Sample of haemoglobin is found to contain `0.333%` of iron. Assuming that each molecule of haemoglobin contains four iron atoms, which of these is the correct molecular mass of haemoglobin ?

Options

A. 67267g/mole
B. 76543g/mole
C. 11218g/mole
D. 30033g/mole

Explanation

To find the molecular mass of hemoglobin based on the given information, we can follow these steps:

### Step 1: Understand the given data
We know that a sample of hemoglobin contains 0.333% of iron. This means that in 100 grams of hemoglobin, there are 0.333 grams of iron.

### Step 2: Calculate the total mass of iron in hemoglobin
Since 0.333 grams of iron is present in 100 grams of hemoglobin, we can express this relationship mathematically.

### Step 3: Determine the mass of iron per molecule of hemoglobin
Each molecule of hemoglobin contains 4 iron atoms. The molar mass of iron (Fe) is 56 g/mol. Therefore, the total mass of iron in one molecule of hemoglobin can be calculated as follows:
\[ \text{Mass of iron in one molecule of hemoglobin} = 4 \times 56 \, \text{g/mol} = 224 \, \text{g/mol} \]

### Step 4: Set up a proportion to find the molecular mass of hemoglobin
We know that 0.333 grams of iron corresponds to 100 grams of hemoglobin. We can set up a proportion to find out how much hemoglobin corresponds to 224 grams of iron:
\[ \frac{0.333 \, \text{g Fe}}{100 \, \text{g Hb}} = \frac{224 \, \text{g Fe}}{x \, \text{g Hb}} \]
Where \( x \) is the mass of hemoglobin we want to find.

### Step 5: Solve for \( x \)
Cross-multiplying gives:
\[ 0.333 \times x = 224 \times 100 \]
\[ 0.333x = 22400 \]
Now, divide both sides by 0.333 to isolate \( x \):
\[ x = \frac{22400}{0.333} \approx 67267 \, \text{g/mol} \]

### Step 6: Conclusion
The molecular mass of hemoglobin is approximately 67,267 g/mol.