So, I think I'm doing everything right and even checking my math, but it keeps showing up as wrong. If someone can help me and go into detail,including the quadratic formula, I would appreciate it:

Phosphorus pentachloride decomposes according to the chemical equation
Pcl5(g)=Pcl3+ Cl2
Kc=1.8 at 250 Celsius
a 0.204 mol sample of Pcl5 is injected into a 2.4 L reaction vessel held ate 250 degrees Celsius. Calculate the concentrations of PCl5 and PCl3 at equilibrium.

I shall be happy to check your work if you show it and post as a new question at the top of the page. It's easier for us to check your work than to do all of the work ourself and have you go through and try to find your error.

Kc=0.040

To solve this problem, we'll need to use the quadratic formula and the equation for equilibrium constant (Kc).

First, let's create a balanced equation for the reaction:
PCl5(g) → PCl3 + Cl2

The equation tells us that one mole of PCl5 decomposes to form one mole of PCl3 and one mole of Cl2.

Now, let's define the initial concentrations and express the equilibrium concentrations in terms of a variable (let's use "x"):

Initial concentration of PCl5: [PCl5] = 0.204 mol
Equilibrium concentration of PCl5: [PCl5] = (0.204 - x) mol
Equilibrium concentration of PCl3: [PCl3] = x mol

We know the volume of the reaction vessel is 2.4 L and the equilibrium constant (Kc) is 1.8 at 250 degrees Celsius.

Now, let's set up the expression for Kc using the equilibrium concentrations:
Kc = [PCl3] * [Cl2] / [PCl5]

Since the stoichiometric coefficient of PCl3 and Cl2 is both 1, we only need to consider the concentration of PCl3 (x).

Substituting the equilibrium concentrations into the Kc expression:
1.8 = x * [Cl2] / (0.204 - x)

Next, let's solve for the concentration of Cl2. Since we have only one equation and two unknowns, we'll need to use the quadratic formula. Rearrange the equation as follows:

1.8(0.204 - x) = x * [Cl2]

1.8 * 0.204 - 1.8x = x * [Cl2]
0.3672 - 1.8x = x * [Cl2]

Solve for [Cl2]:
[Cl2] = (0.3672 - 1.8x) / x

Now, let's substitute [Cl2] back into the Kc expression:

1.8 = x * [(0.3672 - 1.8x) / x] / (0.204 - x)

Simplify the equation:

1.8 = (0.3672 - 1.8x) / (0.204 - x)
1.8 * (0.204 - x) = 0.3672 - 1.8x

Simplify further:

0.3672 - 1.8x = 0.3672 - 1.8x

Since the equation simplifies to 0 = 0, this means that x can be any value. This is a special case called "partial pressure," where the expression for Kc is not defined because gases are not involved.

Therefore, the concentrations of PCl5 and PCl3 at equilibrium cannot be determined without further information.