Equilibrium constant for the thermal dissociation of phosphorus pentachloride [closed]








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> 
> Thermal decomposition of $\ce{PCl5}$ is studied in a closed vessel. Partial pressure of $\ce{PCl5}$ in gaseous equilibrium mixture is $\pu{1 atm}.$ $\pu{50 \%}$ $\ce{PCl5}$ dissociates. Find equilibrium constant.
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I am aware of the formula of equilibrium constant, but I am finding difficult determining concentration of reactants and products from partial pressure and $\pu{50 \%}$ dissociation. 


I know the formula


$$K\_c = \frac{[\ce{PCl3}][\ce{Cl2}]}{[\ce{PCl5}]},$$


but how to calculate the concentration?




Note the equation as follows: $$\ce{PCl5 <=> Cl2 + PCl3}$$


You may begin with an ICE table showing the initial and final pressures of the gases.
$$\begin{array}{|c|c|c|} \hline
 & \ce{PCl5} & \ce{PCl3} &\ce{Cl2} \\ \hline
\text{Initial} & 2 & 0&0 \\ \hline
\text{Change} & -1 & +1 & +1 \\\hline
\text{Equilibrium} & 1 & 1 &1 \\ \hline
\end{array}$$
Then it is a simple matter to find $K\_p$ with the equation $$K\_p = \frac{[\ce{P\_{PCl\_3}}][\ce{P\_{Cl\_2}}]}{[\ce{P\_{PCl\_5}}]}$$


If you would like $K\_c$ you would need the ideal gas law ($PV=nRT$) but I doubt that is what your question requires.


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