Question

ionic crystals find use in the frequency manipulation of laser light. one specific example is doubling the frequency of light (halving the wavelength), by combining two laser light photons into one of double the energy. this is the way that green laser light is usually made from an infrared laser. this frequency doubling can be performed using the ionic crystal potassium dihydrogen phosphate (kdp), the lewis structure is shown in the image, it consists of a potassium cation and a polyanion (an anion where the negative charge is spread over more than one atom). one problem with kdp is that it is quite water soluble, and has to be used in a chamber that protects it from atmospheric water vapor. in principle, the potassium ion could be replaced with either a lithium ion (li+), a sodium ion (na+) or a rubidium ion (rb+). which of these replacement cations would be best to reduce water solubility? assume that ionic solids with larger lattice energies, meaning the strongest ionic bonding, are less water soluble, and take guidance from coulombs law to predict which cation will lead to a salt with the highest lattice energy/strongest ionic bonding.
lithium ion
sodium ion
rubidium
dont test me yet, i am trying to gain an understanding before attempting to answer this question.

Explanation:

Step1: Recall Coulomb's law for ionic - bonding

Coulomb's law states that the force of attraction \(F\) between two charged particles is \(F = k\frac{q_1q_2}{r^2}\), where \(k\) is a constant, \(q_1\) and \(q_2\) are the charges of the two particles, and \(r\) is the distance between them. In ionic crystals, the lattice energy is related to this force of attraction between cations and anions.

Step2: Analyze ion - size effect on lattice energy

Smaller cations lead to stronger ionic bonding and higher lattice energy. Among lithium ion (\(Li^+\)), sodium ion (\(Na^+\)), and rubidium ion (\(Rb^+\)), the ionic radius increases in the order \(Li^+

Step3: Determine the ion for highest lattice energy

Since lithium ion (\(Li^+\)) has the smallest ionic radius among the given options, it will lead to the strongest ionic bonding and the highest lattice energy when replacing the potassium ion in the ionic crystal.

Answer:

Lithium ion