Myoglobin stores oxygen for metabolic process in muscle. Chemical analysis shows that it contains 0.32% Fe by mass. If there is one Fe atom per molecule of myoglobin, what is the molar mass of myoglobin? (at. mass of Fe = 56 u)

Options

A. `1.75 xx 10^4 g/mol`
B. `3.5 xx 10^5 g/mol`
C. `1 xx 10^4 g/mol`
D. `2.5 xx 10^5 g/mol`

Answer

To find the molar mass of myoglobin given that it contains 0.32% Fe by mass, we can follow these steps:

### Step 1: Understand the percentage composition
The problem states that myoglobin contains 0.32% Fe by mass. This means that in 100 grams of myoglobin, there are 0.32 grams of Fe.

### Step 2: Set up the relationship
Let the molar mass of myoglobin be represented as \( M \) (in grams per mole). Since there is one Fe atom per molecule of myoglobin, we can relate the mass of Fe in myoglobin to its molar mass.

### Step 3: Calculate the mass of Fe in terms of molar mass
In \( M \) grams of myoglobin, the mass of Fe can be expressed as:
\[ \text{Mass of Fe in } M \text{ grams of myoglobin} = \frac{0.32}{100} \times M \]

### Step 4: Set the mass of Fe equal to its atomic mass
Since there is one Fe atom in one molecule of myoglobin, the mass of Fe in \( M \) grams of myoglobin must equal the atomic mass of Fe, which is 56 grams. Therefore, we can set up the equation:
\[ \frac{0.32}{100} \times M = 56 \]

### Step 5: Solve for \( M \)
To find \( M \), we can rearrange the equation:
\[ M = \frac{56 \times 100}{0.32} \]

Calculating this gives:
\[ M = \frac{5600}{0.32} = 17500 \text{ grams per mole} \]

### Step 6: Express the final answer in scientific notation
We can express 17500 grams per mole in scientific notation:
\[ M = 1.75 \times 10^4 \text{ grams per mole} \]

### Final Answer:
The molar mass of myoglobin is \( 1.75 \times 10^4 \) grams per mole.

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