Use data from Appendix C, Figure 7.9, and Figure 7.11 to calculate the lattice energy of RbCl. Is this value greater than or less than the lattice energy of NaCl? Explain.
The Correct Answer and Explanation is :
To calculate the lattice energy of RbCl (Rubidium Chloride), we need to use the Born-Haber cycle, which is a method of calculating lattice energy based on thermodynamic data. We use data provided from Appendix C, Figure 7.9, and Figure 7.11 for these calculations.
Steps for Calculating the Lattice Energy:
- Sublimation Energy:
The energy required to convert solid Rb to gaseous Rb atoms is the sublimation enthalpy. From Figure 7.9, we find the sublimation energy for Rb. - Ionization Energy:
The ionization energy is the energy required to remove an electron from a gaseous Rb atom to form Rb⁺. This value is found from Figure 7.9 for Rb. - Bond Dissociation Energy:
This is the energy needed to break the Cl₂ molecule into two Cl atoms. This data can be found in Figure 7.11 for chlorine. - Electron Affinity:
The energy released when a chlorine atom gains an electron to form Cl⁻. From Figure 7.9, we use the electron affinity of chlorine. - Lattice Energy Calculation:
Finally, the lattice energy of RbCl is calculated using the Born-Haber cycle. The lattice energy is the energy released when Rb⁺ and Cl⁻ ions combine to form solid RbCl, and it is calculated as: [
\text{Lattice Energy} = \text{Sublimation Energy} + \text{Ionization Energy} + \text{Bond Dissociation Energy} – \text{Electron Affinity}
] After gathering the values for Rb and Cl from the given charts, we substitute them into the formula to calculate the lattice energy of RbCl.
Comparison to NaCl:
The lattice energy of RbCl is generally less than that of NaCl. This is due to the larger ionic radius of Rb⁺ compared to Na⁺. As the size of the cation increases, the lattice energy decreases because the electrostatic attraction between the ions becomes weaker. Rb⁺ is larger than Na⁺, and the distance between the ions in the lattice is greater, leading to a lower lattice energy for RbCl compared to NaCl.
In conclusion, the lattice energy of RbCl is lower than that of NaCl because the ionic bond in RbCl is weaker due to the larger ionic size of rubidium. This results in a lower lattice energy.
If you need the calculations or a diagram based on these figures, feel free to provide more details!