Question

Fungal laccase, a blue protein found in wood-rotting fungi, is 0.390\(\% \mathrm{Cu}\) by mass. If a fungal laccase molecule contains four copper atoms, what is the molar mass of fungal laccase?

Short answer

The molar mass of fungal laccase is approximately \(65303.08\) g/mol.

Step-by-step solution

Determine the mass of the copper atoms in one fungal laccase molecule

We know that there are 4 copper atoms in one fungal laccase molecule. We can use the molar mass of copper from the periodic table, which is 63.55 g/mol. Therefore, the mass of 4 copper atoms is mass of 4 copper atoms = 4 × 63.55 g/mol

Calculate the total mass of the fungal laccase molecule

We know that copper accounts for 0.390% of the total mass of the fungal laccase molecule. First, we will convert the percentage to a decimal by dividing it by 100. Then, we will set up the following equation to find the mass of the fungal laccase molecule (x): mass of 4 copper atoms = (0.390 ÷ 100) × x 4 × 63.55 = 0.0039x

Calculate the molar mass of fungal laccase

Let's solve the equation from Step 2 for x by dividing both sides by 0.0039. x will give us the total molar mass of the fungal laccase molecule. x = (4 × 63.55) ÷ 0.0039 Now, by calculating the value of x, we get the molar mass of fungal laccase: Molar mass of fungal laccase ≈ \( (4 \times 63.55) \div 0.0039 \approx 65303.08\) g/mol.

Key concepts

Copper Atoms

Copper atoms are small particles of the element copper that have a significant role in various chemical compounds. In the case of fungal laccase, each molecule contains exactly four copper atoms. This makes copper a crucial component of the fungal laccase's structure.

• The molar mass of a single copper atom is 63.55 g/mol. This value is found on the periodic table and is essential for calculating the mass of copper in larger molecules.
• In our exercise, the presence of four copper atoms in each molecule of fungal laccase means we need to multiply the molar mass by four.
• Thus, the total mass contributed by the copper atoms can be calculated: \[4 \times 63.55 \text{ g/mol} = 254.2 \text{ g/mol}\]

Understanding how copper atoms contribute to the overall mass of a compound is pivotal for determining percentage by mass and other related calculations in chemistry.

Percentage by Mass

Percentage by mass is a way to express the concentration of a specific element within a compound. It tells you what percentage of the total mass of the compound is due to one particular component.

• In fungal laccase, we know copper contributes 0.390% of the total mass.
• To express the percentage of copper as a decimal, simply divide by 100: \[0.390\% = \frac{0.390}{100} = 0.0039\]
• This conversion is essential for later calculations, such as determining the total molar mass of the compound.

By using the percentage by mass, we can establish relationships between the parts and whole of a compound, which is essential for stoichiometry and molecular calculations.

Chemical Formula

A chemical formula is a symbolic representation of the composition of a molecule, showing the types and numbers of atoms present. The formula provides a direct insight into the composition and molecular structure of the compound.

• A fungal laccase molecule includes not only copper atoms but also other atoms and molecules, which are represented by the chemical formula.
• Although the exercise focuses on copper, knowing the chemical formula is crucial for understanding the total makeup of the molecule.
• This formula helps determine the molar mass by adding up the masses of all the atoms present.

While this exercise narrows down to copper, in practice, the complete chemical formula of fungal laccase would detail all graphite contained within the molecule, serving as the foundation for any quantitative chemical evaluations.

Fungal Laccase

Fungal laccase is a fascinating enzyme primarily found in certain fungi that decompose wood. It plays an important role in the breakdown of complex plant materials, assisting in the nutrient cycle.

• This enzyme is characterized by its blue color due to the presence of copper atoms, which is a distinct feature linked to its function.
• The molar mass of fungal laccase, which is calculated at approximately 65,303.08 g/mol, includes contributions from its four copper atoms and other elements that form its complex structure.
• Understanding the composition and molecular weight of fungal laccase is critical not only for academic purposes but also for its applications in biotechnology and environmental science.

Fungal laccases have potential applications in fields like bioremediation and industrial processes, emphasizing the relevance of its molecular study.