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Bond Order and Enthalpy

If the bond d...

Question

If the bond dissociation energies of $X Y, X_{2}$ and $Y_{2}$ (all diatomic molecules) are in the ratio of $1 : 1 : 0.5$ and $Δ H_{f}$ for the formation of $X Y$ is $- 200 k J {m o l}^{- 1}$ , the bond dissociation energy of $X_{2}$ will be:

A

100 k J {m o l}^{- 1}

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B

300 k J {m o l}^{- 1}

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C

200 k J {m o l}^{- 1}

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D

800 k J {m o l}^{- 1}

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Solution

The correct option is D $800 k J {m o l}^{- 1}$
$X_{2} + Y_{2} ⟶ X Y$
$Δ H = {(B E)}_{X - X} + {(B E)}_{Y - Y} - 2 {(B E)}_{X - Y}$
If $B E$ of $(X - Y) = a$
then $B E$ of $(X - X) = a$
and $B E$ of $(Y - Y) = \frac{a}{2}$
$Δ H_{f} = (X - Y) = - 200 k J {m o l}^{- 1}$
$∴ - 400 = a + \frac{a}{2} - 2 a$
$- 400 = - \frac{a}{2}$
or $a = + 800 k J$

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