how is equilibrium constant (Kc) calculated? (given initial number of moles, volume and number of moles at equilibrium)

Question

anonymous · Answer

For a reaction, aA + bB --> cC + dD, the equilibrium constant is expressed as follow
$$K= (C ^{c}\times D ^{d})\div(A ^{a}\times B ^{b})$$ where little the concentration of A,B,C and D are concentration at equilibrium. Solids and pure liquids are not taken into account.
Example for  2C(s) + 2H2O(g) --> 2CO(g) + 2H2(g)  (I placed coefficient in front to show) but reaction is really C(s) + H2O(g) --> CO(g) + H2(g)
Equilibrium constant is  $$K= ([CO] ^{2}\times  [H2]^{2})\div([H2O]^{2})$$

anonymous · Answer

Q: consider the following reaction:
$$PCl _{5}(g) \leftarrow \rightarrow PCl _{3}(g) + Cl _{2}$$

initially, 0.42 moles of $$PCl _{5}$$ (g) was placed in flask of volume 2.0L. At equilibrium o.36 moles of $$PCl _{5}$$ (g) was present. What is the value of the equilibrium constant (Kc) for this reaction at this temperature?

(a) 0.0025 mol dm
(b) 0.005 mol dm
(c) 0.013 mol dm
(d) 200 mol dm

how do i apply that to this question?