Myoglobin stores oxygen for metabolic processes in muscle. Chemical analysis shows that it contains `0.34%` Fe by mass. Minimum molecular mass of myoglobin is

Options

A. 16470 gm
B. 16176 gm
C. 17500 gm
D. 1647 gm

Answer

To find the minimum molecular mass of myoglobin, we can follow these steps:

### Step 1: Set up the equation
Let the mass of myoglobin be \( x \) grams. According to the problem, myoglobin contains \( 0.34\% \) iron (Fe) by mass. Therefore, the mass of iron in myoglobin can be expressed as:

\[ \text{Mass of Fe} = 0.34\% \times x = \frac{0.34}{100} \times x \]

### Step 2: Relate mass of iron to the number of iron atoms
Let \( y \) be the number of iron atoms in myoglobin. The molar mass of iron (Fe) is approximately \( 56 \, \text{g/mol} \). Therefore, the total mass of iron in myoglobin can also be expressed as:

\[ \text{Mass of Fe} = y \times 56 \, \text{g} \]

### Step 3: Set the two expressions for mass of iron equal
Now we can set the two expressions for the mass of iron equal to each other:

\[ \frac{0.34}{100} \times x = y \times 56 \]

### Step 4: Solve for \( x \)
Rearranging the equation gives us:

\[ x = \frac{y \times 56 \times 100}{0.34} \]

### Step 5: Minimize \( x \)
To find the minimum molecular mass of myoglobin, we need to minimize \( x \). This occurs when \( y = 1 \) (i.e., there is one iron atom in myoglobin):

\[ x = \frac{1 \times 56 \times 100}{0.34} \]

### Step 6: Calculate \( x \)
Now we can calculate \( x \):

\[ x = \frac{5600}{0.34} \approx 16470.59 \, \text{g/mol} \]

### Conclusion
Thus, the minimum molecular mass of myoglobin is approximately \( 16470.59 \, \text{g/mol} \).