Problem 72 - General Chemistry: Principles and Modern Applications

Question

In each case, identify the element in question. (a) The mass number of an atom is 234 and the atom has \(60.0 \%\) more neutrons than protons. (b) An ion with a \(2+\) charge has \(10.0 \%\) more protons than electrons. (c) An ion with a mass number of 110 and a \(2+\) charge has \(25.0 \%\) more neutrons than electrons.

Step-by-Step Solution

Answer

For (a), the atom has \(p\) protons and can be identified using the atomic number. For (b), the ion has \(e\) electrons and can be identified using the number of protons. For (c), the ion has an atomic number equal to the number of protons calculated and can be identified accordingly.

Step 1: Determine the stating equation for (a)

In an atom, the mass number equals to the sum of protons and neutrons. Given in the problem, mass Number is 234 and there are 60 % more neutrons than protons. We can form the equation as follows: \(234 = p + 1.6p\).

Step 2: Solve the equation for (a)

Solving this equation will give the number of protons, p. This can be solved as \(234 = 2.6p\), so \(p = 234 / 2.6\). Calculate to find the number of protons, p.

Step 3: Identify the atom for (a)

The number of protons is the atomic number, which can be used to identify the atom from a periodic table

Step 4: Determine the stating equation for (b)

A 2+ ion means it has 2 more protons than electrons. If there are 10% more protons than electrons, we can form the equation as follows: \(p = e + 2 = 1.1e\).

Step 5: Solve the equation for (b)

Solving this equation will give the number of electrons, e. This can be solved as \(e = 2 / 0.1\). Calculate to find the number of electrons, e.

Step 6: Identify the ion for (b)

The number of protons is the atomic number, which can be used to identify the ion from a periodic table.

Step 7: Determine the stating equation for (c)

In atom, the mass number equals to the sum of protons and neutrons. The 2+ charge means there are 2 more protons than electrons. If there are 25% more neutrons than electrons, we can form the equations as follows: \(110 = p + n\) and \(n = 1.25e\) and \(p = e + 2\)

Step 8: Solve the equations for (c)

First substitute the neutrons in terms of electrons in the mass number equation: \(110 = e + 2 + 1.25e\). Solve for the number of electrons, e. Then, calculate the number of protons and neutrons using the defined relationships.

Step 9: Identify the ion for (c)

The number of protons is the atomic number, which can be used to identify the ion from a periodic table.

Key Concepts

Mass Number

The mass number of an atom is crucial for understanding its structural composition. It represents the sum of the protons and neutrons within an atom's nucleus. So, if an atom has a mass number of 234, this means that the total number of protons and neutrons combined in its nucleus is 234.

This can be expressed as the following equation:

• \[ \text{Mass Number} = \text{Number of Protons} + \text{Number of Neutrons}\]

Whether you're talking about a stable atom or an ion, this formula always applies. However, it's important to remember that a mass number does not offer insight into the element's chemical behavior—it simply helps us quantify its mass.

Mass numbers are not the same as atomic weights found on the periodic table, which consider isotopic distributions. Instead, they are specific to individual atoms or isotopes, which gives them a distinct identity in nuclear chemistry.

Protons

Protons are subatomic particles present in the nucleus of an atom. They carry a positive charge, and the number of protons in an atom defines its atomic number and consequently, the identity of the element. For example, an element with 6 protons is carbon, while one with 7 protons is nitrogen.

The characteristics of protons:

• Protons have a positive charge (+1).
• The number of protons determines the atomic number.
• Protons, along with neutrons, contribute to the mass number of an atom.

The number of protons remains constant in a stable atom. In ions, however, there can be a difference in the balance between protons and electrons because ions result from atoms losing or gaining electrons. For example, if an atom has more protons than electrons, it would be a positively charged ion.

Understanding protons is vital, as they not only define the element itself but also can provide clues to understanding an atom's or ion's charge, mass, and position in the periodic table.

Neutrons

Neutrons are neutral subatomic particles found in the nucleus of an atom. They don't carry any charge, unlike protons and electrons, but they are crucial in the structure and stability of atoms.

• Neutrons have no electrical charge.
• They contribute to the atomic mass but not the atomic number.
• Neutrons help stabilize the nucleus and prevent protons from repelling each other due to their positive charge.

The number of neutrons in an atom can vary even among atoms of the same element, leading to different isotopes of that element. Isotopes are atoms that have the same number of protons but differ in the number of neutrons.

For example, in the problem where the mass number is 234 and there are 60% more neutrons than protons, it shows that neutrons significantly impact atomic mass. In various isotopes, this can lead to alternative physical properties without altering the chemical properties of the element, which is an intriguing characteristic of atomic structure.