A mixture contains atoms of fluorine and chlorine. The removal of an electron from each atom of sample absorbs \(284 \mathrm{~kJ}\) while the addition of an electron to each atom of mixture releases \(68.8 \mathrm{~kJ}\). Determine the percentage composition of mixture. Given \(\mathrm{IE}_{1}\) for \(\mathrm{F}\) and \(\mathrm{Cl}\) are \(27.91 \times 10^{-22}\) and \(20.77 \times 10^{-22} \mathrm{~kJ} /\) atom respectively and \(\mathrm{EA}_{1}\) for \(\mathrm{F}\) and \(\mathrm{Cl}\) are \(-5.53 \times 10^{-22}\) and \(-5.78 \times 10^{-22} \mathrm{~kJ} /\) atom respectively.

Ionization energy (IE) is the energy required to remove an electron from an isolated atom or ion. The greater the ionization energy, the more difficult it is to remove an electron, which indicates a stronger attraction between the negatively charged electrons and the positively charged nucleus. To understand this concept in the context of our exercise, we consider fluorine (F) and chlorine (Cl). Both elements require energy to remove an electron, with F having a higher IE (27.91x10^-22 kJ/atom) compared to Cl (20.77x10^-22 kJ/atom). This difference reflects the tighter hold F's nucleus has on its electrons due to its higher electronegativity.

In a chemical mixture analysis using ionization energies, knowing the individual IEs helps us determine how much energy is needed overall to ionize atoms in a sample, as showcased in our step-by-step solution. When we calculate the total energy needed for electron removal from each atom in the mixture, the IEs of both elements directly influence the final percentage composition of the mixture.

Electron affinity (EA) measures the energy change when an electron is added to a neutral atom. Unlike ionization energy, which is always a positive value as it requires energy input, electron affinity can be positive or negative. A negative electron affinity indicates the process is exothermic, releasing energy as the atom gains an electron. This is typical for nonmetals, which have a tendency to gain electrons and complete their valence shells.

In our exercise, F's EA is -5.53x10^-22 kJ/atom, and Cl's EA is -5.78x10^-22 kJ/atom, showing that both elements release energy when they capture an electron. However, Cl releases slightly more energy, pointed out as a difference in how favorably the two elements acquire electrons. Incorporating electron affinity into our chemical mixture analysis provides us with a complete picture of energy interactions during electron gains and losses, allowing for a precise calculation of percentage composition in the sample.

Chemical mixture analysis is a critical tool in chemistry that enables us to determine the composition of a multi-component sample. It often involves using known properties, such as ionization energy and electron affinity, to establish mathematical relationships and calculate the amount of each component in a mixture.

In the given exercise, we utilize the values of IEs and EAs, alongside the total energy changes for electron removal and addition, to derive equations representing the sample's behavior. Once we establish equations for the energy changes due to ionization and electron affinity, we combine them with the known energy values provided (284 kJ for ionization and 68.8 kJ for electron attachment to the mixture).

After setting up these equations, our next step is to link the atomic counts of F and Cl with their percentage presence in the sample, leading to a system of equations that, when solved, reveals the ratio of the two elements within the mixture. This systematic approach to analyzing chemical mixtures is invaluable for researchers and students alike when interpreting experimental data or solving textbook problems.