Haemoglobin contains 0.25% iron by weight. If one molecule of haemoglobin contains 4 atoms of iron, find the molecular mass of haemoglobin

Answer

To find the molecular mass of hemoglobin given that it contains 0.25% iron by weight and that one molecule of hemoglobin contains 4 atoms of iron, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Percentage Composition**:
- Given that hemoglobin contains 0.25% iron by weight, this means that in 100 grams of hemoglobin, there are 0.25 grams of iron.

2. **Set Up the Relationship**:
- If we denote the mass of hemoglobin as \( x \) grams, then the amount of iron in \( x \) grams of hemoglobin can be expressed as:
\[ \text{Iron in } x \text{ grams of hemoglobin} = \frac{0.25}{100} \times x = \frac{0.25x}{100} \text{ grams} \]

3. **Calculate the Mass of Iron in One Molecule**:
- The atomic mass of iron (Fe) is approximately 56 grams per mole. Since one molecule of hemoglobin contains 4 atoms of iron, the total mass of iron in one molecule of hemoglobin is:
\[ \text{Mass of iron in one molecule of hemoglobin} = 4 \times 56 = 224 \text{ grams} \]

4. **Set Up the Equation**:
- According to the information given, the amount of iron in \( x \) grams of hemoglobin should equal the mass of iron in one molecule of hemoglobin:
\[ \frac{0.25x}{100} = 224 \]

5. **Solve for \( x \)**:
- Rearranging the equation to solve for \( x \):
\[ 0.25x = 224 \times 100 \]
\[ 0.25x = 22400 \]
\[ x = \frac{22400}{0.25} = 89600 \text{ grams} \]

6. **Final Result**:
- Therefore, the molecular mass of hemoglobin is:
\[ x = 89600 \text{ grams/mol} \text{ or } 8.96 \times 10^4 \text{ grams/mol} \]