Respuesta :
Answer:
The answer to this question is
The lattice energy of the salt AB is ≅ -2600 kJ/mol rounded to three significant figures
Explanation:
To solve this we list out the known variables and the required unkown, then we look for the appropriate relation between the known and the unknown thus
Lattice energy of KI = -649 kJ/mol
Latice energy of salt AB = unknown
Charge on A²⁺ =+2
Charge on B²⁻ = -2
radius of A²⁺ = radius of K⁺
radius of B²⁻ = radius of I⁻
the Born-Lande equation for lattice energies is as follows
[tex]E=-\frac{N_{A} Mz^{+}z^{-} e^{2} }{4\pi e_{0} r_{0} } (1-\frac{1}{n})[/tex]
[tex]E=-\frac{N_{A} M e^{2} }{4\pi e_{0} } (1-\frac{1}{n})\frac{|z|^{+}|z|^{-}}{r_{0}}[/tex]
Where to the above question, the following terms are important
z+ = positive ion charge
z− = negative ion charge
r₀ → distance between the positive and the negative ions;
Taking all variables of KI and AB as identical we have.
[tex]E=-\frac{N_{A} M e^{2} }{4\pi e_{0} } (1-\frac{1}{n})\frac{|z|^{+}|z|^{-}}{r_{0}}[/tex]
[tex]E=CONSTANT\frac{|z|^{+}|z|^{-}}{r_{0}}[/tex]
Where radius of A²⁺ = radius of K⁺ and
radius of B²⁻ = radius of I⁻ = r₀
we have
[tex]E_{AB} = E_{KI} (|z|^{+} |z|^{-} )[/tex]
As for AB z⁺ = +2 and z⁻ = -2 we have
[tex]E_{AB} = E_{KI} (|+2|^{+} |-2|^{-} ) = 4E_{KI}[/tex]
= 4 ×(-649 kJ/mol) = -2596 kJ/mol
[tex]E_{AB}[/tex] ≅ -2600 kJ/mol rounded to three significant figures
The lattice energy of [tex]AB[/tex][tex]=-2596 \ kJ/mol.[/tex]
[tex]\Delta H_{Lattice}=\frac{C\left ( z^{+} \right )\left ( z^{-} \right )}{R_{o}}[/tex]
where,
c=constant
[tex]( z^{+} \right) )\left, ( z^{-} \right )}[/tex]= Charges on ions.
[tex]{R_{o}}[/tex]= Interionic distance (radius of cation+anion).
From the lattice energy formula, we know that lattice energy is directly proportional to the charge of the ions and inversely proportional to the radius of the ions.
In the given question charge of the ions doubled so lattice energy will be increased four-fold.
The lattice energy of AB[tex]=Lattice \ energy \ of \ kl\times4[/tex]
[tex]=-649\times4[/tex]
The lattice energy of [tex]AB[/tex][tex]=-2596 \ kJ/mol.[/tex]
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