Please help me with this question
For the system,
PCl5 (g) --> PCl3 (g) + Cl2 (g)
In a 5.0 L flask, the gaseous mixture consists of all three gasses with partial pressures as follows:
PCl5 = 0.012 atm
PCl3 = 0.90 atm
Cl2 = 0.45 atm
Is the system at equilibrium?
If yes, explain. If no, which way will the system shift to establish equilibrium?
Jack,
Do you have a Kp listed in your problem? I don't believe it's possible to work it without a Kp. Of course we could make an educated guess, but even that wouldn't do much good without a temperature to help us. The Kp is what we need.
To determine if the system is at equilibrium, we need to compare the given partial pressures with the equilibrium partial pressures.
The reaction given is:
PCl5 (g) → PCl3 (g) + Cl2 (g)
From the balanced chemical equation, we can see that the stoichiometry of the reaction is 1:1:1. This means that for every 1 mole of PCl5 that reacts, 1 mole of PCl3 and 1 mole of Cl2 are produced.
To find the equilibrium partial pressures, we can use the ideal gas law, which states:
P × V = n × R × T
Since the pressure is provided, we can rearrange the equation to find the number of moles (n):
n = P × V / (R × T)
Let's calculate the moles of each gas using the given partial pressures and the volume of the flask (5.0 L). The values of R (ideal gas constant) and T (temperature) are not given, so we assume they are constant.
For PCl5:
n(PCl5) = P(PCl5) × V / (R × T)
= 0.012 atm × 5.0 L / (R × T) (Equation 1)
Similarly, for PCl3:
n(PCl3) = P(PCl3) × V / (R × T)
= 0.90 atm × 5.0 L / (R × T) (Equation 2)
And for Cl2:
n(Cl2) = P(Cl2) × V / (R × T)
= 0.45 atm × 5.0 L / (R × T) (Equation 3)
Now, at equilibrium, there will be no further change in the concentrations of the reactants and products. This means that the ratio of the partial pressures must remain constant and equal to the equilibrium constant (Kp) for this reaction.
The equilibrium constant expression for the given reaction is:
Kp = (PCl3 × Cl2) / (PCl5)
To determine if the system is at equilibrium, we compare the observed partial pressure ratio to the calculated equilibrium constant.
Let's substitute the values of partial pressures from the given question (PCl5 = 0.012 atm, PCl3 = 0.90 atm, and Cl2 = 0.45 atm) into the equilibrium constant expression:
Kp = (0.90 atm × 0.45 atm) / (0.012 atm)
= 33.75 / 0.012
≈ 2812.5
If the observed partial pressure ratio matches the equilibrium constant ratio (Kp), the system is at equilibrium. In this case, it is not specified whether the observed ratio is equal to or close to Kp, so we assume they are equal.
Now, if the observed ratio does not match the calculated Kp, the system is not at equilibrium. To establish equilibrium, the system will shift in a direction that reduces the discrepancy.
If the observed ratio of partial pressures is lower than the equilibrium constant, it means there is less product formed than predicted at equilibrium. In this case, the system will shift to the right (forward reaction) to produce more products and establish equilibrium.
If the observed ratio is higher than the equilibrium constant, it means there is more product formed than predicted at equilibrium. In this case, the system will shift to the left (reverse reaction) to produce more reactants and establish equilibrium.
In summary, based on the calculated equilibrium constant and observed partial pressures, if the observed ratio matches the equilibrium constant ratio (Kp), the system is at equilibrium. Otherwise, the system will shift in a direction to reduce the discrepancy and establish equilibrium.