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% iron by mass, we can follow these steps:

### Step 1: Understand the relationship between mass percentage and molar mass
The mass percentage of iron in myoglobin is given as 0.32%. This means that in 100 grams of myoglobin, there are 0.32 grams of iron.

### Step 2: Set up the equation for the mass of iron
Let the molar mass of myoglobin be \( M \) grams per mole. Since there is one iron atom per molecule of myoglobin, we can express the mass of iron in terms of the molar mass of myoglobin:
\[ \text{Mass of Fe in myoglobin} = \frac{0.32}{100} \times M \]

### Step 3: Relate the mass of iron to its atomic mass
The atomic mass of iron (Fe) is given as 56 u. Since there is one iron atom per molecule of myoglobin, the mass of iron in one mole of myoglobin is equal to the atomic mass of iron:
\[ \frac{0.32}{100} \times M = 56 \]

### Step 4: Solve for the molar mass of myoglobin
To find \( M \), we can rearrange the equation:
\[ M = 56 \times \frac{100}{0.32} \]
Calculating this gives:
\[ M = 56 \times 312.5 = 17500 \text{ grams per mole} \]

### Step 5: Final result
Thus, the molar mass of myoglobin is:
\[ M = 17500 \text{ g/mol} \]