At 250ºC, the equilibrium constant Kp for the reaction PCl5(g) PCl3(g) + Cl2(g)is 1.80. Sufficient PCl5 is put into a reaction vessel to give an initial pressure of 2.74atm at 250ºC. Calculate the pressure of PCl5 after the system has reached equilibrium

To calculate the pressure of PCl5 at equilibrium, we can use the equilibrium constant (Kp) and the initial pressure of PCl5.

The equation for the reaction is:
PCl5(g) ⇌ PCl3(g) + Cl2(g)

We are given that Kp = 1.80, and the initial pressure of PCl5 is 2.74 atm.

At equilibrium, the expression for Kp is given by:
Kp = (PCl3)(Cl2) / (PCl5)

Let's assume that the equilibrium pressure of PCl5 is x atm. The equilibrium pressure of PCl3 and Cl2 would be (2.74 - x) atm each, since PCl5 is being converted into PCl3 and Cl2.

Substituting the equilibrium pressures into the Kp expression, we get:
1.80 = ((2.74 - x)(2.74 - x)) / x

Simplifying the equation, we have:
1.80x = (2.74 - x)(2.74 - x)

Expanding the right side of the equation:
1.80x = (7.5076 - 5.48x + x^2)

Rearranging the equation and combining like terms:
x^2 - 4.68x + 7.5076 = 0

Solving this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = -4.68, and c = 7.5076.

Substituting these values into the quadratic formula, we get:
x = (-(-4.68) ± √((-4.68)^2 - 4(1)(7.5076))) / (2(1))

Simplifying further, we have:
x = (4.68 ± √(21.8104 - 30.0304)) / 2
x = (4.68 ± √(-8.22)) / 2

Since the square root of a negative number is not defined in the real number system, there are no real solutions to this equation. It implies that the reaction does not go to completion, and PCl5 is not completely consumed to form PCl3 and Cl2.

Therefore, the pressure of PCl5 at equilibrium would be equal to the initial pressure of 2.74 atm.

To calculate the pressure of PCl5 after the system has reached equilibrium, we need to use the equilibrium constant and the initial pressure of PCl5.

Step 1: Write the balanced equation for the reaction:
PCl5(g) ⇌ PCl3(g) + Cl2(g)

Step 2: Set up the equilibrium expression using the equilibrium constant:
Kp = [PCl3] * [Cl2] / [PCl5]

Step 3: Substitute the given equilibrium constant value:
Kp = 1.80

Step 4: Use the given initial pressure of PCl5:
P(initial PCl5) = 2.74 atm

Step 5: Let's assume the pressure of PCl5 at equilibrium is P(PCl5).

Step 6: At equilibrium, the pressure of PCl3 and Cl2 will be zero since we have assumed that all the PCl5 has been converted to PCl3 and Cl2.

Step 7: Substitute the equilibrium pressures into the equilibrium expression:
Kp = [PCl3] * [Cl2] / [PCl5]
Since [PCl3] and [Cl2] are both assumed to be zero, the equation becomes:
Kp = 0 / P(PCl5).

Step 8: Rearrange the equation to solve for P(PCl5):
P(PCl5) = 0 / Kp

Step 9: Calculate P(PCl5):
P(PCl5) = 0

Therefore, the pressure of PCl5 after the system has reached equilibrium is zero.

The balanced chemical equation for the reaction is:

PCl5(g) ⇋ PCl3(g) + Cl2(g)

The equilibrium constant expression for this reaction is:

Kp = (P[PCl3] * P[Cl2])/P[PCl5]

We are given that:

- Kp = 1.80
- P[PCl5] = 2.74 atm

We need to find the pressure of PCl5 after the system has reached equilibrium. Let's assume that the equilibrium pressure of PCl5 is x atm.

At equilibrium, the partial pressures of PCl3 and Cl2 are related to the equilibrium pressure of PCl5 by the stoichiometry of the reaction:

P[PCl3] = x atm
P[Cl2] = x atm

We can now substitute these values into the equilibrium constant expression and solve for x:

1.80 = (x * x)/2.74
x^2 = 4.8972
x = 2.210 atm

Therefore, the pressure of PCl5 at equilibrium is 2.210 atm.