beans, and lentils, are unique among plants due to their ability to naturally fix atmospheric nitrogen. They do this through a symbiotic relationship with Rhizobia bacteria, which occurs in special structures called root nodules. Within these nodules, nitrogenase enzymes convert nitrogen gas into ammonia, providing the plant with essential nutrients.

This ability makes legumes incredibly valuable to agriculture as they enrich the soil without the need for artificial fertilizers. By improving soil fertility, legumes help in sustainable farming practices, reducing reliance on chemical inputs.

• Legumes work with Rhizobia bacteria.
• They naturally enrich soil with nitrogen.
• Reduction of chemical fertilizer use is a significant benefit.

Understanding how legumes interact with nitrogenase enzymes underscores their importance in ecosystems and agriculture, promoting environmentally friendly practices.