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Factors Affecting Alpha

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Question

The lattice energy of solid $N a C l$ is $180 k c a l m o l^{- 1}$ . The dissolution of the solid in water in the form of ions is endothermic to the extent of 1 $k c a l m o l$ $^{- 1}$ . If the hydration energies of $N a^{+}$ and $C l^{-}$ are in the ratio 6:5, then the enthalpy of hydration of $N a^{+}$ ion is:

A

- 85.6 k c a l m o l^{- 1}

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B

- 97.5 k c a l m o l^{- 1}

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C

- 182.6 k c a l m o l^{- 1}

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D

+ 100 k c a l m o l^{- 1}

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Solution

The correct option is B $- 97.5 k c a l m o l^{- 1}$
$Δ H_{s o l u t i o n} = Δ H_{l a t t i c e} + Δ H_{h y d r a t i o n}$
$∴ 1 k c a l = 180 + Δ H_{h y d r a t i o n}$
$Δ H_{h y d r a t i o n} = - 179$
$Δ H_{(N a^{+} h y d r a t i o n)} + Δ H_{(C l^{-} h y d r a t i o n)} = - 179$
$Δ H_{(N a^{+})} + \frac{5}{6} Δ H_{(N a^{+})} = - 179$
$Δ H_{(N a^{+} h y d r a t i o n)} \approx - 97.5 k c a l$

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