[Kromede]

I exactly don't know how to solve the final part of this exercise.

"PCl₅ is put in a container which is initially empy and of the volume of 10,00 lt. Temperature is 600 °C. When the equilibrium of the reaction is established

PCl₅ PCl₃ + Cl₂

the final pressure in the container is 2,70 atm; 10,40 g of Cl₂ are formed. Calculate K_c and the initial mass of PCl₅"

First of all, I find the  n(Cl₂) in equilibrium: 10,40/70,90 = 0,146 (these ones are also equal to n(PCl₃) in equilibrium.

Thanks to the ideal gas law I can calculate the total numer of moles in equilibrium: n(total) = (p * V) / (R * T) = 0,377

n(PCl₅) in equilibrium is: 0,377 - 0,146 - 0,146 = 0,085

So: Kc = (0,146 * 0,146)/(0.085) * 1/10 = 0,025

Now I don't know how to find the initial moles of PCl_5....  Should they be equal to the total moles in equilibrium or not?

Thanks for help.

[Borek]

Isn't it a trivial stoichiometry? You know moles at equilibrium, from the amount of Cl₂ produced you can calculate how much decomposed.

[Kromede]

So should the PCl₅'s initial moles be 0,441 - 0,085 = 0,356 ?

[Burner]

So should the PCl₅'s initial moles be 0,441 - 0,085 = 0,356 ?

No. Can you construct an ICE table?

[Borek]

So should the PCl₅'s initial moles be 0,441 - 0,085 = 0,356 ?

Where did you got these numbers from? 0.085 is the number of moles of PCl₅ at equilibrium, but what is 0.441?

besides, initial number of moles is not "something minus the final" but rather "something plus the final" - or, more precisely, "number of moles of PCl₅ that decomposed plus number of moles of PCl₅ left".