Problem 85 - Arihant Objective Approach to Organic Chemistry for IIT JEE and NEET all Medical Entrances Part 4

Question

Haemoglobin contains \(0.344 \%\) of iron by weight. If the molecular weight of haemoglobin is approximately 67200 , then the number of iron atoms (at. wt. of Fe is 56) present in one molecule of [P (PMT) 1996] haemoglobin are: (b) 1 (a) 4 (c) 6 (d)' 2

Step-by-Step Solution

Answer

There are 4 iron atoms in one molecule of haemoglobin.

Step 1: Understand the Problem

We are given that haemoglobin contains 0.344% iron by weight, and its molecular weight is approximately 67200. We need to find out how many iron atoms are present in one molecule of haemoglobin.

Step 2: Determine Iron Mass in Haemoglobin

The percentage of iron in haemoglobin is 0.344%, so the mass of iron in a molecule of haemoglobin can be calculated as:\[\text{Mass of iron} = \frac{0.344}{100} \times 67200\]

Step 3: Calculate Iron Mass

Calculate the actual mass of iron using the percentage given:\[\text{Mass of iron} = 0.344 \times 672 = 230.688 \text{ g/mol}\]

Step 4: Calculate the Number of Iron Atoms

Given that the atomic weight of iron (Fe) is 56, we use the mass of iron to find the number of atoms:\[\frac{230.688}{56} \approx 4.12\]

Step 5: Round to Nearest Whole Number

Since the number of atoms must be an integer, round 4.12 to the nearest whole number, which gives us 4. Therefore, there are 4 iron atoms in one molecule of haemoglobin.

Key Concepts

Percentage composition

In the context of chemistry, percentage composition refers to the percentage by mass of each element in a compound. It tells us how much of each element is present in a compound relative to its total mass.
For hemoglobin, which has a molecular mass of 67,200, the percentage composition of iron is provided as 0.344%. This means that out of the entire hemoglobin molecule, 0.344% of its weight is because of iron.

• You can calculate the mass of any constituent in a compound by using its percentage composition.
• The formula used is: \[ \text{Mass of element in compound} = \frac{\text{Percentage of element}}{100} \times \text{Total mass of compound} \]

For hemoglobin, knowing the percentage of iron allows you to determine how much of the total mass is from iron. This step lays the foundation for calculating how many iron atoms are present in each molecule.

Iron atoms count

The task of determining the number of iron atoms in hemoglobin involves two main calculations: determining the total iron mass and using it to find the count of iron atoms.
Firstly, we convert the iron percentage to a tangible mass using the molecule's total weight. For hemoglobin, containing 0.344% iron, we calculated this as roughly 230.688 grams per mole.

• The atomic weight of iron is important here and is given as 56. This weight represents the mass of one mole of iron atoms.
• To estimate the number of iron atoms in a single hemoglobin molecule, use: \[ \text{Number of iron atoms} = \frac{\text{Mass of iron}}{\text{Atomic weight of Fe}} \]

For hemoglobin, dividing the calculated mass of iron by its atomic weight yields approximately 4.12. Rounded to the nearest whole number, you find that there are 4 iron atoms in one molecule of hemoglobin. This rounding reflects the fact that partial atoms cannot be practical for real chemical structures.

Atomic weight

Atomic weight, or atomic mass, is a critical concept in chemistry. It refers to the average mass of atoms of an element, measured in atomic mass units (amu).
For elements, such as iron (Fe), atomic weight gives us an indication of the mass of one mole of its atoms. Iron's atomic weight is 56, which means one mole, or Avogadro's number (6.022 × 10²³), of iron atoms weighs 56 grams.

• This concept allows us to convert between mass and number of atoms or moles.
• With iron in hemoglobin, knowing its atomic weight directly leads to calculating actual numbers of atoms from a given mass.

Therefore, the atomic weight of an element like iron is crucial for determining how many of its atoms are present in mixtures or compounds when you know the mass contribution from that element. This is crucial for understanding the elemental composition of complex molecules like hemoglobin.