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Prove alpha=sqrt((K(p)/(P+K(p)))) for ...

Prove `alpha=sqrt((K_(p)/(P+K_(p))))` for
`PCl_(5) hArr PCl_(3)+Cl_(2)`
where `alpha` is the degree of dissociation at temperature when equilibrium constant is `K_(p)`.

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To prove the equation \( \alpha = \sqrt{\frac{K_p}{P + K_p}} \) for the reaction \( \text{PCl}_5 \rightleftharpoons \text{PCl}_3 + \text{Cl}_2 \), where \( \alpha \) is the degree of dissociation and \( K_p \) is the equilibrium constant, we can follow these steps: ### Step 1: Define Initial Conditions At the start of the reaction (time \( t = 0 \)), we assume we have 1 mole of \( \text{PCl}_5 \) and no products. Therefore: - Initial moles of \( \text{PCl}_5 = 1 \) - Initial moles of \( \text{PCl}_3 = 0 \) - Initial moles of \( \text{Cl}_2 = 0 \) ...
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