Question

For the reaction PCl₅(g) ⇌ PCl₃(g) + Cl₂(g) Kp = 1.45 × 10⁻⁴ at 160 °C. A 1.00 L vessel at 160 °C is filled with PCl₅(g) at an initial pressure of 3.75 atm and allowed to come to equilibrium. What will be the pressure (in atm) of Cl₂(g) at equilibrium?

Answer 1

The pressure of Cl₂(g) at equilibrium is 5.4375 × 10⁻⁴ atm.

Step-by-step explanation:

To determine the pressure of Cl₂(g) at equilibrium, we can use the equilibrium constant (Kp) and the given initial pressure of PCl₅(g). From the balanced equation, we can see that the coefficient of Cl₂(g) is 1. Therefore, the pressure of Cl₂(g) at equilibrium can be calculated using the equation:

PCl₅(g) ⇌ PCl₃(g) + Cl₂(g)

Kp = [Cl₂(g)] / [PCl₅(g)]

Given that Kp = 1.45 × 10⁻⁴ and the initial pressure of PCl₅(g) is 3.75 atm, we can substitute these values into the equation to solve for the pressure of Cl₂(g) at equilibrium:

1.45 × 10⁻⁴ = x / 3.75

Solving for x, the pressure of Cl₂(g) at equilibrium, we find:

x = 1.45 × 10⁻⁴ * 3.75

x = 5.4375 × 10⁻⁴ atm

Therefore, the pressure of Cl₂(g) at equilibrium is 5.4375 × 10⁻⁴ atm.

Answer 2

To find the equilibrium pressure of Cl₂ for the given chemical reaction, we set up an ICE table, apply the equilibrium constant expression, and solve for x, which represents the change in pressure of Cl₂.

Step-by-step explanation:

To calculate the equilibrium pressure of Cl₂(g) for the reaction PCl₅(g) ⇌ PCl₃(g) + Cl₂(g), with a given Kp = 1.45 × 10⁻⁴ at 160 °C, we will use an ICE table (Initial, Change, Equilibrium). Let's set up the table with the initial pressures and the changes that occur as the system reaches equilibrium.

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At equilibrium, the pressures will be:

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Now, we apply the equilibrium expression using the pressure of the gases at equilibrium:

Kp = (P_PCl₃ * P_Cl₂) / P_PCl₅ = (x * x) / (3.75 - x)

Substitute the value of Kp:

1.45 × 10⁻⁴ = (x²) / (3.75 - x)

Solve this quadratic equation for x to find the equilibrium pressure of Cl₂. Note that in most cases, the x value (representing the change in pressure) will be much smaller than the initial pressure, therefore the assumption x << 3.75 can often be made to simplify calculations.