The lattice enthalpies of NACL KCL and AGCL are 787,717 and 916 kj/mol; based on these values , arrange them in increasing order of water solubility and explain the answer.
Based on these data I would go with AgCl(least soluble), NaCl, KCl(most soluble) with the idea being it takes less energy to break the crystal bonds for KCl and most to break the crystal bonds for AgCl. I think the actual solubilities are NaCl most and AgCl least.
To arrange the given ionic compounds (NaCl, KCl, and AgCl) in increasing order of water solubility based on lattice enthalpies, we need to understand the relationship between lattice enthalpy and solubility.
Lattice enthalpy is a measure of the energy released when oppositely charged ions in a solid ionic lattice arrange themselves to form a crystal lattice structure. The higher the lattice enthalpy value, the stronger the ionic bond and the more energy required to break the lattice and dissolve the compound in water.
In general, the solubility of ionic compounds in water depends on two factors: lattice enthalpy and hydration enthalpy. Lattice enthalpy tends to decrease as the size of the ions increase, while hydration enthalpy tends to increase as the size of the ions increase.
To compare the water solubility of NaCl, KCl, and AgCl, we need to consider both the lattice enthalpy and the relative sizes of the ions:
1. NaCl (lattice enthalpy: 787 kJ/mol): Sodium chloride has smaller ions compared to the other two compounds. This means that the lattice enthalpy is relatively high due to the stronger electrostatic forces between the smaller ions, resulting in a higher energy requirement for dissolution. However, the relatively smaller size of the ions enables them to form stronger hydration shells, which helps in the dissolution process. Overall, due to a combination of moderate lattice enthalpy and strong hydration enthalpy, NaCl has greater water solubility compared to the other two compounds.
2. KCl (lattice enthalpy: 717 kJ/mol): Potassium chloride has larger ions compared to sodium chloride but smaller ions compared to silver chloride. The larger size of the ions reduces the strength of the electrostatic forces, resulting in a lower lattice enthalpy compared to NaCl. However, the ions are still small enough to form relatively strong hydration shells. Thus, KCl has higher water solubility than AgCl but lower water solubility compared to NaCl.
3. AgCl (lattice enthalpy: 916 kJ/mol): Silver chloride has the largest ions among the three compounds. The larger size of the ions weakens the electrostatic forces, resulting in a lower lattice enthalpy. While the weak lattice enthalpy facilitates dissolution, the larger size of the ions hinders strong hydration shells. As a result, AgCl has the lowest water solubility among the three compounds.
Therefore, arranging the compounds in increasing order of water solubility based on lattice enthalpies, we have: AgCl < KCl < NaCl.