Question

Consider the following gas phase dissociation, PCl$_5$(g) $\rightleftharpoons$ PCl$_3$(g) + Cl$_2$(g) with equilibrium constant K$_p$ at a particular temperature and at pressure P. The degree of dissociation ($\alpha$) for PCl$_5$(g) is
PCl$_5$(g) $\rightleftharpoons$ PCl$_3$(g) + Cl$_2$(g)

• A. $\alpha = \left(\frac{K_p}{K_p+P}\right)^{1/3}$
• B. $\alpha = \left(\frac{K_p}{K_p+P}\right)$
• C. $\alpha = \left(\frac{K_p}{K_p+P}\right)^{1/2}$
• D. $\alpha = \left(\frac{K_p}{K_p+P}\right)^{2}$

Hint:

Using a simple frame or just bolding for the box
Key Points:
Use an ICE table with the degree of dissociation ($\alpha$).
Calculate total moles at equilibrium to find mole fractions.
Partial pressure = Mole Fraction $\times$ Total Pressure (P).
Write the K$_p$ expression in terms of partial pressures.
Substitute and solve for $\alpha$.
Remember the difference of squares: $(1+\alpha)(1-\alpha) = 1-\alpha^2$.