$AB$,$A_2$,and $B_2$ are diatomic molecules. Enthalpies of dissociation of $AB$,$A_2$,and $B_2$ are in the ratio of $1:1:0.5$. Enthalpy of formation of $AB$,$\Delta_f H = -100 \ kJ \ mol^{-1}$. Find the dissociation enthalpy of $A_2$?
Reaction : $\frac{1}{2} A_2 + \frac{1}{2} B_2 \to AB$
Reaction : $\frac{1}{2} A_2 + \frac{1}{2} B_2 \to AB$
(400) Let the dissociation enthalpy (bond energy) of $A_2$ be $X$.
Given the ratio $1:1:0.5$ for $AB:A_2:B_2$,the bond energy of $AB$ is $X$ and the bond energy of $B_2$ is $0.5X$.
The enthalpy of formation reaction is: $\frac{1}{2} A_2 + \frac{1}{2} B_2 \to AB ; \Delta_f H = -100 \ kJ \ mol^{-1}$.
Using the bond energy formula: $\Delta_f H = \Sigma BE_{\text{reactants}} - \Sigma BE_{\text{products}}$.
$-100 = (\frac{1}{2} \times BE_{A_2} + \frac{1}{2} \times BE_{B_2}) - BE_{AB}$.
$-100 = (\frac{1}{2} X + \frac{1}{2} \times 0.5X) - X$.
$-100 = (0.5X + 0.25X) - X$.
$-100 = 0.75X - X$.
$-100 = -0.25X$.
$X = \frac{100}{0.25} = 400 \ kJ \ mol^{-1}$.
Given the ratio $1:1:0.5$ for $AB:A_2:B_2$,the bond energy of $AB$ is $X$ and the bond energy of $B_2$ is $0.5X$.
The enthalpy of formation reaction is: $\frac{1}{2} A_2 + \frac{1}{2} B_2 \to AB ; \Delta_f H = -100 \ kJ \ mol^{-1}$.
Using the bond energy formula: $\Delta_f H = \Sigma BE_{\text{reactants}} - \Sigma BE_{\text{products}}$.
$-100 = (\frac{1}{2} \times BE_{A_2} + \frac{1}{2} \times BE_{B_2}) - BE_{AB}$.
$-100 = (\frac{1}{2} X + \frac{1}{2} \times 0.5X) - X$.
$-100 = (0.5X + 0.25X) - X$.
$-100 = 0.75X - X$.
$-100 = -0.25X$.
$X = \frac{100}{0.25} = 400 \ kJ \ mol^{-1}$.
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