Question

Write balanced equations that represent the processes that correspond to the first and second ionization energies for magnesium.

Short answer

The balanced equation for the first ionization energy of magnesium is \( Mg \rightarrow Mg^{+} + e^{-} \) and for the second ionization energy it is \( Mg^{+} \rightarrow Mg^{2+} + e^{-} \).

Step-by-step solution

First Ionization Energy of Magnesium

For the first ionization energy, we start with a neutral magnesium atom 'Mg' and remove one electron 'e−' to form a positive ion 'Mg+'. The balanced equation is: \[ Mg \rightarrow Mg^{+} + e^{-} \]

Second Ionization Energy of Magnesium

For the second ionization energy, we take the cation formed after the first ionization 'Mg+' and remove another electron to form a more positively charged ion 'Mg2+'. The balanced equation is: \[ Mg^{+} \rightarrow Mg^{2+} + e^{-} \]

Key concepts

First Ionization Energy

Understanding the first ionization energy involves knowing how much energy is required to remove the outermost electron from a neutral atom in its gaseous phase. For magnesium, the process can be represented by the equation \[ Mg \rightarrow Mg^{+} + e^{-} \]. The first ionization energy is significant because it provides insights into the reactivity of an element; elements with low ionization energy lose electrons easily and are more reactive.

When teaching about the first ionization energy, it's important to emphasize that it is an indicator of an element's position on the periodic table. Generally, the ionization energy increases across a period and decreases down a group. Magnesium, located in the second group, requires less energy to remove the first electron compared to elements further to the right in the same period.

Second Ionization Energy

The second ionization energy refers to the energy required to remove a second electron after the first has already been removed, forming a doubly positive ion. The equation for magnesium's second ionization can be shown as \[ Mg^{+} \rightarrow Mg^{2+} + e^{-} \]. It's typically higher than the first ionization energy because, after losing one electron, the resulting positively charged ion holds onto the remaining electrons more tightly.

This is a prime example to show students how the positive charge of an ion affects the energy needed to remove an electron. The increasing nuclear charge over the fewer remaining electrons leads to a larger attraction between the nucleus and the electrons, hence more energy is needed to overcome this attraction in the second ionization process.

Balanced Chemical Equations

Both first and second ionization energy processes for magnesium can be expressed through balanced chemical equations. A balanced chemical equation respects the law of conservation of mass, meaning the number of atoms for every element must be equal on both sides of the reaction. For the first ionization, we have \[ Mg \rightarrow Mg^{+} + e^{-} \] and for the second ionization \[ Mg^{+} \rightarrow Mg^{2+} + e^{-} \].

When instructing on balanced equations, ensure students understand that every chemical equation must balance—it's like a mathematical equation but for atoms. The coefficients (numbers before molecules) are used to balance the equation; however, since a single atom of magnesium goes through ionization, coefficients aren't necessary in these simple reactions.

Electron Removal from Atoms

The ionization energy processes are essentially about the electron removal from atoms. When students understand that atoms consist of a nucleus surrounded by electrons, they can appreciate the energy requirement to remove electrons given the attractive force they experience from the positively charged nucleus.

The two equations for magnesium's ionization energies serve as great illustrations of this concept. As electrons are removed, the remaining electrons experience a greater effective nuclear charge, making subsequent removals more energy-intensive. Educators should stress the point that as the positive charge of an ion increases, it becomes more challenging to remove additional electrons due to the stronger electrostatic attraction to the nucleus.