Question

Determine the only possible \(2+\) ion for which the following two conditions are both satisfied: \(\bullet\) The net ionic charge is one-tenth the nuclear charge. \(\bullet\) The number of neutrons is four more than the number of electrons.

Short answer

The only possible \(2+\) ion for which both conditions are satisfied is an atomic ion with 20 protons (nuclear charge), 18 electrons, and 22 neutrons. This corresponds to the isotope of Calcium, represented as \(^{42}Ca^{2+}\).

Step-by-step solution

Interpret the conditions into equations

The conditions given can be expressed as follows: 1. The net ionic charge is one-tenth the nuclear charge. The net ionic charge (nuclear charge - number of electrons) is \(2+\), and the nuclear charge is the number of protons (let's denote this as \(p\)). Therefore, this condition can be written as \(2 = p/10\). 2. The number of neutrons is four more than the number of electrons. Let's denote the number of neutrons as \(n\) and the number of electrons as \(e\). This can be written as \(n = e + 4\).

Solve the first equation

Solving the first equation \(2 = p/10\) for \(p\), we find that \(p = 20\). So, the ion has 20 protons.

Determine the number of electrons

Knowing that it's a \(2+\) ion, it means that the ion has lost 2 electrons. So, the number of electrons (\(e\)) would be 20 (the number of protons) - 2 (due to the \(2+\) charge), which gives us 18 electrons.

Solve the second equation

Now, substituting the number of electrons into the second equation \(n = e + 4\), we get \(n = 18 + 4 = 22\). So, the ion has 22 neutrons.

Key concepts

Ionic Charge Calculation

Calculating ionic charge is a vital part of understanding how ions form and interact in chemistry. An ion's charge is determined by the difference between the number of protons and electrons in an atom.
For instance, an atom that has more protons than electrons is positively charged, known as a cation, while an atom with more electrons is negatively charged, known as an anion.

To find the ionic charge, you need to subtract the number of electrons from the number of protons:

• Net Ionic Charge = Number of Protons - Number of Electrons

In our exercise, we are figuring out a specific ion with a charge that's clearly defined as 2+. This means the ion has lost two electrons, giving it a positive charge.
To start, interpret the statement "The net ionic charge is one-tenth the nuclear charge" using the given conditions. If we let the nuclear charge (i.e., number of protons) be represented as variable \( p \), then:

• \( 2 = \frac{p}{10} \)

Solving this equation for \( p \) helps us conclude that the number of protons, hence the nuclear charge, is 20. This helps establish the ionic structure of the element.

Nuclear Charge

Nuclear charge is fundamentally the same as the number of protons in an atom's nucleus. It is an important concept because it affects how strongly the protons can attract electrons. The higher the nuclear charge, the stronger the pull on the electrons.

Having a clear understanding of nuclear charge aids in solving problems related to ion formation and behavior. In our problem, determining that the nuclear charge is 20 tells us that the element we're dealing with is Calcium (Ca), since Calcium has 20 protons.

The nuclear charge also affects the ion's chemical properties. As a rule of thumb, knowing the atomic number or nuclear charge helps in:

• Identifying the element.
• Predicting reactivity and potential ionization states.

In Calcium's case, losing or gaining electrons leads to common ionic states, such as a 2+ charge when it loses two electrons, mirroring an important aspect of the exercise.

Neutron and Electron Relationship

Understanding the relationship between neutrons and electrons can help you predict the overall atomic structure and properties of an atom. Neutrons are neutral particles located in the nucleus, while electrons orbit around and contribute to the ion's charge.

In the given exercise, the relationship is specifically stated: "The number of neutrons is four more than the number of electrons." This provides a critical connection between the atomic nucleus and its electronic structure.
To find out the number of neutrons, utilize the equation provided in the exercise:

• \( n = e + 4 \)

Substituting the known electron count of 18 into the equation, gives us \( n = 18 + 4 = 22 \). This means the ion has 22 neutrons, a typical value for some isotopes of Calcium.
This neutron to electron relationship not only ties into the atom's mass but also influences its isotopic characteristics, which can have implications on its stability and behavior in reactions.