Phosphorus pentachloride decomposes to phosphorus trichloride at high temperatures according to the equation: PCl5(g) = PCl3(g) + Cl2(gu)
at 250 Co , 0.125M PCl5 is added to the flask , if Kc=1.80, what are the equilibrium concentrations of each gas?
A) [PCl5]=0.0625M,[PCl3]=0.0335M, and [Cl2]=0.335M
B) [PCl5]=1.80M,[PCl3]=1.80M, and [Cl2]=1.80M
C) [PCl5]=0 M,[PCl3]=1.34M, and [Cl2]=1.34M
D) [PCl5]=0.00765M,[PCl3]=0.117M, and [Cl2]=0.0.117M
E) [PCl5]=3.96M,[PCl3]=3.83M, and [Cl2]=3.83M

D) [PCl5]=0.00765M,[PCl3]=0.117M,and [Cl2]=0.0.117M

Explanation:

Based on the reaction:

PCl₅(g) ⇄ PCl₃(g) + Cl₂(g)

And knowing:

Kc = [PCl₃] [Cl₂] / [PCl₅] = 1.80

When you add PCl₅ into a flask, this gas will react producing PCl₃ and Cl₂ until [PCl₃] [Cl₂] / [PCl₅] = 1.80

This could be written as:

[PCl₃] = X

[Cl₂] = X

[PCl₅] = 0.125M - X

Where X represents the moles of PCl₅ that react, reaction coordinate.

Replacing in Kc expression:

[PCl₃] [Cl₂] / [PCl₅] = 1.80

[X [X] / [0.125 - X] = 1.80

X² = 0.225 - 1.80X

0 = -X² -1.80X + 0.225

Solving for X:

X = -1.9M → False solution, there is no negative concentrations

X = 0.11735M → Right solution.

Replacing, concentrations in equilibrium are:

[PCl₃] = X

[Cl₂] = X

[PCl₅] = 0.125M - X

[PCl₃] = 0.117M

[Cl₂] = 0.117M

[PCl₅] = 0.00765M

And right option is: