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Hess' Law

The lattice e...

Question

The lattice energy of solid $K C l$ is 181 kcal/mol. The enthalpy of solution of $K C l$ in water is 1 kcal/mol. If the hydration enthalpies of potassium and chloride ions are in the ratio $2 : 1$ , what is the hydration enthalpy (kcal/mol) of potassium ions?

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Solution

$Δ H_{s o l u t i o n} = Δ H_{l a t t i c e} + Δ H_{h y d r a t i o n}$
$1 = 181 + Δ H_{h y d K^{+}} + Δ H_{h y d C l^{-}}$
$- 180 = Δ H_{h y d K^{+}} + \frac{1}{2} Δ H_{h y d K^{+}}$
$- 180 = \frac{3}{2} Δ H_{h y d K^{+}}$
$- 180 \times \frac{2}{3} = Δ H_{h y d K^{+}}$
$Δ H_{h y d K^{+}} = - 120 k c a l / m o l$

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