When \(\mathrm{BF}_{3}\) is bombarded with neutrons, the boron undergoes an \(\alpha\) decay, but the F is unaffected. \(\mathrm{A} 0.20\) -mol sample of \(\mathrm{BF}_{3}\) contained in a \(3.0-\mathrm{L}\) container at 298 \(\mathrm{K}\) is bombarded with neutrons until half of the \(\mathrm{BF}_{3}\) has reacted. What is the pressure in the container at 298 \(\mathrm{K} ?\)

Nuclear chemistry is the subfield of chemistry dealing with radioactivity, nuclear processes, and transformations in the nuclei of atoms. One key process in nuclear chemistry is alpha decay, which is a type of radioactive decay where an unstable atom emits an alpha particle - consisting of two protons and two neutrons (equivalent to a helium-4 nucleus) - to form a new, more stable nucleus.

For example, when Boron (\textbf{B}) in boron trifluoride (\textbf{BF}\(_3\)) undergoes alpha decay, it emits an alpha particle and transforms into a lighter element. This process is critical in nuclear chemistry because it changes the element's identity as well as its chemical properties. Unlike chemical reactions that involve the electrons outside of the nucleus, nuclear reactions involve changes in the nucleus and can lead to a change in one element into another.

Chemical reactions involve the rearrangement of atoms to form new substances, and these reactions abide by the laws of conservation of mass and energy. In contrast to nuclear reactions, chemical reactions do not change the nuclei of atoms but rather involve the breaking and forming of chemical bonds.

In the case of \textbf{BF}\(_3\) being bombarded with neutrons, the boron is affected at the nuclear level (alpha decay), however, the fluorine atoms remain chemically unchanged. The resulting products post-decay are therefore significantly different from the reactants as from a nuclear perspective, but chemically, especially for the fluorine atoms, there might be no visible change. This highlights the difference between nuclear transformations and chemical reactions, where the former can lead to the creation of new elements, and the latter deals with the reorganization of existing atoms.

The \textbf{Ideal Gas Law}, represented by the equation \textbf{PV = nRT}, relates the pressure (\textbf{P}), volume (\textbf{V}), number of moles (\textbf{n}), ideal gas constant (\textbf{R}), and temperature (\textbf{T}) of an ideal gas. In solving our example problem, the alpha particles released during decay are considered to behave like an ideal gas, which allows us to use this law to calculate the final pressure in the container.

An ideal gas is a hypothetical gas composed of non-interacting point particles that undergo elastic collisions with each other and the walls of their container. These assumptions simplify the mathematical treatment of gases and allow us to predict their behavior under various conditions with reasonable accuracy.

Applying the Ideal Gas Law

During the alpha decay reaction in the \textbf{BF}\(_3\) exercise, the number of gas moles increases due to the production of alpha particles. By using the Ideal Gas Law, we determined the new pressure in the container by considering the change in the total number of moles.

Understanding how to manipulate and apply this equation is vital for students in chemistry because it is widely applicable to various scenarios involving gases, including reactions that release gases, such as the alpha decay of boron in \textbf{BF}\(_3\).