Problem 5 - Chemistry and Chemical Reactivity

Question

Give the complete symbol \(\left(_{Z}^{A} \mathrm{X}\right),\) including atomic number and mass number, for each of the following atoms: (a) magnesium with 15 neutrons, (b) titanium with 26 neutrons, and (c) zinc with 32 neutrons.

Step-by-Step Solution

Answer

(a) \(\left(_{12}^{27} \mathrm{Mg}\right)\), (b) \(\left(_{22}^{48} \mathrm{Ti}\right)\), (c) \(\left(_{30}^{62} \mathrm{Zn}\right)\).

Step 1: Understand the Notation

The notation \( \left(_{Z}^{A} \mathrm{X}\right) \) represents an element \( \mathrm{X} \) with atomic number \( Z \) and mass number \( A \). The atomic number \( Z \) is the number of protons, and the mass number \( A \) is the sum of protons and neutrons.

Step 2: Find Atomic Number for Magnesium, Titanium, and Zinc

Use the periodic table to find the atomic numbers: for magnesium (Mg), \( Z = 12 \); for titanium (Ti), \( Z = 22 \); and for zinc (Zn), \( Z = 30 \).

Step 3: Calculate Mass Number for Each Atom

The mass number \( A \) is calculated as the sum of protons (atomic number) and neutrons. - For magnesium, \( A = 12 + 15 = 27 \). - For titanium, \( A = 22 + 26 = 48 \). - For zinc, \( A = 30 + 32 = 62 \).

Step 4: Write the Complete Symbol for Each Element

Now use the calculated mass numbers and known atomic numbers to write the notation for each element: - (a) Magnesium: \( \left( _{12}^{27} \mathrm{Mg}\right) \) - (b) Titanium: \( \left( _{22}^{48} \mathrm{Ti}\right) \) - (c) Zinc: \( \left( _{30}^{62} \mathrm{Zn}\right) \)

Key Concepts

Atomic Number

The atomic number is a fundamental property of an element. It represents the number of protons found in the nucleus of an atom. This number is crucial because it identifies the element. For instance, hydrogen has an atomic number of 1, which means it has one proton in its nucleus.
Every element on the periodic table has a unique atomic number. For magnesium (Mg), the atomic number is 12, indicating it has 12 protons. Similarly, titanium (Ti) has an atomic number of 22, and zinc (Zn) has 30 protons.

• The atomic number dictates the chemical properties of an element.
• It's usually denoted by the symbol 'Z' in isotopic notation.
• Elements are arranged on the periodic table in order of increasing atomic number.

Understanding the atomic number is essential for determining various characteristics of elements, including their position on the periodic table and the configuration of electrons around the nucleus. This intrinsic property helps distinguish one element from another, making it a key concept in chemistry.

Mass Number

Mass number, unlike the atomic number, is not fixed for a given element. It represents the total number of protons and neutrons in an atom’s nucleus. Simply put, it is the sum of the atomic number (protons) and the number of neutrons. For example, the mass number of magnesium with 15 neutrons is 27; given its atomic number of 12, the calculation is straightforward: \( A = Z + ext{neutrons} = 12 + 15 = 27 \).
This means:

• Mass number = Protons + Neutrons
• Denoted by the symbol 'A' in isotopic notation.
• Mass number can differ for isotopes of the same element.

While the atomic number never changes for an element, the mass number can vary, leading to different isotopes. Isotopes have the same number of protons but different numbers of neutrons, which affects the mass number. This variation in mass number is significant in fields like nuclear physics and chemistry, where isotopic composition plays a role in element analysis and reactions.

Periodic Table

The periodic table is a powerful tool in chemistry, organizing all known elements in a tabular format based on their atomic numbers, electron configurations, and recurring chemical properties. Each element in the periodic table is listed with its atomic number and symbol, helping you quickly identify its properties.
Here’s why the periodic table is indispensable:

• It arranges elements in increasing order of atomic number.
• Elements in the same group (vertical columns) often share similar chemical properties.
• It helps predict the properties of unknown or undiscovered elements.
• By its structure, it illustrates trends such as atomic radius, electronegativity, and ionization energy.

For example, finding that magnesium has an atomic number of 12 is straightforward using the periodic table, which allows you to easily deduce that it should have certain properties consistent with Group 2 elements. The beauty of the periodic table lies in its ability to convey numerous characteristics of elements through a simple, organized framework, making it essential for scientific research, education, and practical applications.