Problem 8 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

The most abundant elements by mass in the body of a healthy human adult are : [Main 2017] Oxygen \((61.4 \%) ;\) Carbon \((22.9 \%)\), Hydrogen \((10.0 \%) ;\) and Nitrogen ( \(2.6 \%\) ). The weight which a \(75 \mathrm{~kg}\) person would gain if all \({ }^{1} \mathrm{H}\) atoms are replaced by \({ }^{2} \mathrm{H}\) atoms is (a) \(15 \mathrm{~kg}\) (b) \(37.5 \mathrm{~kg}\) (c) \(7.5 \mathrm{~kg}\) (d) \(10 \mathrm{~kg}\)

Step-by-Step Solution

Answer

The weight gain would be 7.5 kg, option (c).

Step 1: Calculate the mass of hydrogen in the body

The percentage of hydrogen by mass in a human body is given as 10.0% and the total mass of the person is 75 kg. To find the mass of hydrogen: \[\text{Mass of hydrogen} = 0.10 \times 75 \text{ kg} = 7.5 \text{ kg}\]

Step 2: Determine the increase in mass when replacing \( ^{1} \mathrm{H} \) with \( ^{2} \mathrm{H} \)

The mass of an atom of \( ^{1} \mathrm{H} \) is 1 amu, while \( ^{2} \mathrm{H} \), also known as deuterium, is 2 amu. Replacing hydrogen with deuterium doubles the mass of the hydrogen portion:\[\text{Weight Gain} = 7.5 \text{ kg} \times \left(\frac{2 \text{ amu}}{1 \text{ amu}} - 1\right) = 7.5 \text{ kg}\]This represents the gain in mass.

Step 3: Verify and conclude

The total weight gained by replacing all \( ^{1} \mathrm{H} \) atoms with \( ^{2} \mathrm{H} \) is 7.5 kg. Comparing with the given options, the correct answer is option (c) 7.5 kg.

Key Concepts

Understanding Deuterium

Deuterium is an isotope of hydrogen, often represented by the symbol \(^2\mathrm{H}\) or simply D. Isotopes are variants of a particular chemical element that differ in neutron number. While all isotopes of an element have the same number of protons, deuterium contains one neutron, in contrast to the common hydrogen isotope, \(^1\mathrm{H}\), also known as protium, which has none.

This neutron addition doubles the atomic mass of deuterium compared to protium, giving \(^2\mathrm{H}\) an atomic mass of approximately 2 amu, whereas \(^1\mathrm{H}\) has an atomic mass of about 1 amu. Despite this extra neutron increase, deuterium is chemically similar to regular hydrogen and behaves in almost the same way in chemical reactions.

In nature, deuterium is relatively rare, comprising only about 0.015% of all hydrogen found on Earth. It occurs naturally in water, often termed "heavy water," where deuterium replaces one of the hydrogen atoms in the water molecule.

Role of Atomic Mass in Calculations

Atomic mass, often expressed in atomic mass units (amu), is a crucial concept when dealing with isotopes like deuterium. Each element has characteristic isotopes, and these isotopes have different atomic masses depending on the number of neutrons they contain. The standard atomic mass listed on the periodic table usually reflects a weighted average that considers the abundance of each isotope in a natural sample of the element.

When calculating the effects of isotopic substitutions, such as replacing \(^1\mathrm{H}\) with \(^2\mathrm{H}\), it's essential to understand that the atomic mass directly influences these outcomes. For example, if an element, like hydrogen, doubles in atomic mass because of isotopic substitution, the relative change in mass can be drastic, as demonstrated when protium in a person is entirely replaced with deuterium. The increased mass, influenced by atomic mass, affects the overall weight calculations for chemical and biological systems.

Human Body Composition and Element Abundance

The human body is primarily composed of only a few key elements, with oxygen, carbon, hydrogen, and nitrogen being the most abundant. Oxygen makes up about 61.4% of the body's mass, largely due to its presence in water and organic compounds. Carbon, making up approximately 22.9%, forms the backbone of all organic molecules, including proteins, lipids, and carbohydrates.

Hydrogen is another critical element, accounting for around 10.0% of body mass. Despite its smaller proportion by mass, hydrogen atoms are abundant in number due to their low atomic mass. Nitrogen, comprising 2.6% of body mass, is a key component of amino acids and nucleic acids.

When considering isotopic substitution, such as with hydrogen in the human body, the percentage composition can lead to significant changes in overall mass. Replacing all \(^1\mathrm{H}\) (the most prevalent hydrogen) with \(^2\mathrm{H}\) results in a noticeable weight increase, illustrating the remarkable influence that atomic properties and isotopic variations have on biological entities.