Problem 89 - A Complete Resource Book in Chemistry for JEE Main

Question

Haemoglobin contains \(0.33 \%\) of iron by weight. The molecular weight of haemoglobin is approximately 67200\. The number of iron atom (at. wt of \(\mathrm{Fe}\) is 56 ) present in one molecule of haemoglobin are (a) 1 (b) 6 (c) 4 (d) 2

Step-by-Step Solution

Answer

There are 4 iron atoms in one molecule of haemoglobin.

Step 1: Calculate the weight of iron in one molecule of haemoglobin

Since haemoglobin contains 0.33% iron by weight, we first calculate the total weight of iron in one molecule of haemoglobin. The molecular weight of haemoglobin is given as 67200. Thus, the weight of iron in one molecule is \( 0.33\% \times 67200 = \frac{0.33}{100} \times 67200 = 221.76 \text{ amu} \).

Step 2: Determine the number of iron atoms in one molecule of haemoglobin

The atomic weight of iron (\( \mathrm{Fe} \)) is 56 amu per atom. To find the number of iron atoms, divide the total weight of iron by the weight of a single iron atom: \[\text{Number of iron atoms} = \frac{221.76}{56} = 3.96\]. Since the number of atoms must be an integer, the closest whole number is 4.

Key Concepts

Atomic Structure

Atoms are the fundamental building blocks of matter. Each atom consists of a nucleus, which contains protons and neutrons, and an electron cloud surrounding it. The atomic structure gives rise to an element's unique properties.

- **Protons** are positively charged particles found in the nucleus. They define the element's identity and atomic number. For example, all atoms with 26 protons are iron (Fe). - **Neutrons** carry no charge and add mass to the nucleus. They help to stabilize the nucleus. - **Electrons** are negatively charged particles orbiting the nucleus. They are essential for chemical interactions and determine the atom's size.

The arrangement of these particles in iron atoms is crucial for understanding how iron integrates into molecules like haemoglobin. The atomic weight, often measured in atomic mass units (amu), reflects the total mass of protons and neutrons.

Molecular Weight Calculation

Molecular weight, also known as molecular mass, is the sum of the atomic weights of all atoms in a molecule. This value is crucial when determining the composition of complex molecules like haemoglobin. Let's break it down:

- **Atomic Weights**: The weight of individual atoms measured in amu. For instance, the atomic weight of iron (Fe) is 56 amu. - **Summation**: To find the molecular weight, multiply the atomic weight by its occurrence in the molecule and sum these values for all atoms in the molecule.

In the case of haemoglobin, we start with its overall molecular weight, which is 67,200 amu as provided. We use this figure to calculate the weight contribution of specific atoms or groups of atoms. By understanding how each component contributes to the total molecular weight, we can discern the composition and functionality of the molecule.

Elemental Composition Analysis

Elemental composition analysis helps determine the number and types of atoms present in a molecule. In haemoglobin, knowing its iron content is essential because it determines the number of iron atoms it can hold, impacting its functionality in oxygen transport.

Here's a step-by-step approach:

• **Percentage Composition**: Begin by recognizing that haemoglobin contains 0.33% iron by weight. Calculate the specific weight of iron using this percentage and the total molecular weight.
• **Iron Atom Calculation**: Determine the number of iron atoms by dividing the weight of iron by the atomic weight of iron (56 amu). This tells you how many atoms are present.

Using these calculations, for example, haemoglobin has approximately 221.76 amu of iron. When divided by 56, it suggests about four iron atoms per molecule. Understanding the elemental composition provides insight into the biological roles and interactions of haemoglobin.