Please help me with this question
For the system,
PCl5 (g) --> PCl3 (g) + Cl2 (g) K= 26 @ 3000C
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?
What is the question?
To determine whether the system is at equilibrium, we need to compare the given partial pressures with the calculated equilibrium constant (K) for the reaction.
The equilibrium expression for the given reaction is:
K = [PCl3] * [Cl2] / [PCl5]
We are given the partial pressures of PCl5, PCl3, and Cl2 in the 5.0 L flask, and we can convert these pressures to concentrations using the Ideal Gas Law.
To do this, we can use the equation:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
First, we need to convert the given partial pressures to concentrations. Since the volume (V) is given as 5.0 L, we have:
[PCl5] = 0.012 atm * (5.0 L)/(0.0821 L.atm/mol.K * 300 K) = 0.003 mol/L
[PCl3] = 0.90 atm * (5.0 L)/(0.0821 L.atm/mol.K * 300 K) = 0.225 mol/L
[Cl2] = 0.45 atm * (5.0 L)/(0.0821 L.atm/mol.K * 300 K) = 0.1125 mol/L
Now, we can substitute these concentrations into the equilibrium expression:
K = (0.225 mol/L) * (0.1125 mol/L) / (0.003 mol/L)
K = 9
Comparing the calculated equilibrium constant (K = 9) with the given equilibrium constant (K = 26), we see that the system is not at equilibrium.
Since the calculated K value is lower than the given K value, the system will shift to the right to establish equilibrium. This means that more PCl3 and Cl2 will be produced, and PCl5 will be consumed in order to increase their concentrations.