a) How much energy does it take to remove an electron from one \(\mathrm{H}\) atom? b) How much total energy would it take to remove the electrons from two H atoms? c) How much total energy would it take to remove the electrons from a mole of \(\mathrm{H}\) atoms? Express this energy in units of \(\mathrm{J}\) and in units of \(\mathrm{MJ} .\)

One of the first concepts we encounter in chemistry is the conversion of energy units. Since energy can be expressed in various scales, comprehending these conversions is crucial for understanding chemical processes.

In the context of ionization energy, we often measure the energy needed to remove an electron in electron volts (eV). However, most chemical reactions are quantified in joules (J), the SI unit of energy. To convert electron volts to joules, we use the relation where 1 eV equals to \(1.6 \times 10^{-19}\) J. By knowing this conversion factor, we can seamlessly transition from the atomic scale of electron movements to the macro scale in which we measure chemical reactions and processes.

Avogadro's number, \(6.022 \times 10^{23}\), signifies the number of units in one mole of any substance. This fundamental constant bridges the gap between the microscopic world, where we speak about individual atoms and molecules, and the macroscopic world that deals with moles, a unit practical for laboratory measurements.

Each mole of a substance contains an Avogadro number of entities, allowing us to calculate the amount of substance required or produced. This number is pivotal when scaling up ionization energy from a single atom, as in the hydrogen atom case, to a mole's worth of atoms, enabling us to work with quantities that are tangible in experimental chemistry.

Electron removal energy, commonly known as ionization energy, is the amount of energy necessary to remove an electron from an atom or molecule. This is a critical concept because it reflects the strength by which an electron is bound to the nucleus.

The first ionization energy is the energy required to remove the outermost, or least bound electron. In hydrogen's case\(-\)the simplest atom with one electron\(-\)the ionization energy is 13.6 eV per atom. As seen in the exercise solution, understanding this energy, and its conversion to usable units such as joules, is essential to comprehend the energetic demands of chemical changes at the atomic level.

Understanding atomic structure is crucial for grasping concepts such as ionization energy. The basic structure of an atom consists of a nucleus, made of protons and neutrons, and an electron cloud, where electrons reside. The energies associated with electrons are quantized, meaning electrons occupy specific energy levels or shells.

In the ionization process in hydrogen, the electron transitions from its ground state to an infinite level, essentially leaving the atom. This requires energy equivalent to the electron's binding energy. The energy levels of electrons define the chemistry of an atom, as they determine how an atom interacts with others and the energies involved in these interactions.