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The lattice energy of solid NaCl is 180 kcal mol^-1 and enthalpy of solution is 1 kcal mol^-1. If the hydration energies of Na^+ and Cl^- ions are in the ratio 3 : 2, what is the enthalpy of hydration of sodium ion?

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The lattice energy of solid NaCl is 180 kcal mol-1 and enthalpy of solution is 1 kcal mol-1. If the hydration energies of Na+ and Cl- ions are in the ratio 3 : 2, what is the enthalpy of hydration of sodium ion?

(a) -107.4 kcal mol-1

(b) 107.4 kcal mol-1

(c) 71.6 kcal mol-1

(d) -71.6 kcal mol-1

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Correct answer: (a) -107.4 kcal mol-1

Explanation:

ΔHhyd. = ΔHsol. - ΔHlattice

= 1 - 180 = -179 kcal mol-1

Then ΔHhyd.(Na+) + ΔHhyd.(Cl-) = -179

or ΔHhyd.(Na+) + 2/3ΔHhyd. = -179

or ΔHhyd.(Na+) = -107.4 kcal mol-1

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