Problem 46 - A Complete Resource Book in Chemistry for JEE Main

Question

The samples of \(\mathrm{NaCl}\) are produced when Na combines separately with two isotopes of chlorine \(\mathrm{Cl}^{35}\) and \(\mathrm{Cl}^{57}\). Which law is illustrated? (a) Law of constant volume (b) Law of multiple proportions (c) Law of reciprocal proportions (d) None of these

Step-by-Step Solution

Answer

The illustrated law is not listed; therefore, the answer is (d) None of these.

Step 1: Understanding the Isotopes

In this problem, sodium (Na) is combining with two different isotopes of chlorine, namely \( \mathrm{Cl}^{35} \) and \( \mathrm{Cl}^{37} \). The role of isotopes here indicates that the sodium chloride (NaCl) formed will differ only in the mass of the chlorine atoms, not in their chemical proportions.

Step 2: Analyzing the Law of Constant Composition

The Law of Constant Composition, also known as the Law of Definite Proportions, states that a chemical compound always contains exactly the same proportion of elements by mass. Sodium chloride always has sodium and chlorine in a specific ratio by mass, regardless of the isotopes involved.

Step 3: Comparing the Laws and Isotopes

The options are about different laws. The law relevant to compounds having consistent element ratios (as defined by mass ratios) regardless of isotopic differences is the Law of Constant Composition. This law indicates that sodium chloride, whether formed with \( \mathrm{Cl}^{35} \) or \( \mathrm{Cl}^{37} \), maintains its chemical proportions by mass.

Step 4: Defining the Illustrated Law

While the Law of Constant Composition fits the situation due to the constant ratio of sodium to chlorine by mass, it's not explicitly listed in the options. Thus, the closest concept involving consistent ratios despite isotopic differences is not given, leading to the answer: (d) None of these.

Key Concepts

Chemical Isotopes

Isotopes are atoms of the same element that have the same number of protons but a different number of neutrons. This difference in neutrons causes isotopes to have different atomic masses, but their chemical properties remain largely the same. For example, chlorine has common isotopes such as \( \mathrm{Cl}^{35} \) and \( \mathrm{Cl}^{37} \), each having different masses due to differences in the neutron count, while the number of protons remains 17 for both.
Isotopes play a significant role in understanding chemical reactions and compounds. Despite different masses, isotopes tend to behave similarly in chemical reactions because chemical reactions are primarily concerned with electron interactions, and these remain unchanged between isotopes of the same element.

• Chlorine-35 has 18 neutrons (mass number 35 - proton number 17).
• Chlorine-37 has 20 neutrons (mass number 37 - proton number 17).

In the context of forming compounds like sodium chloride (NaCl), isotopic variation results only in mass differences in the compound. Chemical proportions remain constant, illustrating how isotopes do not affect chemical consistency, adhering to the Law of Definite Proportions.

Mass Ratio

Mass ratio in chemistry refers to the proportion of masses of elements in a compound based on their chemical formula. This concept is integral to the Law of Definite Proportions, which states that a given chemical compound will always consist of the same elements in the same proportion by mass.
For example, in sodium chloride (\( \mathrm{NaCl} \)), sodium and chlorine combine in a fixed mass ratio, which remains constant regardless of the chlorine isotope used. Regardless of whether \( \mathrm{Cl}^{35} \) or \( \mathrm{Cl}^{37} \) combines with sodium, the mass ratio of Na to Cl remains consistent because the number of atoms involved does not change.

• Sodium (Na) has an atomic mass of about 23 u.
• Chlorine (Cl) has atomic masses of about 35 u and 37 u, depending on the isotope.
• The mass ratio of Na to Cl in NaCl is calculated by dividing the mass of sodium by the mass of chlorine.

This ensures that the compound's overall mass is proportionate to its formula, demonstrating why even isotopes do not alter elemental proportions.

Atomic Structure

At the core of understanding chemical isotopes and mass ratio lies the atomic structure, which reveals why isotopes exist and how chemical properties remain unchanged despite isotopic variation.
Each atom consists of protons, neutrons, and electrons. The number of protons determine the chemical element, and for chlorine, this number is 17. Electrons, which equal the number of protons in a neutral atom, define the atom's charge. Neutrons add mass but do not affect the chemical behavior, allowing isotopes to exist.

• Protons have a positive charge.
• Neutrons are neutral with no charge.
• Electrons have a negative charge.

The atomic structure accounts for why the Law of Definite Proportions holds true, even with different isotopes. The chemical compound remains chemically stable and proportionate because atomic properties that define chemical reactions are not altered by the number of neutrons in isotopes. Understanding the atomic structure thereby provides clarity on why isotopic variation results in mass differences rather than chemical disparity.