The potential energy at which neutralization occurs for atoms X and Y in a diatomic salt corresponds to the ions X⁺ and Y^- being 0.7 nm apart. What is the value, in kJ/mol, of the change in internal energy required for this to occur?

Question

Quizplus · Accepted Answer

The change in internal energy for the neutralization process can be calculated using Coulomb's law for the potential energy between two charges, which is given by the equation $U = \frac{k \cdot q_1 \cdot q_2}{r}$, where $k$ is Coulomb's constant ($8.99 \times 10^9 \, \text{Nm}^2/\text{C}^2$), $q_1$ and $q_2$ are the charges of the ions (in coulombs), and $r$ is the distance between the centers of the ions (in meters). For ions in a salt, $q_1 = +e$ and $q_2 = -e$, where $e$ is the elementary charge ($1.602 \times 10^{-19} \, \text{C}$). The distance $r$ is given as 0.7 nm, which is $0.7 \times 10^{-9}$ meters.Substituting these values into the equation gives:$$U = \frac{(8.99 \times 10^9) \cdot (1.602 \times 10^{-19})^2}{0.7 \times 10^{-9}}$$Calculating this gives a value in joules. To convert to kJ/mol, we multiply by Avogadro's number ($6.022 \times 10^{23} \, \text{mol}^{-1}$) and divide by $1000$:$$U = \frac{(8.99 \times 10^9) \cdot (1.602 \times 10^{-19})^2}{0.7 \times 10^{-9}} \cdot 6.022 \times 10^{23} / 1000$$This calculation yields a value close to 198 kJ/mol, making option B the correct answer.

The Potential Energy at Which Neutralization Occurs for Atoms X