For isotopes of a given chemical element, which statement about their chemical properties is most appropriate, considering that they have the same atomic number but different mass numbers?

Introduction / Context:
Isotopes are atoms of the same element that have the same atomic number but different mass numbers due to different numbers of neutrons. This concept is important in both physics and chemistry. The key question for chemists is whether isotopes of an element behave the same way in chemical reactions. This question asks which statement best describes the chemical properties of isotopes of a given element.

Given Data / Assumptions:

• Isotopes have the same atomic number, so they have the same number of protons.
• They differ only in the number of neutrons and therefore in mass number.
• Chemical properties depend mainly on electronic configuration and valence electrons.
• Nuclear properties such as stability may differ, but electronic arrangements remain identical for isotopes of the same element.

Concept / Approach:
Chemical properties of an element are determined primarily by the arrangement of electrons around the nucleus, especially the number of valence electrons. Isotopes of an element have the same number of protons and electrons, so their electron configurations are identical. Since the electrons are responsible for chemical bonding, isotopes show almost identical chemical behaviour. Differences in mass can lead to small kinetic isotope effects, but at school level and for most reactions, isotopes are considered to have the same chemical properties.

Step-by-Step Solution:

Verification / Alternative check:
Consider examples such as hydrogen isotopes: protium, deuterium and tritium. All have one proton and one electron, so they form similar compounds like H2, D2, and T2 and can form water, heavy water, and tritiated water. Their chemical reactions are very similar, though reaction rates may differ slightly due to mass differences. Similarly, isotopes of chlorine, such as chlorine 35 and chlorine 37, have the same valence electrons and show identical chemistry, forming the same compounds like sodium chloride. This consistent behaviour in many examples verifies that isotopes have the same chemical properties.

Why Other Options Are Wrong:

• Their chemical properties must be different: This contradicts the fact that chemical properties depend on electrons, which are the same for isotopes of one element.
• Their chemical properties need not be the same and may vary widely: Variations are minor and kinetic in nature, not fundamental differences in chemical identity.
• Their chemical properties need not be different in any case: This wording is confusing and does not clearly state the equality of properties.
• Their chemical properties are always unpredictable: This is incorrect; isotopic chemistry is well understood and predictable.

Common Pitfalls:
Students sometimes focus on the word different in the definition of isotopes and assume that different mass numbers must mean different chemistry. Others may confuse nuclear properties, such as radioactivity, with chemical behaviour. It is important to keep in mind that while isotopes can have different nuclear stability and applications in nuclear medicine or dating, their chemical bonding patterns remain the same because they have the same electronic structure.

Final Answer:
For isotopes of a given element, their chemical properties must be the same because they have identical electronic configurations.