A gaseous reaction mixture contains SO2, Cl2, and SO2Cl2 in a 2 L container with the gases having the following partial pressures: P(SO2)=0.35 atm, P(SO2Cl2)=0.19 atm, P(Cl2)=0.24 atm. Kp=91 for the equilibrium system:
SO2 (g) + Cl2 (g) -> SO2Cl2 (g)
Is the system at equilibrium?
I thought that to solve this I had to do something with Qc, but we have Kp and not Kc and you can't compare Kp and Qc, so I am really really confused. PLEASE HELP!
You can do it the long way, then check the short way and see if they are the same.
Using partial pressure and V = 2L, calculate mols and calculate mols/2L for concentration.
Then change Kp to Kc and use Qc.
That way you will be sure what you are doing is legitimate.
Then try just using Qp the same way you would use Qc but substitute partical pressures to arrive at Qp. See if the equilibrium is attained by going the same direction.
To determine if the system is at equilibrium, we can compare the given partial pressures to the equilibrium constant Kp. However, since we only have Kp and not Kc in this case, we need to convert Kp to Kc before we can compare it to Qc.
To do this, we need to use the ideal gas law, PV = nRT, where P represents pressure, V represents volume, n represents the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's calculate the number of moles for each gas using the given partial pressures and volume.
For SO2:
P(SO2) = 0.35 atm
V = 2 L
R = 0.0821 L.atm/mol.K (ideal gas constant)
T = (assuming it is constant and not given)
Using the ideal gas law, we can rearrange it to solve for n:
n(SO2) = (P(SO2) * V) / (R * T)
n(SO2) = (0.35 atm * 2 L) / (0.0821 L.atm/mol.K * T)
n(SO2) = 8.518 / T
Similarly, we can calculate the moles for Cl2 and SO2Cl2:
n(Cl2) = (P(Cl2) * V) / (R * T)
n(SO2Cl2) = (P(SO2Cl2) * V) / (R * T)
Divide the number of moles by the volume (2L) to get the concentration of each gas:
[SO2] = n(SO2) / V
[Cl2] = n(Cl2) / V
[SO2Cl2] = n(SO2Cl2) / V
Now, we have the concentrations in mol/L, which allows us to compare it to Qc.
To convert Kp to Kc, we use the following equation:
Kp = Kc(RT)^(delta n)
Where delta n represents the change in the number of moles of gaseous products minus the number of moles of gaseous reactants.
In this reaction, we have one mole of SO2Cl2 as the product and one mole of SO2 and one mole of Cl2 as the reactants, so delta n = 1 - (1 + 1) = -1.
To convert Kp to Kc, we need to multiply Kp by (RT)^(-1):
Kc = Kp / (RT)
Now that we have Kc, we can compare it with Qc to determine if the system is at equilibrium.
Alternatively, you can skip the conversion step and directly compare the given partial pressures to the equilibrium constant Kp. Calculate Qp by using the partial pressures of SO2, Cl2, and SO2Cl2 in the same way you would use concentrations for Qc.
If Qp is equal to Kp, the system is at equilibrium. If Qp is greater than Kp, the system is not at equilibrium and will need to proceed in the forward direction to reach equilibrium. If Qp is less than Kp, the system is also not at equilibrium and will need to proceed in the reverse direction to reach equilibrium.
By using either of these methods, you can determine whether the system in question is at equilibrium or not.